能谱CT不完备数据重建

The exterior CT problem is a special x-ray CT imaging problem, which is often used for nondestructive inspections of large tubular samples. It can image a pipeline wall with a relatively small detector. However, exterior imaging is challenging owing to the incomplete data obtained. In this paper, we propose a regularization model for the exterior CT problem, in which an edge-preserving diffusion and edge-preserving smoothing regularizer is employed. In addition, the polychromatic characteristic of the emitted x-rays is also considered so that the model is closer to the actual physical process. Using the linearization strategy, a corresponding solution algorithm is derived. The proposed model and the algorithm are verified with both simulated data and real data. It is shown that the two type of artifacts, exterior problem artifacts and beam-hardening artifacts, can be effectively suppressed.

PURPOSE Dual-energy computed tomography (DECT) enables the differentiation of different materials. Additionally, DECT images consist of multiple scans of the same sample, revealing information similarity within the energy domain. To leverage this information similarity and address safety concerns related to excessive radiation exposure in DECT imaging, sparse view DECT imaging is proposed as a solution. However, this imaging method can impact image quality. Therefore, this paper presents a hybrid spectrum data generative diffusion reconstruction model (HSGDM) to improve imaging quality. METHOD To exploit the spectral similarity of DECT, we use interleaved angles for sparse scanning to obtain low- and high-energy CT images with complementary incomplete views. Furthermore, we organize low- and high-energy CT image views into multichannel forms for training and inference and promote information exchange between low-energy features and high-energy features, thus improving the reconstruction quality while reducing the radiation dose. In the HSGDM, we build two types of diffusion model constraint terms trained by the image space and wavelet space. The wavelet space diffusion model exploits mainly the orientation and scale features of artifacts. By integrating the image space diffusion model, we establish a hybrid constraint for the iterative reconstruction framework. Ultimately, we transform the iterative approach into a cohesive sampling process guided by the measurement data, which collaboratively produces high-quality and consistent reconstructions of sparse view DECT. RESULTS Compared with the comparison methods, this approach is competitive in terms of the precision of the CT values, the preservation of details, and the elimination of artifacts. In the reconstruction of 30 sparse views, with increases of 3.51 dB for the peak signal-to-noise ratio (PSNR), 0.03 for the structural similarity index measure (SSIM), and a reduction of 74.47 for the Fréchet inception distance (FID) score on the test dataset. In the ablation study, we determined the effectiveness of our proposed hybrid prior, consisting of the wavelet prior module and the image prior module, by comparing the visual effects and quantitative results of the methods using an image space model, a wavelet space model, and our hybrid model approach. Both qualitative and quantitative analyses of the results indicate that the proposed method performs well in sparse DECT reconstruction tasks. CONCLUSION We have developed a unified optimized mathematical model that integrates the image space and wavelet space prior knowledge into an iterative model. This model is more practical and interpretable than existing approaches are. The experimental results demonstrate the competitive performance of the proposed model.

Background Spectral computed tomography (CT) demonstrates significant potential for clinical application by providing rich structural and compositional information about scanned objects. However, sparse-view scanning introduces streak artifacts during image reconstruction, severely degrading image quality. Conventional regularization-based methods exhibit inherent limitations in preserving fine details and edge structures. To address this challenge, this study aimed to enhance reconstruction quality by developing a novel framework that synergistically integrates subspace decomposition with deep generative priors, effectively leveraging both low-rank properties and data-driven representations inherent to spectral CT images. Methods To address these challenges, we proposed an unsupervised reconstruction framework for sparse-view imaging that synergistically integrates subspace representation with a score-based generative model (SGM), which exploits intrinsic information in the measurement signals. This framework leverages the low-rank prior of the subspace representation to guide the SGM in generating images that highly coincide with the ground truth. Specifically, high-dimensional spectral CT images are first decomposed into orthogonal subspace basis components and corresponding eigen-images, effectively reducing dimensionality while preserving spectral correlations. Subsequently, we employed a data-driven SGM to learn the statistical distribution of the image. This deep prior knowledge effectively supplements the limitations of low-rank regularization in capturing complex probability distribution of image. Afterward, we integrated an efficient alternating optimization algorithm that alternately updates subspace coefficients, enforcing consistency between physical measurements and learned priors. This integration results in a synergetic effect between model-driven low-rank priors and the data-driven distribution learning, significantly enhancing the accuracy of image and the model’s generalization across diverse datasets. Results In the simulation experiment, compared with the optimal comparison algorithm (Wavelet-SGM), the proposed algorithm has increased the peak signal-to-noise ratio (PSNR) by at least 3dB, and the structural similarity index measure (SSIM) by 2.54%. In the real data experiment, the results of this paper were the closest to the ground truth, with minimum error. Both qualitative and quantitative analysis demonstrated the promising and competitive performance of the proposed method in preserving details and reducing streaking artifacts. Conclusions Our framework established a new paradigm for spectral CT reconstruction through the synthesis of the model-driven low-rank prior with a data-driven deep prior, which yielded mutual enhancement and complementarity, collectively improving the overall quality of the reconstructed images. This dual mechanism enables comprehensive utilization of measurement signals while preventing hallucinated structures—a critical advancement for clinical applications where artifact-induced misdiagnosis carries significant risks. Our experimental results clearly demonstrate that the proposed method significantly outperforms baseline methods. On the whole, our work introduces a robust and practical sparse-view spectral CT reconstruction technique that exhibits exceptional detail preservation capabilities.

Objective. Spectral computed tomography (CT) is a critical tool in clinical practice, offering capabilities in multi-energy spectrum imaging and material identification. The limited-angle (LA) scanning strategy has attracted attention for its advantages in fast data acquisition and reduced radiation exposure, aligning with the as low as reasonably achievable principle. However, most deep learning-based methods require separate models for each LA setting, which limits their flexibility in adapting to new conditions. In this study, we developed a novel visual-language model (VLMs)-assisted spectral CT reconstruction (VLSR) method to address LA artifacts and enable multi-setting adaptation within a single model. Approach. The VLSR method integrates the image-text perception ability of VLMs and the image generation potential of diffusion models. Prompt engineering is introduced to better represent LA artifact characteristics, further improving artifact accuracy. Additionally, a collaborative sampling framework combining data consistency, low-rank regularization, and image-domain diffusion models is developed to produce high-quality and consistent spectral CT reconstructions. Main results. The performance of VLSR is superior to other comparison methods. Under the scanning angles of 90° and 60° for simulated data, the VLSR method improves peak signal noise ratio by at least 0.41 dB and 1.13 dB compared with other methods. Significance. VLSR method can reconstruct high-quality spectral CT images under diverse LA configurations, allowing faster and more flexible scans with dose reductions.

The insufficiency of photon counting in spectral CT leads to statistical noise in the reconstructed images and the deviation of material decomposition. Currently, deep learning is an effective method for removing image noise.

Sparse-view Computed Tomography (CT) is an effective method for reducing radiation dose. However, the incompleteness of the projection results in streaking artifacts in the reconstructed images. Dual energy CT Data complementarity and diversity in both the projection and image domains represent a promising solution to recover the missing information from sparse views. We proposed an end-to-end sparse-view dual-domain improved dual-energy CT reconstruction network (DdDe-Net) to recover the missing information due to the reduced number of projections. The network is comprised of a projection domain data correction module (PDDC-Net) and an image domain data correction module (IDDC-Net). In PDDC-Net, ResNet and Transformer architectures are combined with a residual module to create a hybrid encoder structure, effectively suppressing noise and artifacts in the projection domain. The IDDC-Net further reduces streaking artifacts and preserves tissue details through the prior image and differential learning process. DdDe-Net was trained and validated on a sparse-view extended dataset of simulated breast DECT data and an abdominal slice simulation dataset. Compared to several mainstream CT image reconstruction algorithms, our proposed algorithm demonstrates a notable advantage, achieving a RMSE of 0.0118 ± 0.0032, a SSIM of 0.9688 ± 0.0177, and a PSNR of 39.83 ± 1.14 dB. The experimental results indicate that DdDe-Net effectively mitigates artifacts while preserving image details in sparse-view DECT, underscoring its potential for practical applications.

Spectral computed tomography (CT) plays a crucial role in various fields. However, the cumulative radiation dose from repeated x‐ray CT examinations has raised concerns about potential health risks. Reducing the projection view is an effective strategy to reduce the radiation dose, but this will lead to a notable degradation in image quality, resulting in streaking artifacts.

In medical applications, the diffusion of contrast agents in tissue can reflect the physiological function of organisms, so it is valuable to quantify the distribution and content of contrast agents in the body over a period. Spectral CT has the advantages of multi-energy projection acquisition and material decomposition, which can quantify K-edge contrast agents. However, multiple repetitive spectral CT scans can cause excessive radiation doses. Sparse-view scanning is commonly used to reduce dose and scan time, but its reconstructed images are usually accompanied by streaking artifacts, which leads to inaccurate quantification of the contrast agents. To solve this problem, an unsupervised sparse-view spectral CT reconstruction and material decomposition algorithm based on the multi-channel score-based generative model (SGM) is proposed in this paper. First, multi-energy images and tissue images are used as multi-channel input data for SGM training. Secondly, the organism is multiply scanned in sparse views, and the trained SGM is utilized to generate multi-energy images and tissue images driven by sparse-view projections. After that, a material decomposition algorithm using tissue images generated by SGM as prior images for solving contrast agent images is established. Finally, the distribution and content of the contrast agents are obtained. The comparison and evaluation of this method are given in this paper, and a series of mouse scanning experiments are carried out to verify the effectiveness of the method.

Spectral computed tomography (spectral CT) is a promising medical imaging technology because of its ability to provide information on material characterization and quantification. However, the difficulty of decomposition increases due to the nonlinearity of the measurements and the text ill-condition of the problem, especially in the case of geometric inconsistency, which typically leads to low image qualities. Therefore, it is a crucial issue for inconsistent spectral CT imaging to improve the accuracy of material decomposition while suppressing noise. This paper proposes one-step multi-material algorithms based on a statistical reconstruction model with different priors. In these approaches, the gradient sparsity based and convolutional neural network based methods are designed for the case of the consistent numbers of material and energies. Furthermore, volume conservation constraint is developed while the two numbers are not equal. An efficient Newton descent method is adopted based on a simple surrogate function. For simulation experiments with different noise levels, the largest peak signal-to-noise ratio (PSNR) obtained by the proposed method approximately increases by 20.924 dB and 18.283 dB compared with those of other algorithms. Magnified areas of real data also demonstrated that the proposed methods have a better ability to suppress noise. Numerical experiments verify that the proposed methods efficiently reconstruct the material maps and reduced noise compared with the state-of-the-art methods.

Spectral computed tomography (CT) is a medical imaging technology that utilizes the measurement of X-ray energy absorption in human tissue to obtain image information. It can provide more accurate and detailed image information, thereby improving the accuracy of diagnosis. However, the process of spectral CT imaging is usually accompanied by a large amount of radiation and noise, which makes it difficult to obtain high-quality spectral CT image. Therefore, this paper constructs a basic third-order tensor unit based on the self-similarity of patches in the spatial domain and spectral domain while proposing nonlocal spectral CT image reconstruction methods to obtain high-quality spectral CT image. Specifically, the algorithm decomposes the recombination tensor into a low-rank tensor and a sparse tensor, which are applied by weighted tensor nuclear norm (WTNN) and weighted tensor total variation (WTTV) norm to improve the reconstruction quality, respectively. In order to further improve algorithm performance, this paper also uses weighted tensor correlated total variation regularization(WTCTV) to simultaneously characterize the low rankness and smoothness of low-rank tensor, while the sparse tensor uses weighted tensor total variation regularization (WTTV) to represent the piecewise smooth structure of the spatial domain and the similarity between pixels and adjacent frames in the spectral domain. Hence, the proposed models can effectively provide faithful underlying information of spectral CT image while maintaining spatial structure. In addition, this paper uses the Alternating Direction Method of Multipliers(ADMM) to optimize the proposed spectral CT image reconstruction models. To verify the performance of the proposed algorithms, we conducted a large number of experiments on numerical phantom and clinic patient data. The experimental results indicate that incorporating weighted regularization outperforms the results without weighted regularization, and nonlocal similarity can achieve better results than that without nonlocal similarity. Compared with existing popular algorithms, the proposed models significantly reduce running time and improve the quality of spectral CT image, thereby assisting doctors in more accurate diagnosis and treatment of diseases.

Spectral computed tomography (CT) has a wide range of applications in material discrimination, clinical diagnosis and tissue representation. However, the photon counting detector measurements are subject to serious quantum noise caused by photon starvation, photon accumulation, charge sharing, and other factors, which will lead to a decrease in the quality of the reconstructed image and make clinical diagnosis more difficult. To tackle with this problem, this paper proposes a spectral CT reconstruction technique that exploits the spatial sparsity of inter-channel images and the high correlation of images between different energy channels. Specifically, similar patches from spatial and spectral domains are extracted to form the low-rank tensors. Then the tensor-train rank, which is derived from a well-balanced matricization technique, is adopted to depict the high correlation among different energy channels. To capture the self-similarity of the low-rank tensors, the L0-norm of the image gradient is employed for image smoothing. An efficient algorithm is devised to solve the reconstruction model utilizing the Alternating Direction Method of Multipliers. For the sake of testing and verifying the effectiveness of the proposed algorithm, numerical simulations and real data experiments are conducted. Qualitatively, the designed method demonstrates a clear advantage in image quality over the existing state-of-the-art algorithms. For instance, when taking the full energy bin image as an example, the proposed method reduces the Root Mean Square Error (RMSE) by 52.07%, 38.69%, 35.13%, 12.67%, respectively, compared to the competing methods. Quantitative and qualitative assessment indices have revealed that the suggested method has excellent noise suppression, artifact elimination, and image detail preservation properties.

In spectral CT reconstruction, the basis materials decomposition involves solving a large-scale nonlinear system of integral equations, which is highly ill-posed mathematically. This paper proposes a model that parameterizes the attenuation coefficients of the object using a neural field representation, thereby avoiding the complex calculations of pixel-driven projection coefficient matrices during the discretization process of line integrals. It introduces a lightweight discretization method for line integrals based on a ray-driven neural field, enhancing the accuracy of the integral approximation during the discretization process. The basis materials are represented as continuous vector-valued implicit functions to establish a neural field parameterization model for the basis materials. The auto-differentiation framework of deep learning is then used to solve the implicit continuous function of the neural base-material fields. This method is not limited by the spatial resolution of reconstructed images, and the network has compact and regular properties. Experimental validation shows that our method performs exceptionally well in addressing the spectral CT reconstruction. Additionally, it fulfils the requirements for the generation of high-resolution reconstruction images.

Spectral computed tomography (CT) provides the potential to generate attenuation maps at varying spectral bins, which can subsequently be employed for the resolve of tissue materials. However, the majority of reconstruction algorithms employed for every projection energy bin typically exhibit a considerable degree of noise. Recently, a series of techniques have been designed in spectral CT reconstruction based on traditional iterative models or deep learning (DL) methods. However, these works are independent or simply coupled, often neglecting the dependency relationships of spatial and spectrum. Additionally, the interpretability and generalization capabilities remain as formidable challenges for current methods. To effectively address these challenges, we initially introduce a spatial-spectral convolutional sparse coding (SS-CSC) framework, which aims to jointly represent spatial and spectral features in a unified manner. Subsequently, we devise a novel deep unfolding network, inspired by SS-CSC, for spectral CT image representation. We refer to this component as the SS-CSC module. Furthermore, we expand the iterative reconstruction scheme for constructing an interpretable deep SS-CSC iterative reconstruction network (SS-CSC-Net) model for spectral CT imaging. The SS-CSC-Net is composed of several iteration blocks, with each block containing two modules: image reconstruction and SS-CSC modules. The spectral CT image is updated using a deep learning-based spatial-spectral prior constraint. Experimental results from both qualitative results and quantitative analyses indicate that the proposed SS-CSC-Net excels in noise reduction and in maintaining tissue edge integrity, delivering superior overall performance.

Photon‐counting detector‐based computed tomography (PCD‐CT) is an advanced realization of spectral CT, the multi‐energy projection data is captured from the same object, hence, CT images can provide additional spectral resolution, making it possible to perform material decomposition. However, multiple projections may have a low signal‐to‐noise ratio (SNR), such that CT images suffer from noise. To handle this problem, a spectral CT image reconstruction method based on anisotropic sparse transformation (AST) is proposed. To increase the quality of reconstruction, AST through an anisotropic guided filter (AGF) and quasi norm is proposed. Then, as a new regularization, AST is introduced into an iterative reconstruction process, generating an AST‐based method. Moreover, to utilize the correlation among projection data, the average image serves as the guidance image of AGF, it varies with the iterative index, resulting in a technique of dynamic average image (DAI). The AST‐based model involves quasi norm minimization, hence an effective strategy is employed to solve the corresponding problem. A series of experiments were performed. The experiment showed that, compared to other listed methods, the result of the AST‐based method can achieve better visualization and higher quantitative indexes, hence it has application potential in the medical imaging field.

Spectral computed tomography (CT) is an imaging technology that utilizes the absorption characteristics of different X-ray energies to obtain the X-ray attenuation characteristics of objects in different energy ranges. However, the limited number of photons detected by spectral CT under a specific X-ray spectrum leads to obvious projection data noise. Making full use of the various properties of the original data is an effective way to recover a clean image from a small amount of noisy projection data. This paper proposes a spectral CT reconstruction method based on representative coefficient image denoising under a low-rank decomposition framework. This method integrates model-driven internal low-rank and nonlocal priors, and data-driven external deep priors, aiming to fully exploit the inherent spectral correlation, nonlocal self-similarity and deep spatial features in spectral CT images. Specifically, we use low-rank decomposition to characterize the global low-rankness of spectral CT images under a plug-and-play framework, and jointly utilize nonlocal low-rankness and smoothness as well as deep image priors to denoise representative coefficient images. Therefore, the proposed method faithfully represents the real underlying information of images by cleverly combining internal and external, nonlocal and local priors. Meanwhile, we design an effective proximal alternating minimization (PAM) algorithm to solve the proposed reconstruction model and establish the theoretical guarantee of the proposed algorithm. Experimental results show that compared with existing popular algorithms, the proposed method can significantly reduce running time while improving spectral CT images quality.

No abstract available

Spectral computed tomography (CT) offers the possibility to reconstruct attenuation images at different energy levels, which can be then used for material decomposition. However, traditional methods reconstruct each energy bin individually and are vulnerable to noise. In this article, we propose a novel synergistic method for spectral CT reconstruction, namely, Uconnect. It utilizes trained convolutional neural networks (CNNs) to connect the energy bins to a latent image so that the full binned data is used synergistically. We experiment on two types of low-dose data: 1) simulated and 2) real patient data. Qualitative and quantitative analysis show that our proposed Uconnect outperforms state-of-the-art model-based iterative reconstruction (MBIR) techniques as well as CNN-based denoising.

Objective: Compared with traditional computed tomography (CT), dual spectral CT (DSCT) exhibits superior material distinguishability and thus has broad prospects in industrial and medical fields. In iterative DSCT algorithms, accurately modeling forward-projection functions is crucial, but it is very difficult to analytically provide accurate functions. Methods: In this article, we propose a locally weighted linear regression look-up table-based (LWLR-LUT) iterative reconstruction method for DSCT. First, the proposed method uses LWLR to establish LUTs for the forward-projection functions through calibration phantoms, achieving good local information calibration. Second, the reconstructed images can be iteratively obtained through the established LUTs. The proposed method not only does not require knowledge of the X-ray spectra and the attenuation coefficients, but also implicitly accounts for some scattered radiation while fitting locally the forward-projection functions in the calibration space. Results: Both numerical simulations and real data experiments demonstrate that the proposed method can achieve highly accurate polychromatic forward-projection functions and greatly improve the quality of the images reconstructed from scattering-free and scattering projections. Conclusion: The proposed method is simple and practical, and achieves good material decomposition effects for objects with different complex structures through simple calibration phantoms.

Photon-counting detector CT (PCD-CT) is a revolutionary technology in decades in the field of CT. Its potential benefits in lowering noise, dose reduction, and material-specific imaging enable completely new clinical applications. Spectral reconstruction of basis material maps requires knowledge of the x-ray spectrum and the spectral response calibration of the detector. However, spectrum estimation errors caused by inaccurate energy threshold calibration will degrade the accuracy of the reconstructions. Existing spectrum estimation methods are not adequately modeled for bias in energy threshold position. Besides, directly solving a big number of variables of the pixel-wise effective spectra for PCD is an ill-conditioned problem so that stable solution is hardly achievable. In this paper, we assumed the effective spectra variation across the detector mainly comes from the calibration error in the energy threshold positions as well as the intrinsic threshold distribution. We propose a joint reconstruction and spectrum refinement algorithm (JoSR) that introduces an innovative spectrum model based on non-negative matrix factorization (NMF) to significantly reduce the dimension of unknowns so that makes the problem well-conditioned. The polychromatic spectral imaging model and the basis material decomposition method together form an optimization objective. The proximal regularized block coordinate descent algorithm is adopted to deal with the non-convex optimization problem to ensure convergence. Simulation studies and experiments on a laboratory PCD-CT system validated the proposed JoSR method. The results demonstrate its advantages on image quality and quantitative accuracy over other state-of-the-art methods in the field.

No abstract available

Spectral computed tomography (CT) is an emerging technology, that generates a multienergy attenuation map for the interior of an object and extends the traditional image volume into a 4-D form. Compared with traditional CT based on energy-integrating detectors, spectral CT can make full use of spectral information, resulting in high resolution and providing accurate material quantification. Numerous model-based iterative reconstruction methods have been proposed for spectral CT reconstruction. However, these methods usually suffer from difficulties such as laborious parameter selection and expensive computational costs. In addition, due to the image similarity of different energy bins, spectral CT usually implies a strong low-rank prior, which has been widely adopted in current iterative reconstruction models. Singular value thresholding (SVT) is an effective algorithm to solve the low-rank constrained model. However, the SVT method requires a manual selection of thresholds, which may lead to suboptimal results. To relieve these problems, in this article, we propose a sparse and low-rank unrolling network (SOUL-Net) for spectral CT image reconstruction, that learns the parameters and thresholds in a data-driven manner. Furthermore, a Taylor expansion-based neural network backpropagation method is introduced to improve the numerical stability. The qualitative and quantitative results demonstrate that the proposed method outperforms several representative state-of-the-art algorithms in terms of detail preservation and artifact reduction.

Objective: With the development of computed tomography (CT) imaging technology, it is possible to acquire multi-energy data by spectral CT. Being different from conventional CT, the X-ray energy spectrum of spectral CT is cut into several narrow bins which leads to the result that only a part of photon can be collected in each individual energy channel.This can severely degrade the image qualities. To address this problem, we propose a spectral CT reconstruction algorithm based on low-rank representation and structure preserving regularization in this paper. Approach: To make full use of the prior knowledge about both the inter-channel correlation and the sparsity in gradient domain of inner-channel data, this paper combines a low-rank correlation descriptor with a structure extraction operator as priori regularization terms for spectral CT reconstruction. Furthermore, a split-Bregman based iterative algorithm is developed to solve the reconstruction model. Finally, we propose a multi-channel adaptive parameters generation strategy according to CT values of each individual energy channel. Main results: Experimental results on numerical simulations and real mouse data indicate that the proposed algorithm achieves higher accuracy on both reconstruction and material decomposition than the methods based on simultaneous algebraic reconstruction technique (SART), total variation minimization (TVM), total variation with low-rank (LRTV), and spatial-spectral cube matching frame (SSCMF). Compared with SART, our algorithm improves the feature similarity (FSIM) by 40.4% on average for numerical simulation reconstruction, whereas TVM, LRTV, and SSCMF correspond to 26.1%, 28.2%, and 29.5%, respectively. Significance: We outline a multi-channel reconstruction algorithm tailored for spectral CT. The qualitative and quantitative comparisons present a significant improvement of image quality, indicating its promising potential in spectral CT imaging.

Spectral computed tomography (CT) reconstructs images from different spectral data through photon counting detectors (PCDs). However, due to the limited number of photons and the counting rate in the corresponding spectral segment, the reconstructed spectral images are usually affected by severe noise. In this paper, we propose a fourth-order nonlocal tensor decomposition model for spectral CT image reconstruction (FONT-SIR). To maintain the original spatial relationships among similar patches and improve the imaging quality, similar patches without vectorization are grouped in both spectral and spatial domains simultaneously to form the fourth-order processing tensor unit. The similarity of different patches is measured with the cosine similarity of latent features extracted using principal component analysis (PCA). By imposing the constraints of the weighted nuclear and total variation (TV) norms, each fourth-order tensor unit is decomposed into a low-rank component and a sparse component, which can efficiently remove noise and artifacts while preserving the structural details. Moreover, the alternating direction method of multipliers (ADMM) is employed to solve the decomposition model. Extensive experimental results on both simulated and real data sets demonstrate that the proposed FONT-SIR achieves superior qualitative and quantitative performance compared with several state-of-the-art methods.

Multi-spectral CT (MSCT) is increasingly used in industrial non-destructive testing and medical diagnosis because of its outstanding performance like material distinguishability. The process of obtaining MSCT data can be modeled as a nonlinear system and the basis material decomposition comes down to the inverse problem of the nonlinear system. For different spectra data, geometric inconsistent parameters cause geometrical inconsistent rays, which will lead to the mismatched nonlinear system. How to solve the mismatched nonlinear equations accurately and quickly is a hot issue. This paper proposes a general iterative method (SOMA) to invert the mismatched nonlinear equations. The SOMA method gives different equations different confidence and searches along the more accurate hyperplane by Schmidt orthogonalization, which can get the optimal solution quickly. The validity of the SOMA method is verified by MSCT basis material decomposition experiments. The results show that the SOMA method can decompose the basis material images accurately and improve the convergence speed greatly.

It is challenging to obtain good image quality in spectral computed tomography (CT) as the photon-number for the photon-counting detectors is limited for each narrow energy bin. This results in a lower signal to noise ratio (SNR) for the projections. To handle this issue, we first formulate the weight bidirectional image gradient with L0-norm constraint of spectral CT image. Then, as a new regularizer, bidirectional image gradient with L0-norm constraint is introduced into the tensor decomposition model, generating the Spectral-Image Tensor and Bidirectional Image-gradient Minimization (SITBIM) algorithm. Finally, the split-Bregman method is employed to optimize the proposed SITBIM mathematical model. The experiments on the numerical mouse phantom and real mouse experiments are designed to validate and evaluate the SITBIM method. The results demonstrate that the SITBIM can outperform other state-of-the-art methods (including TVM, TV + LR, SSCMF and NLCTF). INDEX TERMS: -spectral CT, image reconstruction, tensor decomposition, unidirectional image gradient, image similarity.

Spectral computed tomography based on a photon-counting detector (PCD) attracts more and more attentions since it has the capability to provide more accurate identification and quantitative analysis for biomedical materials. The limited number of photons within narrow energy bins leads to imaging results of low signal-noise ratio. The existing supervised deep reconstruction networks for CT reconstruction are difficult to address these challenges because it is usually impossible to acquire noise-free clinical images with clear structures as references. In this paper, we propose an iterative deep reconstruction network to synergize unsupervised method and data priors into a unified framework, named as Spectral2Spectral. Our Spectral2Spectral employs an unsupervised deep training strategy to obtain high-quality images from noisy data in an end-to-end fashion. The structural similarity prior within image-spectral domain is refined as a regularization term to further constrain the network training. The weights of neural network are automatically updated to capture image features and structures within the iterative process. Three large-scale preclinical datasets experiments demonstrate that the Spectral2spectral reconstructs better image quality than other the state-of-the-art methods.

Photon-counting detector based spectral computed tomography (CT) has great potential in material decomposition, tissue characterization, lesion detection, and other applications. For a fixed total photon number or radiation dose, the increase of channel number will lead to the decrease of the photon number in each channel, resulting in degraded image quality of the reconstructed image. This is difficult to meet the practical applications for material decomposition, tissue characterization, lesion detection, etc. To improve the quality of image reconstruction, we propose a spectral CT reconstruction algorithm based on joint multi-channel total generalized variation (TGV) minimization and tensor decomposition. On one hand, the algorithm takes joint multi-channel TGV function as regularization. The total generalized variation is extended to the vector, and the sparsity of singular value is used to promote the linear dependence of the image gradient. On the other hand, the multi-channel images share the same physical structure, and the algorithm employs the non-local feature similarity in the image domain. Similar image blocks are clustered into a four-order tensor group, and the noise was reduced by sparse representation of high-dimensional tensors. Experiment results show the proposed algorithm can further improve the quality of reconstructed image and preserve the edge and details of the spectral CT image.

No abstract available

Spectral-computed tomography (CT) has been demonstrating its great advantages in lesion detection, tissue characterization, and material decomposition. However, the quality of images is often significantly corrupted with various noises, which brings a great challenge for its applications. Because the channel-wise images from different energy interval share similar structure and physical message, the spatial sparsity, global correlation across the spectrum (GCS), and nonlocal self-similarity (NSS) as three important characteristics are employed to spectral CT reconstruction. In this study, we propose a spectral-image decomposition with energy-fusion sensing (SIDES) reconstruction method, which encourages to obtain better quality spectral images and material decomposition results by establishing a unified tensor decomposition model. First, considering the noise distribution in channel-wise and the difference of linear attenuation coefficients within channel-cross, an adaptive weighted full-spectrum prior image as additional supervised information is incorporated to formulate a new weighted prior image-based tensor. Cooperating with original image tensor, they fully explore the spatial sparsity, GCS, and NSS properties. Then, we formulate nonlocal similar patch-based tensor groups to encode the NSS property from image-domain and residual-image-domain (which is expanded by prior-image and image-self). Next, low-rank regularized Tucker tensor decomposition is employed to fully explore the intrinsic knowledge with the help of prior-image supervision. Finally, the relaxed convex optimization model is optimized by dividing reconstruction model into several subproblem using split-Bregman method. Numerical simulations and real experiments are designed to validate and evaluate the SIDES method and the results demonstrate that the SIDES reconstruction outperforms the state-of-the-art.

This work considers synergistic multi-spectral CT reconstruction where information from all available energy channels is combined to improve the reconstruction of each individual channel. We propose to fuse these available data (represented by a single sinogram) to obtain a polyenergetic image which keeps structural information shared by the energy channels with increased signal-to-noise ratio. This new image is used as prior information during a channel-by-channel minimization process through the directional total variation. We analyse the use of directional total variation within variational regularization and iterative regularization. Our numerical results on simulated and experimental data show improvements in terms of image quality and in computational speed. This article is part of the theme issue ‘Synergistic tomographic image reconstruction: part 2’.

Using the convexity of each component of the forward operator, we propose an extended primal-dual algorithm framework for solving a kind of nonconvex and probably nonsmooth optimization problems in spectral computed tomography (CT) image reconstruction. Following the proposed algorithm framework, we present six different iterative schemes or algorithms, and then establish the relationship to some existing algorithms. Under appropriate conditions, we prove the convergence of these schemes for the general case. Moreover, when the proposed schemes are applied to solving a specific problem in spectral CT image reconstruction, namely, total variation regularized nonlinear least-squares problem with nonnegative constraint, we also prove the particular convergence for these schemes by using some special properties. The numerical experiments with densely and sparsely data demonstrate the convergence and accuracy of the proposed algorithm framework in terms of visual inspection of images of realistic anatomic complexity and quantitative analysis with metrics structural similarity, peak signal-to-noise ratio, mean square error and maximum pixel difference. We analyze the computational complexity of these schemes, and discuss the extended applications of this algorithm framework in other nonlinear imaging problems.

The work seeks to develop an algorithm for image reconstruction by directly inverting the non-linear data model in spectral CT. Using the non-linear data model, we formulate the image-reconstruction problem as a non-convex optimization program, and develop a non-convex primal-dual (NCPD) algorithm to solve the program. We devise multiple convergence conditions and perform verification studies numerically to demonstrate that the NCPD algorithm can solve the non-convex optimization program and under appropriate data condition, can invert the non-linear data model. Using the NCPD algorithm, we then reconstruct monochromatic images from simulated and real data of numerical and physical phantoms acquired with a standard, full-scan dual-energy configuration. The result of the reconstruction studies shows that the NCPD algorithm can correct accurately for the non-linear beam-hardening effect. Furthermore, we apply the NCPD algorithm to simulated and real data of the numerical and physical phantoms collected with non-standard, short-scan dual-energy configurations, and obtain monochromatic images comparable to those of the standard, full-scan study, thus revealing the potential of the NCPD algorithm for enabling non-standard scanning configurations in spectral CT, where the existing indirect methods are limited.

The photon-counting detector based spectral computed tomography (CT) is promising for lesion detection, tissue characterization, and material decomposition. However, the lower signal-to-noise ratio within multi-energy projection dataset can result in poorly reconstructed image quality. Recently, as prior information, a high-quality spectral mean image was introduced into the prior image constrained compressed sensing (PICCS) framework to suppress noise, leading to spectral PICCS (SPICCS). In the original SPICCS model, the image gradient L1-norm is employed, and it can cause blurred edge structures in the reconstructed images. Encouraged by the advantages in edge preservation and finer structure recovering, the image gradient L0-norm was incorporated into the PICCS model. Furthermore, due to the difference of energy spectrum in different channels, a weighting factor is introduced and adaptively adjusted for different channel-wise images, leading to an L0-norm based adaptive SPICCS (L0-ASPICCS) algorithm for low-dose spectral CT reconstruction. The split-Bregman method is employed to minimize the objective function. Extensive numerical simulations and physical phantom experiments are performed to evaluate the proposed method. By comparing with the state-of-the-art algorithms, such as the simultaneous algebraic reconstruction technique, total variation minimization, and SPICCS, the advantages of our proposed method are demonstrated in terms of both qualitative and quantitative evaluation results.

Photon-counting spectral computed tomography (CT) is capable of material characterization and can improve diagnostic performance over traditional clinical CT. However, it suffers from photon count starving for each individual energy channel which may cause severe artifacts in the reconstructed images. Furthermore, since the images in different energy channels describe the same object, there are high correlations among different channels. To make full use of the inter-channel correlations and minimize the count starving effect while maintaining clinically meaningful texture information, this paper combines a region-specific texture model with a low-rank correlation descriptor as an a priori regularization to explore a superior texture preserving Bayesian reconstruction of spectral CT. Specifically, the inter-channel correlations are characterized by the low-rank representation, and the inner-channel regional textures are modeled by a texture preserving Markov random field. In other words, this paper integrates the spectral and spatial information into a unified Bayesian reconstruction framework. The widely-used Split-Bregman algorithm is employed to minimize the objective function because of the non-differentiable property of the low-rank representation. To evaluate the tissue texture preserving performance of the proposed method for each channel, three references are built for comparison: one is the traditional CT image from energy integration detection. The second one is spectral images from dual-energy CT. The third one is individual channels images from custom-made photon-counting spectral CT. As expected, the proposed method produced promising results in terms of not only preserving texture features but also suppressing image noise in each channel, comparing to existing methods of total variation (TV), low-rank TV and tensor dictionary learning, by both visual inspection and quantitative indexes of root mean square error, peak signal to noise ratio, structural similarity and feature similarity.

No abstract available

In spectral computed tomography (CT), the object is respectively scanned under different x-ray spectra. Multiple projection data can be collectively used for reconstructing basis images and virtual monochromatic images, which have been used in material decomposition, beam-hardening correction, bone removal, and so on. In practice, projection data may be obtained in a limited scanning angular range. Images reconstructed from limited-angle data by conventional spectral CT reconstruction methods will be deteriorated by limited-angle related artifacts and basis image decomposition errors. Motivated by observations of limited-angle spectral CT, we propose a sequential regularization-based limited-angle spectral CT reconstruction model and its numerical solver. Both simulated and real data experiments validate that our method is capable of suppressing artifacts, preserving edges and reducing decomposition errors.

Spectral CT is an emerging technology capable of providing high chemical specificity, which is crucial for many applications such as detecting threats in luggage. Such applications often require both fast and high-quality image reconstruction based on sparse-view (few) projections. The conventional FBP method is fast but it produces low-quality images dominated by noise and artifacts when few projections are available. Iterative methods with, e.g., TV regularizers can circumvent that but they are computationally expensive, with the computational load proportionally increasing with the number of spectral channels. Instead, we propose an approach for fast reconstruction of sparse-view spectral CT data using U-Net with multi-channel input and output. The network is trained to output high-quality images from input images reconstructed by FBP. The network is fast at run-time and because the internal convolutions are shared between the channels, the computation load increases only at the first and last layers, making it an efficient approach to process spectral data with a large number of channels. We validated our approach using real CT scans. The results show qualitatively and quantitatively that our approach is able to outperform the state-of-the-art iterative methods. Furthermore, the results indicate that the network is able to exploit the coupling of the channels to enhance the overall quality and robustness.

No abstract available

Objective. Limited-angle dual-energy (DE) cone-beam CT (CBCT) is considered as a potential solution to achieve fast and low-dose DE imaging on current CBCT scanners without hardware modification. However, its clinical implementations are hindered by the challenging image reconstruction from limited-angle projections. While optimization-based and deep learning-based methods have been proposed for image reconstruction, their utilization is limited by the requirement for x-ray spectra measurement or paired datasets for model training. This work aims to facilitate the clinical applications of fast and low-dose DE-CBCT by developing a practical solution for image reconstruction in limited-angle DE-CBCT. Approach. An inter-spectral structural similarity-based regularization was integrated into the iterative image reconstruction in limited-angle DE-CBCT. By enforcing the similarity between the DE images, limited-angle artifacts were efficiently reduced in the reconstructed DECBCT images. The proposed method was evaluated using two physical phantoms and three digital phantoms, demonstrating its efficacy in quantitative DECBCT imaging. Main results. In all the studies, the proposed method achieves accurate image reconstruction without visible residual artifacts from limited-angle DE-CBCT projection data. In the digital phantom studies, the proposed method reduces the mean-absolute-error from 309/290 HU to 14/20 HU, increases the peak signal-to-noise ratio from 40/39 dB to 70/67 dB, and improves the structural similarity index measurement from 0.74/0.72–1.00/1.00. Significance. The proposed method can efficiently reduce limited-angle artifacts during the image reconstruction, enabling quantitative DE-CBCT with comparable data acquisition time and radiation dose to that of a single-energy scan on current onboard scanners without hardware modification. This work is of great clinical significance and can boost the clinical application of DE-CBCT in image-guided radiation therapy and surgical interventions.

Dual-energy computed tomography (DECT) plays a crucial role in clinical practice due to its capabilities in material identification and quantification. However, complete DECT scans expose patients to additional radiation. To mitigate such a problem, one method is to reduce the CT scan angular range, which may cause limited-angle (LA) artifacts. This work utilized multistage dual-domain networks (MsDu-Nets) for dual-energy LA reconstruction that only requires a 180° scan. MsDu-Nets consist of multiple stages, where data processing is performed in both the sinogram domain and image domain within each stage. A filtered back projection (FBP) module is used to connect these two domains. MsDu-Nets leveraged the informative prior obtained by directly concatenating the dual-energy projection data and directly reconstructing it after applying Parker weights, which helps the network focus more on anatomical information. Self-augmentation is also employed to mitigate the streak artifacts introduced by the informative prior and enables the transmission of original information across stages. Comparison experiments and material decomposition experiments demonstrate that the proposed method is capable of obtaining high-quality dual-energy reconstructed images. The ablation experiments also validate the roles of different modules or components of the method.

Limited angle Breast Computed Tomography uses lower energy and low projection angle to detect early breast cancer or other malignant tissues in the breast. The sensitivity of breast CT can be improved by applying dual energy technology. The general challenge which hampers full exploration of dual energy imaging is noise accumulation as a result of spectral overlaps from two different images. The author proposed hybrid optimization method (HOM) which leverages on fast convergence of simultaneous algebraic reconstruction techniques (SART) and good de-noising and artefacts removal of dictionary learning (DL) to minimizes noise in each image of dual energy and then apply decomposition on the noiseless dual data. The HOM algorithm is formulated as optimization problem which find good atoms from the dictionary obtained and dictionary atom are learned from training data set. The reconstructed images which are noise-free are then decomposed using DECT algorithm into two material basis. 2D phantom known as mbat-phantom consisting of two material basis (microcalcification and normal breast tissue) were simulated to test the algorithm. Noisy projection data were also simulated under the same condition by adding poison noise. The performance of the method was evaluated by estimating some image quality indices on reconstructed images and decomposed images. The proposed method shows the highest average structural similarity index map (SSIM) of 0.9987 and 0.9921 and peak signal to-noise ratio (PSNR) of 49.24 and 46.96 for reconstructed image without noise and noisy image respectively. Also, there is a reduction in average standard deviation (STD) error of decomposed image. Our method performs excellently in streak artefact removal and noise suppression which is capable of reconstructing faithful image in presence of noisy data.

Dual-energy computed tomography (DECT) can simultaneously provide the anatomical structure and material-specific information of the scanned object, having many applications in industry and medicine. Different from conventional CT, DECT acquires two attenuation measurements of the same object at two different X-ray spectra, resulting in apparent redundant information. This article exploits this kind of redundancy to develop the self-prior information enhanced deep iterative reconstruction (SPIE-DIR) algorithm for limited-angle DECT. Unlike the routine practice in model-based deep learning (DL) algorithms, the SPIE-DIR method simultaneously performs constraints in the projection, residual, and image domains, corresponding to three modules: projection inpainting, residual correction, and image refinement. During this stage, the prior image and prior projection derived from two complementary limited-angle scans are used to improve the algorithm performance. Besides, to avoid the blurring effect caused by minimizing the Euclidean distance, the Wasserstein generative adversarial network with gradient penalty is adopted to enhance the visual perception of the generated results. Experiments on the simulated data and real rat data have demonstrated that the proposed SPIE-DIR algorithm has the potential to obtain high-quality DECT images from two limited-angle scans. Furthermore, visual and quantitative assessments have shown the promising performance of SPIE-DIR in artifact removal, structural fidelity, CT number preservation, and visual perception enhancement.

Dual-energy computed tomography (DECT) has capability to improve material differentiation, but most scanning schemes require two sets of full-scan measurements at different x-ray spectra, limiting its application to imaging system with incomplete scan. In this study, using one half-scan and a second limited-angle scan, we propose a DECT reconstruction method by exploiting the consistent information of gradient images at high- and low-energy spectra, which relaxes the requirement of data acquisition of DECT. Based on the theory of sampling condition analysis, the complementary support set of gradient images plays an important role in image reconstruction because it constitutes the sufficient and necessary condition for accurate CT reconstruction. For DECT, the gradient images of high- and low-energy CT images ideally share the same complementary support set for the same object. Inspired by this idea, we extract the prior knowledge of complementary support set (Pri-CSS) from the gradient image of the first half-scan CT image to promote the second limited-angle CT reconstruction. Pri-CSS will be incorporated into total variation regularization model in the form of constrains. Alternative direction method is applied to iteratively solve the modified optimization model, thereby deriving the proposed algorithm to recover low-energy CT image from limited-angle measurements. The qualitative and quantitative experiments on digital and real data are performed to validate the proposed method. The results show that the proposed method outperforms its counterparts and achieve high reconstruction quality for the designed scanning configuration.

X-ray inspection systems are critical in medical, non-destructive testing, and security applications, with systems typically measuring attenuation along straight-line paths connecting sources and detectors. Computed tomography (CT) systems can provide higher-quality images than single- or dual-view systems, but the need to measure many projections leads to greater system cost and complexity. Typically, off-angle Compton scattered photons are treated as noise during tomographic inversion. We seek to maximize the image quality of limited-view systems by combining attenuation data with measurements of Compton-scattered photons, exploiting the fact that the broken-ray paths followed by scattered photons provide additional geometric sampling of the scene. We describe a single-scatter forward model for Compton-scatter data measured with energy-resolving detectors, and demonstrate a reconstruction algorithm for density that combines both attenuation and scatter measurements. The experimental results suggest that including Compton-scattered data in the reconstruction process can improve image quality for density reconstruction using limited-view systems.

Image reconstruction from data collected over full-angular range (FAR) in dual-energy CT (DECT) is well-studied. There exists interest in DECT with advanced scan configurations in which data are collected only over limited-angular ranges (LARs) for meeting unique workflow needs in certain practical imaging applications, and thus in the algorithm development for image reconstruction from such LAR data. The objective of the work is to investigate and prototype image reconstructions in DECT with LAR scans. We investigate and prototype optimization programs with various designs of constraints on the directional-total-variations (DTVs) of virtual monochromatic images and/or basis images, and derive the DTV algorithms to numerically solve the optimization programs for achieving accurate image reconstruction from data collected in a slew of different LAR scans. Using simulated and real data acquired with low- and high-kV spectra over LARs, we conduct quantitative studies to demonstrate and evaluate the optimization programs and their DTV algorithms developed. As the results of the numerical studies reveal, while the DTV algorithms yield images of visual quality and quantitative accuracy comparable to that of the existing algorithms from FAR data, the former reconstruct images with improved visualization, reduced artifacts, and also enhanced quantitative accuracy when applied to LAR data in DECT. Optimization-based, one-step algorithms, including the DTV algorithms demonstrated, can be developed for quantitative image reconstruction from spectral data collected over LARs of extents that are considerably smaller than the FAR in DECT. The theoretical and numerical results obtained can be exploited for prototyping designs of optimization-based reconstructions and LAR scans in DECT, and they may also yield insights into the development of reconstruction procedures in practical DECT applications. The approach and algorithms developed can naturally be applied to investigating image reconstruction from LAR data in multi-spectral and photon-counting CT.

Dual-energy cone-beam computed tomography (DE-CBCT) is a promising imaging technique with foreseeable clinical applications. DE-CBCT images acquired with two different spectra can provide material-specific information. Meanwhile, the anatomical consistency and energy-domain correlation result in significant information redundancy, which could be exploited to improve image quality. In this context, this paper develops the Transformer-Integrated Multi-Encoder Network (TIME-Net) for DE-CBCT to remove the limited-angle artifacts. TIME-Net comprises three encoders (image encoder, prior encoder, and transformer encoder), two decoders (low- and high-energy decoders), and one feature fusion module. Three encoders extract various features for image restoration. The feature fusion module compresses these features into more compact shared features and feeds them to the decoders. Two decoders perform differential learning for DE-CBCT images. By design, TIME-Net could obtain high-quality DE-CBCT images using two complementary quarter-scans, holding great potential to reduce radiation dose and shorten the acquisition time. Qualitative and quantitative analyses based on simulated data and real rat data have demonstrated the promising performance of TIME-Net in artifact removal, subtle structure restoration, and reconstruction accuracy preservation. Two clinical applications, virtual non-contrast (VNC) imaging and iodine quantification, have proved the potential utility of the DE-CBCT images provided by TIME-Net.

Two-dimensional X-ray inspection systems are widely used in aviation security applications; however, they have inherent limitations in recognizing the three-dimensional (3D) shapes of hidden objects. Therefore, there is a growing demand for the implementation of advanced 3D X-ray inspection systems at airports for more accurate detection of threats in luggage and personal belongings. In this study, we designed a new stationary computed tomography (CT) baggage scanner with π-angle sparsity (i.e., 20 pairs of X-ray sources and line detectors were placed within a scan angle of 180°) and compressed sensing (CS)-based reconstruction, and implemented a dual-energy material decomposition (DEMD) technique in the proposed system to separate soft and dense materials of an examined object to enhance threat detection. To validate the efficacy of the proposed approach (CS/180°/P20), we conducted a feasibility study using numerical simulation before its practical implementation. Polychromatic projections were emulated at X-ray tube voltages of 60 and 140 kVp, and DEMD was applied to the projections prior to CT reconstruction. Conventional and dual-energy CT images were reconstructed using both standard filtered-backprojection (FBP) and state-of-the-art CS-based algorithms to compare the image quality. According to our simulation results, the CS-reconstructed images were almost unaffected by the clearly evident streak artifacts on the FBP-reconstructed images because of the use of 20 extreme sparse-view projections, and the image quality of the dual-energy CT images obtained using the proposed CT configuration was similar to that obtained using the conventional CT configuration with 720 dense projections, indicating the efficacy of the proposed approach. Consequently, high-quality dual-energy CT images of soft and dense materials were successfully obtained using the proposed stationary CT configuration.

Dual-energy computed tomography (DECT) provides more anatomical and functional information for image diagnosis. Presently, the popular DECT imaging systems need to scan at least full angle (i.e., 360°). In this study, we propose a DECT using complementary limited-angle scan (DECT-CL) technology to reduce the radiation dose and compress the spatial distribution of the imaging system. The dual-energy total scan is 180°, where the low- and high-energy scan range is the first 90° and last 90°, respectively. We describe this dual limited-angle problem as a complementary limited-angle problem, which is challenging to obtain high-quality images using traditional reconstruction algorithms. Furthermore, a complementary-sinogram-inpainting generative adversarial networks (CSI-GAN) with a sinogram loss is proposed to inpainting sinogram to suppress the singularity of truncated sinogram. The sinogram loss focuses on the data distribution of the generated sinogram while approaching the target sinogram. We use the simultaneous algebraic reconstruction technique namely, a total variable (SART-TV) algorithms for image reconstruction. Then, taking reconstructed CT images of pleural and cranial cavity slices as examples, we evaluate the performance of our method and numerically compare different methods based on root mean square error (RMSE), peak signal-to-noise ratio (PSNR) and structural similarity (SSIM). Compared with traditional algorithms, the proposed network shows advantages in numerical terms. Compared with Patch-GAN, the proposed network can also reduce the RMSE of the reconstruction results by an average of 40% and increase the PSNR by an average of 26%. In conclusion, both qualitative and quantitative comparison and analysis demonstrate that our proposed method achieves a good artifact suppression effect and can suitably solve the complementary limited-angle problem.

Dual-energy computed tomography (DECT) has high application prospects in distinguishing and quantifying materials. However, DECT requires at least two full-angle scans at different energies. In this paper, in order to reduce the radiation dose, we use the plug-and-play (PnP) framework to obtain high-quality decomposed materials under sparse angle scanning. Specifically, we design the PnP framework as a combination of the FFDnet denoiser prior and the least square estimation model to suppress artifacts. To verify the applicability of the proposed method in the clinical environment, we simulated the chest cavity for experiments. The results show that the proposed methods can achieve high-quality basis material decomposition under different sparse views.

Compared with conventional computed tomography (CT), dual-energy CT (DECT) provides better material differentiation but requires projection data acquired with two different effective x-ray spectra, limiting DECT applications to specialized scanners. We propose a hardware-based method, known as PM-DECT, which utilizes primary beam modulation to enable single-scan DECT on a conventional CT scanner. PM-DECT inserts an attenuation sheet with a spatially varying pattern—primary beam modulator—between the x-ray source and imaged object. During a CT scan, the modulator selectively hardens the x-ray beam, thereby increasing the average photon energy at specific detector pixel locations. Thus, PM-DECT simultaneously acquires high and low energy data at each projection angle. From the sparse projection data, high and low energy CT images are jointly reconstructed and simultaneously decomposed into basis materials via an iterative CT reconstruction algorithm with gradient weighting and an improved version of similarity based regularization. Studies on Catphan 600 and anthropomorphic head phantoms demonstrate that PM-DECT retains a high level of spatial resolution compared with conventional CT scans. Electron density values calculated from decomposed images indicate a limited error of 1.12% for PM-DECT. Comparison against a two-scan DECT technique shows that PM-DECT’s image reconstruction from sparse data sets contributes only 0.66% error. By granting the opportunity for high-quality single-scan DECT on conventional CT scanners via limited hardware modification, PM-DECT has the potential to liberate DECT from specialized scanners, extending clinical availability, and implementation.

For homeland and transportation security applications, 2D X-ray explosive detection system (EDS) have been widely used, but they have limitations in recognizing 3D shape of the hidden objects. Among various types of 3D computed tomography (CT) systems to address this issue, this paper is interested in a stationary CT using fixed X-ray sources and detectors. However, due to the limited number of projection views, analytic reconstruction algorithms produce severe streaking artifacts. Inspired by recent success of deep learning approach for sparse view CT reconstruction, here we propose a novel image and sinogram domain deep learning architecture for 3D reconstruction from very sparse view measurement. The algorithm has been tested with the real data from a prototype 9-view dual energy stationary CT EDS carry-on baggage scanner developed by GEMSS Medical Systems, Korea, which confirms the superior reconstruction performance over the existing approaches.

Material decomposition in X-ray imaging is essential for enhancing tissue differentiation and reducing the radiation dose, but the clinical adoption of photon-counting detectors (PCDs) is limited by their high cost and technical complexity. To address this, we propose Dual-head Pix2Pix, a PCD-guided deep learning framework that enables simultaneous iodine and bone decomposition from single-energy X-ray projections acquired with conventional energy-integrating detectors. The model was trained and tested on 1440 groups of energy-integrating detector (EID) projections with their corresponding iodine/bone decomposition images. Experimental results demonstrate that the Dual-head Pix2Pix outperforms baseline models. For iodine decomposition, it achieved a mean absolute error (MAE) of 5.30 ± 1.81, representing an ~10% improvement over Pix2Pix (5.92) and a substantial advantage over CycleGAN (10.39). For bone decomposition, the MAE was reduced to 9.55 ± 2.49, an ~6% improvement over Pix2Pix (10.18). Moreover, Dual-head Pix2Pix consistently achieved the highest MS-SSIM, PSNR, and Pearson correlation coefficients across all benchmarks. In addition, we performed a cross-domain validation using projection images acquired from a conventional EID-CT system. The results show that the model successfully achieved the effective separation of iodine and bone in this new domain, demonstrating a strong generalization capability beyond the training distribution. In summary, Dual-head Pix2Pix provides a cost-effective, scalable, and hardware-friendly solution for accurate dual-material decomposition, paving the way for the broader clinical and industrial adoption of material-specific imaging without requiring PCDs.

Dual-energy computed tomography (DECT) is of great clinical significance because it can simultaneously visualize the internal structure of the scanned object and provide material-specific information. DECT obtains two attenuation measurements of the same object at two different X-ray spectra, resulting in obvious redundant information. In this context, this article suggests acquiring dual-energy projection data using two complementary incomplete scans and utilizes a pretrained Prior-Net to generate the artifact-free prior image. Then the prior image is fed into the proposed prior image enhanced artifact removal network (PIE-ARNet) together with the degraded DECT images to improve the artifact removal performance. The generator of PIE-ARNet has two encoders and two decoders, with each component being responsible for a specific task. Two encoders extract and fuse prior information and image features, while two decoders perform differential learning for data in different energy channels. The discriminator of PIE-ARNet is dedicated to transferring the real statistical properties to the generated images, producing results with enhanced visual perception. Please note that Prior-Net could be trained using the freely available conventional single-energy CT data, which will not bring extra demand for DECT data. Experiments based on the simulated data and real rat data have demonstrated the promising performance of the proposed PIE-ARNet in removing artifacts, recovering image details, and preserving reconstruction accuracy.

Dual-energy computed tomography (DECT) is a fully functional instrument for disease detection in clinical practice because of its ability to identify substances and quantify materials. In some practical applications, due to the limitation of scanning conditions, projection data can only be collected from a limited angle, and the consistency of measurement cannot be guaranteed. The existing DECT reconstruction methods fail to address well the severe artifacts and noise in DECT images caused by limited-angle scanning. In this article, we proposed a self-prior enhanced artifact removal network (SPEAR-Net) for limited-angle DECT, which can effectively combine the complementary information in the high- and low-energy domains and self-prior information to contribute positively to the reconstruction of high-quality DECT images. The SPEAR-Net consists of an image-domain self-prior network (IP-Net), two dual-energy image-domain self-prior networks (DIP-Nets), and a dual-energy sinogram-domain self-prior network (DSP-Net). Specifically, the IP-Net and DIP-Net are adopted to extract the features of the DECT reconstructed images under dual quarter scanning as prior information. The self-prior projection obtained from the forward projection of the prior computed tomography (CT) image is harnessed by DSP-Net to complete the dual-energy limited-angle projection data and to facilitate the performance of SPEAR-Net in removing artifacts in the reconstructed dual-energy images. Qualitative and quantitative analyses demonstrate the superior capability of SPEAR-Net in dual-energy limited-angle projection data complementation, detail preservation, and artifact removal. Two popular DECT applications, virtual noncontrast (VNC) imaging and iodine contrast agent quantification, reveal that images reconstructed by SPEAR-Net have promising clinical significance.

This paper presents an end-to-end deep-learning-based (DL-based) segmentation technique for multi-energy sparse-view CT, where a single network achieves local CT reconstruction and segmentation. While recent DL-based CT segmentation outperformed traditional methods in terms of accuracy and automation, these methods input a "reconstructed" CT. Thus, its performance highly depends on the CT image quality. The reliance prohibits the application of these techniques for sparse-view CT, whereas the sparse-view CT is another important technique to reduce radiation dose and image acquisition time. Our end-to-end deep learning technique integrates the reconstruction and segmentation within a single neural network, which allows us to improve the segmentation quality for sparse-view CT data. The proposed method extracts fragments of pixels from each multi-energy projection corresponding to a bar of CT image voxels. In this way, our network, comprising "filtering", "back-projection," and "segmentation" sub-networks, directly obtains the segmented CT image directly from projections. Our CT segmentation on a bar-by-bar basis is significantly memory-efficient due to the independence of memory-expensive 3D convolution. Consequently, our method delivers high-quality segmentation, where the problems of sparse-view artifacts and memory-expensiveness of prior methods are resolved.

Background Multi-energy computed tomography (CT) provides multiple channel-wise reconstructed images, and they can be used for material identification and k-edge imaging. Nonetheless, the projection datasets are frequently corrupted by various noises (e.g., electronic, Poisson) in the acquisition process, resulting in lower signal-noise-ratio (SNR) measurements. Multi-energy CT images have local sparsity, nonlocal self-similarity in spatial dimension, and correlation in spectral dimension. Methods In this paper, we propose an image-spectral decomposition extended-learning assisted by sparsity (IDEAS) method to fully exploit these intrinsic priors for multi-energy CT image reconstruction. Particularly, a nonlocal low-rank Tucker decomposition (TD) is employed to utilize the correlation and nonlocal self-similarity priors. Moreover, considering the advantages of multi-task tensor dictionary learning (TDL) in sparse representation, an adaptive spatial dictionary and an adaptive spectral dictionary are trained during the iterative reconstruction process. Furthermore, a weighted total variation (TV) regularization term is employed to encourage local sparsity. Results Numerical simulation, physical phantom, and preclinical mouse experiments are performed to validate the proposed IDEAS algorithm. Specifically, in the simulation experiments, the proposed IDEAS reconstructed high-quality images that are very close to the references. For example, the root mean square error (RMSE) of IDEAS image in energy bin 1 is as low as 0.0672, while the RMSE of other methods are higher than 0.0843. Besides, the structural similarity (SSIM) of IDEAS reconstructed image in energy bin 1 is greater than 0.98. For material decomposition, the RMSE of IDEAS bone component is as low as 0.0152, and other methods are higher than 0.0199. In addition, the computational cost of IDEAS is as low as 98.8 s for one iteration, and the competing tensor decomposition method is higher than 327 s. Conclusions To further improve the quality of the reconstructed multi-energy CT images, multiple prior regularizations are introduced to the multi-energy CT reconstructed model, leading to an IDEAS method. Both qualitative and quantitative evaluation of our results confirm the outstanding performance of the proposed algorithm compared to the state-of-the-arts.

Multi-energy computed tomography (MCT) has a great potential in material decomposition, tissue characterization, lesion detection, and other applications. However, the severe noise that exists within projections makes it difficult to obtain high-quality MCT images. To overcome this limitation, we propose a method termed Spectral-Image Similarity-based Tensor with Enhanced-sparsity Reconstruction (SISTER) method. SISTER utilizes the non-local feature similarity in the spatial-spectral domain by clustering similar spatial-spectral patches within non-local window to a 4th-order tensor group. Compared with the image gradient L0-norm with tensor dictionary learning (L0TDL) method, by adopting tensor decomposition rather than tensor dictionary learning, SISTER overcomes the instability of tensor dictionary. Besides, in our SISTER method the weight coefficients update strategy is also optimized. Both numerical simulation and preclinical dataset were performed to evaluate and validate the performance of SISTER. Qualitative and quantitative results show that the proposed method can lead to a promising improvement of edge preservation, finer feature recovery, and noise suppression.

Sparse-view sampling in dual-energy computed tomography (DECT) significantly reduces radiation dose and increases imaging speed, yet is highly prone to artifacts. Although diffusion models have demonstrated potential in effectively handling incomplete data, most existing methods in this field focus on the image domain and lack global constraints, which consequently leads to insufficient reconstruction quality. In this study, we propose a dual-domain virtual-mask informed diffusion model for sparse-view reconstruction by leveraging the high inter-channel correlation in DECT. Specifically, the study designs a virtual mask and applies it to the high-energy and low-energy data to perform perturbation operations, thus constructing high-dimensional tensors that serve as the prior information of the diffusion model. In addition, a dual-domain collaboration strategy is adopted to integrate the information of the randomly selected high-frequency components in the wavelet domain with the information in the projection domain, for the purpose of optimizing the global structures and local details. The experimental results show that the method exhibits excellent performance on multiple datasets. Under 30-view sparse sampling conditions, VIP-DECT improves PSNR by at least 1.02 dB and enhances SSIM by 1.91%.

X-ray has been widely used in medical diagnosis and other fields with the non-destructive merit. Recently, the cold cathode X-ray source based on field emission, which are different from traditional hot cathode X-ray source, have overcome the limitations of traditional X-ray source due to their small size, addressable, and integrated characteristics, making CT imaging methods can be further developed. Especially X-ray sources using ZnO nanowires as cold cathodes can densely integrate a large number of X-ray sources into flat panel devices. When we use this flat X-ray source to light up multiple sources to scan an object at the same time, small source spacing will cause inevitable projection aliasing. Therefore, we propose an image restoration algorithm for projection aliasing, and use the method of projection rearrangement to remove projection aliasing. In addition, we estimated the spectrum of the flat-panel X-ray source by solving the spectral model parameters from the attenuation data of materials of different thicknesses, and used the spectral information to simulate the effect of the proposed image restoration method on the new photon counting detector. The results of simulation experiments show the effectiveness of this method and the potential of this new imaging mode.

No abstract available

Background Multi-energy computed tomography (MECT) based on a photon-counting detector is an emerging imaging modality that collects projections at several energy bins with a single scan. However, the limited number of photons collected into the divided, narrow energy bins results in high quantum noise levels in reconstructed images. This study aims to improve MECT image quality by minimizing noise levels while retaining image details. Methods A novel MECT reconstruction method was proposed by exploiting the nonlocal tensor similarity among interchannel images and spatial sparsity in single-channel images. Similar patches were initially extracted from the interchannel images in spectral and spatial domains, then stacked into a new three-order tensor. Intrinsic tensor sparsity regularization that combined the Tuker and canonical polyadic (CP) low-rank decomposition techniques were applied to exploit the nonlocal similarity of the formulated tensor. Spatial sparsity in single-channel images was modeled by total variation (TV) regularization that utilizes the compressibility of gradient image. A new MECT reconstruction model was established by simultaneously incorporating the intrinsic tensor sparsity and TV regularizations. The iterative alternating minimization method was utilized to solve the reconstruction model based on a flexible framework. Results The proposed method was applied to the digital phantom and real mouse data to assess its feasibility and reliability. The reconstruction and decomposition results in the mouse data were encouraging and demonstrated the ability of the proposed method in noise suppression while preserving image details, not observed with other methods. Imaging data from the digital phantom illustrated this method as achieving the best intuitive reconstruction and decomposition results among all compared methods. They reduced the root mean square error (RMSE) by 89.75%, 50.75%, and 36.54% on the reconstructed images compared with analytic, TV-based, and tensor-based methods, respectively. This phenomenon was also observed with decomposition results, where the RMSE was also reduced by 97.96%, 67.74%, 72.05%, respectively. Conclusions In this study, we proposed a reconstruction method for photon counting detector-based MECT, using the intrinsic tensor sparsity and TV regularizations. Improvements in noise suppression and detail preservation in the digital phantom and real mouse data were validated by the qualitative and quantitative evaluations on the reconstruction and decomposition results, verifying the potential of the proposed method in MECT reconstruction.

Multi-material decomposition (MMD) enables quantitative reconstruction of tissue compositions in the human body, supporting a wide range of clinical applications. However, traditional MMD typically requires spectral CT scanners and pre-measured X-ray energy spectra, significantly limiting clinical applicability. To this end, various methods have been developed to perform MMD using conventional (i.e., single-energy, SE) CT systems, commonly referred to as SEMMD. Despite promising progress, most SEMMD methods follow a two-step image decomposition pipeline, which first reconstructs monochromatic CT images using algorithms such as FBP, and then performs decomposition on these images. The initial reconstruction step, however, neglects the energy-dependent attenuation of human tissues, introducing severe nonlinear beam hardening artifacts and noise into the subsequent decomposition. This paper proposes JSover, a fundamentally reformulated one-step SEMMD framework that jointly reconstructs multi-material compositions and estimates the energy spectrum directly from SECT projections. By explicitly incorporating physics-informed spectral priors into the SEMMD process, JSover accurately simulates a virtual spectral CT system from SE acquisitions, thereby improving the reliability and accuracy of decomposition. Furthermore, we introduce implicit neural representation (INR) as an unsupervised deep learning solver for representing the underlying material maps. The inductive bias of INR toward continuous image patterns constrains the solution space and further enhances estimation quality. Extensive experiments on both simulated and real CT datasets show that JSover outperforms state-of-the-art SEMMD methods in accuracy and computational efficiency.

Objective. Sparse-view dual-energy spectral computed tomography (DECT) imaging is a challenging inverse problem. Due to the incompleteness of the collected data, the presence of streak artifacts can result in the degradation of reconstructed spectral images. The subsequent material decomposition task in DECT can further lead to the amplification of artifacts and noise. Approach. To address this problem, we propose a novel one-step inverse generation network (OIGN) for sparse-view dual-energy CT imaging, which can achieve simultaneous imaging of spectral images and materials. The entire OIGN consists of five sub-networks that form four modules, including the pre-reconstruction module, the pre-decomposition module, and the following residual filtering module and residual decomposition module. The residual feedback mechanism is introduced to synchronize the optimization of spectral CT images and materials. Main results. Numerical simulation experiments show that the OIGN has better performance on both reconstruction and material decomposition than other state-of-the-art spectral CT imaging algorithms. OIGN also demonstrates high imaging efficiency by completing two high-quality imaging tasks in just 50 seconds. Additionally, anti-noise testing is conducted to evaluate the robustness of OIGN. Significance. These findings have great potential in high-quality multi-task spectral CT imaging in clinical diagnosis.

Objective. Dual-energy computed tomography (DECT) has the potential to improve contrast and reduce artifacts and the ability to perform material decomposition in advanced imaging applications. The increased number of measurements results in a higher radiation dose, and it is therefore essential to reduce either the number of projections for each energy or the source x-ray intensity, but this makes tomographic reconstruction more ill-posed. Approach. We developed the multi-channel convolutional analysis operator learning (MCAOL) method to exploit common spatial features within attenuation images at different energies and we propose an optimization method which jointly reconstructs the attenuation images at low and high energies with mixed norm regularization on the sparse features obtained by pre-trained convolutional filters through the convolutional analysis operator learning (CAOL) algorithm. Main results. Extensive experiments with simulated and real computed tomography data were performed to validate the effectiveness of the proposed methods, and we report increased reconstruction accuracy compared with CAOL and iterative methods with single and joint total variation regularization. Significance. Qualitative and quantitative results on sparse views and low-dose DECT demonstrate that the proposed MCAOL method outperforms both CAOL applied on each energy independently and several existing state-of-the-art model-based iterative reconstruction techniques, thus paving the way for dose reduction.

Abstract Multi-energy reconstructions have become an important research field in computed tomography in recent years. Since modern reconstruction and postprocessing techniques often employ deep learning strategies, there is a high need for large, diverse and adaptable multi-energy datasets. Therefore, this work proposes a straightforward pipeline for the generation of multi-energy cone-beam CT projection data based on the established XCAT software phantom with arbitrary desired X-ray spectra. We evaluate the effort and time required for dataset generation and utilize the generated data for model-based iterative reconstruction exemplarily. This approach provides an understanding of the current pipeline’s bottlenecks while demonstrating its suitability in producing high-quality projection datasets and reconstructions. Thus, we contribute to open knowledge on generation of large multi-energetic CT datasets for deep learning purposes.

Photon-counting CT has gained significant attention in recent years; however, publicly available datasets for spectral reconstruction and deep learning training remain limited. Consequently, many image process algorithms and deep learning models are developed and validated using simulated rather than real spectral CT data. To address this gap, we present a cone-beam photon-counting CT (PCCT) dataset acquired using a custom-built micro-PCCT system and 15 walnut samples. Each walnut was scanned from four bed positions under dual energy thresholds (15 keV and 30 keV), resulting in a total of 172,800 raw projection images with a resolution of 2063 × 505 pixels. The dataset provides full access to raw multi-energy projections, system parameters, calibration tables, calibration phantom raw projection data and reconstruction code, enabling comprehensive spectral CT studies including spectral CT reconstruction, material decomposition, artifact correction, and deep learning-based methods. It addresses the scarcity of real PCCT datasets for developing and validating data-driven approaches and aims to foster fair and reproducible comparisons across spectral CT image process algorithms.

Photon-counting computed tomography (PCCT) reconstructs multiple energy-channel images to describe the same object, where there exists a strong correlation among different channel images. In addition, reconstruction of each channel image suffers photon count starving problem. To make full use of the correlation among different channel images to suppress the data noise and enhance the texture details in reconstructing each channel image, this paper proposes a tensor neural network (TNN) architecture to learn a multi-channel texture prior for PCCT reconstruction. Specifically, we first learn a spatial texture prior in each individual channel image by modeling the relationship between the center pixels and its corresponding neighbor pixels using a neural network. Then, we merge the single channel spatial texture prior into multi-channel neural network to learn the spectral local correlation information among different channel images. Since our proposed TNN is trained on a series of unpaired small spatial-spectral cubes which are extracted from one single reference multi-channel image, the local correlation in the spatial-spectral cubes is considered by TNN. To boost the TNN performance, a low-rank representation is also employed to consider the global correlation among different channel images. Finally, we integrate the learned TNN and the low-rank representation as priors into Bayesian reconstruction framework. To evaluate the performance of the proposed method, four references are considered. One is simulated images from ultra-high-resolution CT. One is spectral images from dual-energy CT. The other two are animal tissue and preclinical mouse images from a custom-made PCCT systems. Our TNN prior Bayesian reconstruction demonstrated better performance than other state-of-the-art competing algorithms, in terms of not only preserving texture feature but also suppressing image noise in each channel image.

Photon-counting computed tomography (PCCT) may dramatically benefit clinical practice due to its versatility such as dose reduction and material characterization. However, the limited number of photons detected in each individual energy bin can induce severe noise contamination in the reconstructed image. Fortunately, the notable low-rank prior inherent in the PCCT image can guide the reconstruction to a denoised outcome. To fully excavate and leverage the intrinsic low-rankness, we propose a novel reconstruction algorithm based on quaternion representation (QR), called low-rank quaternion reconstruction (LOQUAT). First, we organize a group of nonlocal similar patches into a quaternion matrix. Then, an adjusted weighted Schatten-p norm (AWSN) is introduced and imposed on the matrix to enforce its low-rank nature. Subsequently, we formulate an AWSN-regularized model and devise an alternating direction method of multipliers (ADMM) framework to solve it. Experiments on simulated and real-world data substantiate the superiority of the LOQUAT technique over several state-of-the-art competitors in terms of both visual inspection and quantitative metrics. Moreover, our QR-based method exhibits lower computational complexity than some popular tensor representation (TR) based counterparts. Besides, the global convergence of LOQUAT is theoretically established under a mild condition. These properties bolster the robustness and practicality of LOQUAT, facilitating its application in PCCT clinical scenarios. The source code will be available at https://github.com/linzf23/LOQUAT.

In this study, we propose a statistical image reconstruction method for spectral photon-counting CT (SPCCT). The proposed method consists of two approaches: Method 1, which formulates image reconstruction using energy images as variables, and Method2 which formulates image reconstruction using material images as variables. Both methods incorporate the following key innovations: (1) Utilizing a weighted least squares (WLS) data term that accounts for statistical noise following a Poisson distribution. (2) Incorporating a regularization term in the energy domain that exploits the sparsity of materials constituting the object, in addition to the spatial total variation (TV) regularization term. (3) Reducing computation time through a fast-convergence iterative method based on Dykstra-like splitting, as detailed in [1]. Significantly, the development of an iterative method that exceptionally fast convergence using Dykstra-like splitting to mitigate computational challenges is considered a major achievement.

X-ray photon-counting computed tomography (PCCT) for extremity allows multi-energy high-resolution (HR) imaging but its radiation dose can be further improved. Despite the great potential of deep learning techniques, their application in HR volumetric PCCT reconstruction has been challenged by the large memory burden, training data scarcity, and domain gap issues. In this paper, we propose a deep learning-based approach for PCCT image reconstruction at halved dose and doubled speed validated in a New Zealand clinical trial. Specifically, we design a patch-based volumetric refinement network to alleviate the GPU memory limitation, train network with synthetic data, and use model-based iterative refinement to bridge the gap between synthetic and clinical data. Our results in a reader study of 8 patients from the clinical trial demonstrate a great potential to cut the radiation dose to half that of the clinical PCCT standard without compromising image quality and diagnostic value.

Recently, photon-counting computed tomography (PCCT) has been extensively studied as a promising modality for spectral imaging. PCCT offers some benefits over conventional CT, such as energy-resolved X-ray information and reduced radiation dose owing to its ability to count and discriminate each X-ray photon based on its energy. However, PCCT images in certain energy bands tend to suffer from artifacts and image noise owing to insufficient photon counts. These problems reduce the accuracy and quality of PCCT images, thereby limiting the full potential of energy-resolved imaging. Recently, many studies have been conducted on the application of deep learning to conventional CT for the reduction of image noise and other improvements, which are considered promising. However, the application of deep learning to PCCT has not been thoroughly investigated. In this study, we investigated the effectiveness of deep learning in improving PCCT images and explored a new approach for utilizing energy-resolved PCCT information. For this purpose, we conducted experiments using our PCCT system and acquired data by scanning phantoms and mice. Deep learning was then applied to the data, and the images were evaluated in terms of noise and material-decomposed imaging. Consequently, image noise and artifacts are significantly suppressed by the application of deep learning. In particular, more effective noise reduction was achieved with a model that could refer to and utilize energy information. Improvements were also confirmed in the accuracy of contrast agent discrimination in phantom imaging, as well as in the visualization of accumulated contrast agents in organs in mouse imaging. Consequently, deep learning effectively incorporating energy information was shown to significantly improve the PCCT image quality, demonstrating a new potential for energy information in PCCT.

Photon counting detector (PCD)-CT has demonstrated promise to reduce ionizing radiation exposure further and improve spatial resolution. However, when the radiation exposure or the detector pixel size is reduced, image noise is elevated, and the CT number becomes more inaccurate. This exposure level-dependent CT number inaccuracy is referred to as statistical bias. The issue of CT number statistical bias is rooted in the stochastic nature of the detected photon number, N, and a log transformation used to generate the sinogram projection data. Due to the nonlinear nature of the log transform, the statistical mean of the log-transformed data is different from the desired sinogram, the log transform of the statistical mean of N. Consequently, when a single instance of N is measured, as in clinical imaging, the log-transform leads to an inaccurate sinogram and statistically biased CT numbers after reconstruction. This work presents a nearly unbiased and closed-form statistical estimator of sinogram as a simple yet highly effective method to address the statistical bias issue in PCD-CT. Experimental results validated that the proposed approach addresses the CT number bias problem and improves the quantification accuracy of both non-spectral and spectral PCD-CT images. Additionally, the process can slightly reduce noise without adaptive filtering or iterative reconstruction.

Objective: Photon-counting detector (PCD) is an advanced and innovative X-ray detector, that offers significant advantages such as improved spatial resolution and higher dose efficiency. However, as a new X-ray detection device, PCD faces technical challenges, particularly the non-uniformity among detector units, which can lead to ring artifacts in reconstructed CT images. To address this challenge, we propose a novel image-domain post-processing method to effectively correct ring artifacts in PCD-reconstructed images. Method: The method is specifically designed for a self-developed hybrid spectral CT system equipped with both a PCD and an energy integration detector (EID). The ring artifact-free EID-reconstructed images are used as prior images to guide the correction of ring artifacts in the PCD-reconstructed images. In addition, a carefully designed weight is introduced in the optimization model to prevent the degradation of boundary details in the target images caused by blurred edges in prior images. Results: The effectiveness of the proposed method is validated on both simulated data and real data, demonstrating that the proposed method can efficiently and effectively correct ring artifacts in the reconstructed images of PCD. Significance: This confirms that the proposed method provides a practical solution for hybrid spectral CT imaging.

Photon-counting computed tomography (PCCT) has emerged as a transformative imaging modality, enabling enhanced spatial resolution, and multienergy acquisition with energy-discriminating detectors of significantly smaller detector elements. However, both energy-discriminating power and reduced detector pixel size result in fewer detected photons per measurement, inherently increasing noise in reconstructed images. In this study, we propose ZS4D, a zero-shot self-similarity-steered denoiser for PCCT reconstruction. Specifically, a self-similarity denoiser is pretrained in a self-supervised manner by leveraging spectral correlations through multienergy extraction and capturing volumetric context via the complementary synergy of axial and sagittal planes. The pretrained denoiser is then integrated as a prior into an iterative reconstruction framework, enabling effective noise structural preservation. Extensive experiments demonstrate that ZS4D adapts well to varying noise levels and significantly enhances image quality in both simulated and preclinical PCCT datasets. Also, ZS4D demonstrates effectiveness in deblurring tasks. Furthermore, our denoiser pretrained on clinical PCCT data is shown to enhance the spatial resolution of conventional CT images.

—Photon-counting CT (PCCT) offers improved diagnostic performance through better spatial and energy resolution, but developing high-quality image reconstruction methods that can deal with these large datasets is challenging. Model-based solutions incorporate models of the physical acquisition in order to reconstruct more accurate images, but are dependent on an accurate forward operator and present difficul-ties with finding good regularization. Another approach is deep-learning reconstruction, which has shown great promise in CT. However, fully data-driven solutions typically need large amounts of training data and lack interpretability. To combine the benefits of both methods, while minimizing their respective drawbacks, it is desirable to develop reconstruction algorithms that combine both model-based and data-driven approaches. In this work, we present a novel deep-learning solution for material decomposition in PCCT, based on an unrolled/unfolded iterative network. We evaluate two cases: a learned post-processing, which implicitly utilizes model knowledge, and a learned gradient-descent, which has explicit model-based components in the architecture. With our proposed techniques, we solve a challenging PCCT simulation case: three-material decomposition in abdomen imaging with low dose, iodine contrast, and a very small training sample support. In this scenario, our approach outperforms a maximum likelihood estimation, a variational method, as well as a fully-learned network.

Deep learning (DL) based methods have been widely adopted in computed tomography (CT) field. And they also show a great potential in photon-counting CT (PCCT) imaging field. They usually require a large quantity of paired data to train networks. However, it is time-consuming and expensive to collect such large-scale PCCT dataset. In addition, lots of energy-integrating detector (EID) data are not yet included in the DL-based PCCT reconstruction network training. In this work, to address the issue of limited PCCT data and take advantage of labeled EID data, we propose a novel unsupervised full-spectrum-knowledge-aware DL-based network (FSANet), which contains supervised and unsupervised networks, to produce high-quality PCCT images. Specifically, the supervised network is trained based on paired EID dataset and serves as the prior knowledge to regularize the unsupervised PCCT network training. Moreover, a data-fidelity term for characterizing the PCCT image characteristics is constructed as a self-supervised term. Finally, we train the PCCT network with the prior knowledge and self-supervised terms following an unsupervised learning strategy. Numerical studies on synthesized clinical data are conducted to validate and evaluate the performance of the presented FSANet method, qualitatively and quantitatively. The experimental results demonstrate that presented FSANet method significantly improves the PCCT image quality in the case of limited photon counts.

Photon-counting computed tomography (PCCT) is an industry-recognized next-generation CT technology. By utilizing a photon counting detector that provides information on object interaction that varies with different energy photons, physicians can differentiate materials in objects through material decomposition, enabling numerous medical applications such as detecting tumors or characterizing kidney stones. However, due to charge-sharing effects, application-specific integrated circuit (ASIC) pile-up effects, and Compton scattering in PCCT, there exists a mismatch between the real-world physical effects and the ideal assumptions used in the physics model, which can result in significant errors in material decomposition. To address this problem, this paper proposes a physics-guided deep-learning model for material decomposition. We construct a physics simulation model that can simulate the response of the PCCT system under different physics parameters and use it to build a training dataset. We then train a neural network on this dataset to learn the response of the CT detector and ASIC under different physics parameters. Next, we conduct a calibration experiment to adjust the parameters to reduce the difference between the neural network predictions and the actual data. During imaging, we calculate the thickness information of the detected substance by solving an optimization problem based on the physics parameters of the CT detector and the actual response of the CT detector. In summary, our proposed method addresses the problem of physical effects that deviate from the ideal physics model. Our method uses a small amount of experimental data and could be implemented in a real clinical setting.

Spectral photon-counting CT offers novel potentialities to achieve quantitative decomposition of material components, in comparison with traditional energy-integrating CT or dual-energy CT. Nonetheless, achieving accurate material decomposition, especially for low-concentration materials, is still extremely challenging for current sCT, due to restricted energy resolution stemming from the trade-off between the number of energy bins and undesired factors such as quantum noise.We propose to improve material decomposition by introducing the notion of super-energy-resolution in sCT. The super-energy-resolution material decomposition consists in learning the relationship between simulation and physical phantoms in image domain. To this end, a coupled dictionary learning method is utilized to learn such relationship in a pixel-wise way. The results on both physical phantoms and in vivo data showed that for the same decomposition method using lasso regularization, the proposed super-energy-resolution method achieves much higher decomposition accuracy and detection ability in contrast to traditional image-domain decomposition method using L1-norm regularization.

We propose a spectral distortion correction method for a photon-counting CT system with machine learning. Although the most important advantage of the photon-counting CT system is material-decomposition capability, it is very sensitive to the most serious problem, the pulse pile-up effect. This leads to spectral distortion and material densities could not be accurately measured. In this study, we constructed a neural network for spectral distortion correction. The performance of our network was investigated with a simulation. Our network was trained with a data set of 1000 pairs of original and distorted spectra. The data set was prepared with X-ray spectra whose intensity was high enough to significantly distort the spectra, which were attenuated by targets with various lengths to produce many spectral shapes. We also investigated the loss-function dependence of the spectral distortion correction. We found that our network remarkably corrected the spectral distortion and material densities could be precisely measured. We also found that MAE loss function leads to more accurate measurements. These results suggest that our network is effective for material decomposition and optimizing loss function could lead to better results.

Objective: We explore the feasibility of principal component analysis (PCA) as a form of spectral imaging in photon-counting CT. Methods: Using the data acquired by a prototype system and simulated by computer, we investigate the feasibility of spectral imaging in photon-counting CT via PCA for feature extraction and study the impacts made by data standardization and de-noising on its performance. Results: The PCA in the projection domain maintains the data consistence that is essential for tomographic image reconstruction and performs virtually the same as that in the image domain. The first three primary components account for more than 99.99% covariance of the data. Within anticipation, the contrast-to-noise ratio (CNR) between the target and background in the first principal component image can be larger than that in the image generated from the data acquired in each energy bin. More importantly, the CNR in the first principal component image may be larger than that in the image formed by the summed data acquired in all energy bins (i.e., the conventional polychromatic CT image). In addition, de-noising can not only reduce the noise in images but also improve the effectiveness/efficiency of PCA in feature extraction. Conclusion: The PCA in either projection or image domain provides another form of spectral imaging in photon-counting CT that fits the essential requirements on spectral imaging in true color. Significance: The verification of PCA's feasibility in CT as a form spectral imaging and observation of its potential superiority in CNR over conventional polychromatic CT are meaningful in theory and practice.

Spectral photon-counting computed tomography (sCT) appears as a promising imaging technique for clinical applications thanks to its ability to offer low dose and possibility of quantitatively analyzing the composition of materials in a pixel. However, due to the dispatching of photons into different energy bins, the quality of sCT image at each energy bin is considerably degraded. We propose a reconstruction method for sCT images by combining multi-energy information. The method is based on clustering pixels containing similar material compositions, performing linear fitting within each class for all the energy images two-by-two, projecting the pixel values of the images at other energy bins to the pixel of the image at the current energy bin, and combining the original pixel value and projected pixel values. The results on both simulation and real data demonstrated the effectiveness of the proposed method, in terms of both image reconstruction quality and material decomposition accuracy.

Photon-Counting CT is an emerging imaging technology that promises higher spatial resolution and the possibility for material decomposition in the reconstruction. A major difficulty in Photon-Counting CT is to efficiently model cross-talk between detectors. In this work, we accelerate image reconstruction tasks for Photon-Counting CT by modelling the cross-talk with an appropriately trained deep convolutional neural network. The main result relates to proving convergence when using such a learned cross-talk model in the context of second-order optimisation methods for spectral CT. Another is to evaluate the method through numerical experiments on small-scale CT acquisitions generated using a realistic physics model. Using the reconstruction with a full cross-talk model as ground truth, the learned cross-talk model results in a 20 dB increase in peak-signal-to noise ratio compared to ignoring cross-talk altogether. At the same time, it effectively cuts the computation time of the full cross-talk model in half. Furthermore, the learned cross-talk model generalises well to both unseen data and unseen detector settings. Our results indicate that such a partially learned forward operator is a suitable way of modelling data generation in Photon-Counting CT with a computational benefit that becomes more noticeable for realistic problem sizes.

No abstract available

In this paper, we present an iterative reconstruction for photon-counting CT using prior image constrained total generalized variation (PICTGV). This work aims to exploit structural correlation in the energy domain to reduce image noise in photon-counting CT with narrow energy bins. This is motived by the fact that the similarity between high-quality full-spectrum image and target image is an important prior knowledge for photon-counting CT reconstruction. The PICTGV method is implemented using a splitting-based fast iterative shrinkage-threshold algorithm (FISTA). Evaluations conducted with simulated and real photon-counting CT data demonstrate that PICTGV method outperforms the existing prior image constrained compressed sensing (PICCS) method in terms of noise reduction, artifact suppression and resolution preservation. In the simulated head data study, the average relative root mean squared error is reduced from 2.3% in PICCS method to 1.2% in PICTGV method, and the average universal quality index increases from 0.67 in PICCS method to 0.76 in PICTGV method. The results show that the present PICTGV method improves the performance of the PICCS method for photon-counting CT reconstruction with narrow energy bins.

In a photon counting detector integrated spectral CT scanner, the received photons are counted in several energy channels to generate the corresponding projections. Since the projection in each energy channel is generated using part of the received photons, the reconstructed channel image suffers from severe noise. Therefore, image reconstruction in spectral CT is considered to be a big challenge. Because the inter-channel images are all from the same object but in different energy bins, there exists a strong correlation among these images. Moreover, it is suggested that there are similarities among various patches of CT images in the spatial domain. In this work, we propose average-image-incorporated block-matching and 3D (aiiBM3D) filtering along with low rank regularization for iterative spectral CT reconstruction. The aiiBM3D method is based on filtered 3D data arrays formed by similar 2D blocks using the mapped version of the average image obtained from linear regression. The reconstruction procedure consists of two main steps. First, the alternating direction method of multipliers is employed to solve the problem with low rank regularization where the goal is to exploit the correlation in inter-channel images. Second, our proposed BM3D-based algorithm is applied to all the channel images to make use of the redundant information in the spatial domain and inter-channel. The two steps repeat until the stopping criteria are satisfied. The proposed method is validated on numerically simulated and preclinical datasets. Our results confirm its high performance in terms of signal to noise ratio and structural preservation.

No abstract available

Spectral CT is an emerging modality that uses a data acquisition scheme with varied spectral responses to provide enhanced material discrimination in addition to the structural information of conventional CT. Existing clinical and preclinical designs with this capability include kV-switching, split-filtration, and dual-layer detector systems to provide two spectral channels of projection data. In this work, we examine an alternate design based on a spatial-spectral filter. This source-side filter is made up a linear array of materials that divide the incident x-ray beam into spectrally varied beamlets. This design allows for any number of spectral channels; however, each individual channel is sparse in the projection domain. Model-based iterative reconstruction methods can accommodate such sparse spatial-spectral sampling patterns and allow for the incorporation of advanced regularization. With the goal of an optimized physical design, we characterize the effects of design parameters including filter tile order and filter tile width and their impact on material decomposition performance. We present results of numerical simulations that characterize the impact of each design parameter using a realistic CT geometry and noise model to demonstrate feasibility. Results for filter tile order show little change indicating that filter order is a low-priority design consideration. We observe improved performance for narrower filter widths; however, the performance drop-off is relatively flat indicating that wider filter widths are also feasible designs.

The guideline of “as low as reasonably achievable” (ALARA) for radiation dose has attracted attention to sparse-view spectral computed tomography (CT) imaging. Any missing scanning view in any energy will reduce the quality of image reconstruction and material decomposition. Recently, a series of achievements have been made in optimizing spectral CT imaging based on traditional iterative models or deep learning methods. However, these works are independent or simply coupled, often neglecting the dependency relationships in spectral CT imaging. Moreover, interpretability and generalization ability are still the challenges facing the existing methods. Therefore, we combine the advantages of traditional models and deep learning methods to propose an interpretable hybrid-domain integrative transformer iterative network (HITI-Net) model for synchronously optimizing spectral CT reconstruction and material decomposition of sparse-view measurements. The model fully utilizes prior information in the fields of projection, image, and material while introducing the vision transformer to learn global and long-range image information interactions. Then, the interpretable objective function is solved by the alternating directions method of multipliers (ADMMs) and further optimized the network structure according to the derived expression. In addition, hybrid-domain sparse regularization terms and balance parameters are designed to adaptively learn during the training phase to enhance the generalization ability of the HITI-Net. In simulation and real preclinical experiments, the imaging results of HITI-Net are superior to other comparison methods, with more small features and sharp edges.

Background Sparse-view spectral tomographic image reconstruction represents a typical ill-posed inverse problem, resulting in distortion in image structures and noise surging in basis materials. Nowadays, deep learning (DL) has emerged as a state-of-the-art method in spectral image reconstruction and quantitative material analysis. However, interpretability, generalizability, and data consistency are still challenges for the existing DL-based methods. Additionally, there is no general network framework capable of simultaneously handling a series of dependent tasks in spectral imaging. This study aimed to establish a general framework for integrating multi-scene spectral imaging issues. The spectral imaging tasks, which interact in a cyclic manner during the iterative process and are optimized together. Methods The interpretable cascaded residual iterative network (ICRIN) for spectral tomographic reconstruction and material decomposition was established. First, as a general iterative framework based on hybrid-domain networks, ICRIN integrates physical model-driven, compressed sensing (CS), and data-driven priors to promote model stability and data consistency. Second, a residual iterative mechanism is employed to extract residual image features, which are further emphasized by a transformer attention module. Third, an interpretable objective function is established using the alternating minimization method to jointly optimize spectral images and decomposed materials. Fourth, a feedback mechanism is employed to improve the stability and performance of ICRIN in both tasks. Numerical simulations were conducted on eight patients and real preclinical experiments on 126 mouse slices to evaluate the performance of the proposed model. Results Qualitative and quantitative comparisons between ICRIN and other state-of-the-art methods were conducted. The interpretability and generalizability of the ICRIN model were verified using the change curves of the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) indicators as the number of iterations increased. After iterations, the highest PSNR improvements for low- and high-energy spectral images and bone and tissue materials were approximately 6.9, 6.6, 4.0, and 8.4 dB, respectively. After the introduction of the feedback mechanism, the reconstructed images increased by approximately 3 dB, while the material images improved by approximately 1–3 dB. Conclusions This study established a general iterative framework, referred to as ICRIN, and discussed its advantages in terms of interpretability, generalizability, and data consistency in a mathematical modeling context. ICRIN could be applied across a wider range of spectral computed tomography (CT) imaging tasks, enabling clinical multi-task imaging and material quantification.

Energy-resolved computed tomography (ErCT) with a photon counting detector concurrently produces multiple CT images corresponding to different photon energy ranges. It has the potential to generate energy-dependent images with improved contrast-to-noise ratio and sufficient material-specific information. Since the number of detected photons in one energy bin in ErCT is smaller than that in conventional energy-integrating CT (EiCT), ErCT images are inherently more noisy than EiCT images, which leads to increased noise and bias in the subsequent material estimation. In this work, we first deeply analyze the intrinsic tensor properties of two-dimensional (2D) ErCT images acquired in different energy bins and then present a ${F}$ ull- ${S}$ pectrum-knowledge-aware Tensor analysis and processing (FSTensor) method for ErCT reconstruction to suppress noise-induced artifacts to obtain high-quality ErCT images and high-accuracy material images. The presented method is based on three considerations: (1) 2D ErCT images obtained in different energy bins can be treated as a 3-order tensor with three modes, i.e., width, height and energy bin, and a rich global correlation exists among the three modes, which can be characterized by tensor decomposition. (2) There is a locally piecewise smooth property in the 3-order ErCT images, and it can be captured by a tensor total variation regularization. (3) The images from the full spectrum are much better than the ErCT images with respect to noise variance and structural details and serve as external information to improve the reconstruction performance. We then develop an alternating direction method of multipliers algorithm to numerically solve the presented FSTensor method. We further utilize a genetic algorithm to tackle the parameter selection in ErCT reconstruction, instead of manually determining parameters. Simulation, preclinical and synthesized clinical ErCT results demonstrate that the presented FSTensor method leads to significant improvements over the filtered back-projection, robust principal component analysis, tensor-based dictionary learning and low-rank tensor decomposition with spatial-temporal total variation methods.

We propose a hybrid reconstruction framework for dual-spectral CT (DSCT) that integrates iterative methods with deep learning models. The reconstruction process consists of two complementary components: a knowledge-driven module and a data-driven module. In the knowledge-driven phase, we employ the oblique projection modification technique (OPMT) to reconstruct an intermediate solution of the basis material images from the projection data. We select OPMT for this role because of its fast convergence, which allows it to rapidly generate an intermediate solution that successfully achieves basis material decomposition. Subsequently, in the data-driven phase, we introduce a novel neural network, ResDynUNet++, to refine this intermediate solution. The ResDynUNet++ is built upon a UNet++ backbone by replacing standard convolutions with residual dynamic convolution blocks, which combine the adaptive, input-specific feature extraction of dynamic convolution with the stable training of residual connections. This architecture is designed to address challenges like channel imbalance and near-interface large artifacts in DSCT, producing clean and accurate final solutions. Extensive experiments on both synthetic phantoms and real clinical datasets validate the efficacy and superior performance of the proposed method.

Obtaining multiple CT scans from the same patient is required in many clinical scenarios, such as lung nodule screening and image-guided radiation therapy. Repeated scans would expose patients to higher radiation dose and increase the risk of cancer. In this study, we aim to achieve ultra-low-dose imaging for subsequent scans by collecting extremely undersampled sinogram via regional few-view scanning, and preserve image quality utilizing the preceding fullsampled scan as prior. To fully exploit prior information, we propose a two-stage framework consisting of diffusion model-based sinogram restoration and deep learning-based unrolled iterative reconstruction. Specifically, the undersampled sinogram is first restored by a conditional diffusion model with sinogram-domain prior guidance. Then, we formulate the undersampled data reconstruction problem as an optimization problem combining fidelity terms for both undersampled and restored data, along with a regularization term based on image-domain prior. Next, we propose Prior-aided Alternate Iterative NeTwork (PAINT) to solve the optimization problem. PAINT alternately updates the undersampled or restored data fidelity term, and unrolls the iterations to integrate neural network-based prior regularization. In the case of 112 mm field of view in simulated data experiments, our proposed framework achieved superior performance in terms of CT value accuracy and image details preservation. Clinical data experiments also demonstrated that our proposed framework outperformed the comparison methods in artifact reduction and structure recovery.

In image reconstruction and processing, incorporating prior information, particularly the nonnegativity of pixel values, is essential. Existing computed tomography (CT) iterative reconstruction algorithms, including the algebraic reconstruction technique (ART), simultaneous ART (SART), and the simultaneous iterative reconstruction technique (SIRT), typically address negative components during the iteration process by either setting them to zero, introducing regularization terms to prevent negativity, or leaving them unchanged. This paper establishes a general framework in which enforcing the nonnegativity prior accelerates the convergence of the reconstructed image toward the true solution. Within this framework, we propose two efficient and simple acceleration techniques: setting negative pixel values to their absolute values and updating them to the estimated values from the previous update. Experiments were conducted using ART, SIRT, and SART algorithms, integrated with the corresponding acceleration techniques, on full-angle, limited-angle, and noisy simulated data, as well as real data. The results validate the effectiveness of the proposed acceleration methods by evaluating image quality using the PSNR and SSIM metrics. Notably, the proposed technique that sets negative pixel values to their absolute values is strongly recommended, as it significantly outperforms the existing technique that sets them to zero, both in terms of image quality and iteration time.

Dual-energy computed tomography (DECT) is of great clinical significance because of its material identification and quantification capacity. Although DECT measures attenuation using two different spectra, the anatomical structure of the low- and high-energy CT images are consistent with each other and the images are also correlated in the energy domain, resulting in significant information redundancy. Here this redundancy has been exploited by the proposed CD-Net (Comprehensive Domain Network) with spectral complementarity to improve the image quality and reduce the radiation dose for DECT imaging. CD-Net restores accurate anatomical information from both projection and image domains. It encompasses a projection domain neural network (PD-Net), an analytical reconstruction operator (ARO) and an image domain neural network (ID-Net). Embedding ARO into deep learning framework, the proposed one-step DECT sparse reconstruction method can directly produce high-quality DECT images from projection data acquired with spectral complementarity scheme. Qualitative and quantitative analyses demonstrate the competitive performance of CD-Net in terms of CT number accuracy, detail preservation and artifact removal. Two popular DECT applications, virtual non-contrast (VNC) imaging and iodine contrast agent quantification, reveal that the images reconstructed by CD-Net are promising for clinical applications.

In this work, we proposed the Projection Embedded Schrödinger Bridge (PESB) for CT sparse view reconstruction. PESB constructs Schrödinger Bridges between the distribution of Filtered Back-Projection (FBP) reconstructed images and the distribution of clean images conditioned on measured projections. By embedding projections into the marginal conditions, data consistency is inherently incorporated into the generative process. Experimental results validate the effectiveness of PESB, demonstrating its superior performance in CT sparse view reconstruction compared to several diffusion-based models.

To develop and investigate a deep learning approach that uses sparse-view acquisition in dedicated breast computed tomography for radiation dose reduction, we propose a framework that combines 3D sparse-view cone-beam acquisition with a multi-slice residual dense network (MS-RDN) reconstruction. Projection datasets (300 views, full-scan) from 34 women were reconstructed using the FDK algorithm and served as reference. Sparse-view (100 views, full-scan) projection data were reconstructed using the FDK algorithm. The proposed MS-RDN uses the sparse-view and reference FDK reconstructions as input and label, respectively. Our MS-RDN evaluated with respect to fully sampled FDK reference yields superior performance, quantitatively and visually, compared to conventional compressed sensing methods and state-of-the-art deep learning based methods. The proposed deep learning driven framework can potentially enable low dose breast CT imaging.

Sparse views X-ray computed tomography has emerged as a contemporary technique to mitigate radiation dose. Because of the reduced number of projection views, traditional reconstruction methods can lead to severe artifacts. Recently, research studies utilizing deep learning methods has made promising progress in removing artifacts for Sparse-View Computed Tomography (SVCT). However, given the limitations on the generalization capability of deep learning models, current methods usually train models on fixed sampling rates, affecting the usability and flexibility of model deployment in real clinical settings. To address this issue, our study proposes a adaptive reconstruction method to achieve high-performance SVCT reconstruction at various sampling rate. Specifically, we design a novel imaging degradation operator in the proposed sampling diffusion model for SVCT (CT-SDM) to simulate the projection process in the sinogram domain. Thus, the CT-SDM can gradually add projection views to highly undersampled measurements to generalize the full-view sinograms. By choosing an appropriate starting point in diffusion inference, the proposed model can recover the full-view sinograms from various sampling rate with only one trained model. Experiments on several datasets have verified the effectiveness and robustness of our approach, demonstrating its superiority in reconstructing high-quality images from sparse-view CT scans across various sampling rates.

Spectral computed tomography (CT) has a great superiority in lesion detection, tissue characterization and material decomposition. To further extend its potential clinical applications, in this work, we propose an improved tensor dictionary learning method for low-dose spectral CT reconstruction with a constraint of image gradient ℓ 0-norm, which is named as ℓ 0TDL. The ℓ 0TDL method inherits the advantages of tensor dictionary learning (TDL) by employing the similarity of spectral CT images. On the other hand, by introducing the ℓ 0-norm constraint in gradient image domain, the proposed method emphasizes the spatial sparsity to overcome the weakness of TDL on preserving edge information. The split-bregman method is employed to solve the proposed method. Both numerical simulations and real mouse studies are perform to evaluate the proposed method. The results show that the proposed ℓ 0TDL method outperforms other competing methods, such as total variation (TV) minimization, TV with low rank (TV+LR), and TDL methods.

Spectral computed tomography (CT) reconstructs material-dependent attenuation images from the projections of multiple narrow energy windows, which is meaningful for material identification and decomposition. Unfortunately, the multi-energy projection datasets usually have lower signal-noise ratios (SNR). Very recently, a spatial-spectral cube matching frame (SSCMF) was proposed to explore the non-local spatial-spectral similarities for spectral CT. This method constructs a group by clustering up a series of non-local spatial-spectral cubes. The small size of spatial patches for such a group makes the SSCMF fail to fully encode the sparsity and low-rank properties. The hard-thresholding and collaboration filtering in the SSCMF also cause difficulty in recovering the image features and spatial edges. While all the steps are operated on 4-D group, the huge computational cost and memory load might not be affordable in practice. To avoid the above limitations and further improve the image quality, we first formulate a non-local cube-based tensor instead of group to encode the sparsity and low-rank properties. Then, as a new regularizer, the Kronecker-basis-representation tensor factorization is employed into a basic spectral CT reconstruction model to enhance the capability of image feature extraction and spatial edge preservation, generating a non-local low-rank cube-based tensor factorization (NLCTF) method. Finally, the split-Bregman method is adopted to solve the NLCTF model. Both numerical simulations and preclinical mouse studies are performed to validate and evaluate the NLCTF algorithm. The results show that the NLCTF method outperforms the other state-of-the-art competing algorithms.

No abstract available

Energy spectrum computed tomography (CT) technology based on photon-counting detectors has been widely used in many applications such as lesion detection, material decomposition, and so on. But severe noise in the reconstructed images affects the accuracy of these applications. The method based on tensor decomposition can effectively remove noise by exploring the correlation of energy channels, but it is difficult for traditional tensor decomposition methods to describe the problem of tensor sparsity and low-rank properties of all expansion modules simultaneously. To address this issue, an algorithm for spectral CT reconstruction based on photon-counting detectors is proposed, which combines Kronecker-Basis-Representation (KBR) tensor decomposition and total variational (TV) regularization (namely KBR-TV). The proposed algorithm uses KBR tensor decomposition to unify the sparse measurements of traditional tensor spaces, and constructs a third-order tensor cube through non-local image similarity matching. At the same time, the TV regularization term is introduced into the independent energy spectrum image domain to enhance the sparsity constraint of single-channel images, effectively reduce artifacts, and improve the accuracy of image reconstruction. The proposed objective minimization model has been tackled using the split-Bregman algorithm. To evaluate the algorithm’s performance, both numerical simulations and realistic preclinical mouse studies were conducted. The ultimate findings indicate that the KBR-TV method offers superior enhancement in the quality of spectral CT images in comparison to several existing methods.

Spectral computed tomography (CT) reconstructs multienergy images from data in different energy bins. However, these reconstructed images can be contaminated by noise due to the limited numbers of photons in the corresponding energy bins. In this paper, we propose a spectral CT reconstruction method aided by self-similarity in image-spectral tensors, which utilizes the self-similarity of patches in both spatial and spectral domains. Patches with similar structures identified by a joint spatial and spectral searching strategy form a basic tensor unit, and can be utilized to improve image quality. Specifically, each tensor is decomposed into a low-rank component and a sparse component, which respectively represent the stable structures and feature differences across different energy bins. The augmented Lagrange method is applied to optimize the proposed objective function. To validate the performance of the proposed method, several simulated clinical and real data experiments are performed. The qualitative and quantitative results demonstrate that the proposed method outperforms several representative state-of-the-art algorithms in terms of preserving image details and reducing artifacts.

Spectral computed tomography (CT) reconstructs multi-energy images from data in different energy bins. These reconstructed images can be contaminated by noise due to the limited numbers of photons in the corresponding energy bins. In this paper, we propose a spectral CT reconstruction method aided by self-similarity in image-spectral tensors (ASSIST), which utilizes the self-similarity of patches in both spatial and spectral domains. Patches with similar structures identified by a joint spatial and spectral searching strategy form a basic tensor unit, and can be utilized to improve image quality. Specifically, each tensor is decomposed into a low-rank component and a sparse component, which respectively represent the stable structures and feature differences across different energy bins. The experimental results demonstrate that the proposed method outperforms several representative state-of-the-art algorithms.

Photon-counting computed tomography (PCCT) enables multi-energy spectral imaging from a single scan. However, low photon count in each channel introduces significant noise, reduces spatial resolution, and limits fine detail, especially in low-dose or fine-structure imaging. To tackle these issues, we propose a Separable Attention-based Tensor Neural Network (SATNN) as a Bayesian reconstruction prior for PCCT. SATNN utilizes depthwise separable convolutions for efficient spatial feature extraction and squeeze-and-excitation blocks to enhance critical channel-wise features, allowing focused attention on key features. Following reconstruction, anisotropic diffusion filtering further refines images by suppressing residual noise while preserving textural details. Through realistic PCCT simulation studies, SATNN demonstrated superior performance over the existing algorithms, achieving improved texture preservation, spectral correlation, and noise suppression, making it a robust and effective solution for both research and clinical applications.

The potential huge advantage of spectral computed tomography (CT) is its capability to provide accuracy material identification and quantitative tissue information. This can benefit clinical applications, such as brain angiography, early tumor recognition, etc. To achieve more accurate material components with higher material image quality, we develop a dictionary learning based image-domain material decomposition (DLIMD) for spectral CT in this paper. First, we reconstruct spectral CT image from projections and calculate material coefficients matrix by selecting uniform regions of basis materials from image reconstruction results. Second, we employ the direct inversion (DI) method to obtain initial material decomposition results, and a set of image patches are extracted from the mode-1 unfolding of normalized material image tensor to train a united dictionary by the K-SVD technique. Third, the trained dictionary is employed to explore the similarities from decomposed material images by constructing the DLIMD model. Fourth, more constraints (i.e., volume conservation and the bounds of each pixel within material maps) are further integrated into the model to improve the accuracy of material decomposition. Finally, both physical phantom and preclinical experiments are employed to evaluate the performance of the proposed DLIMD in material decomposition accuracy, material image edge preservation and feature recovery.

Spectral computed tomography (CT) can reconstruct spectral images from different energy bins using photon counting detectors (PCDs). However, due to the limited photons and counting rate in the corresponding spectral fraction, the reconstructed spectral images usually suffer from severe noise. In this paper, a fourth-order nonlocal tensor decomposition model for spectral CT image reconstruction (FONT-SIR) method is proposed. Similar patches are collected in both spatial and spectral dimensions simultaneously to form the basic tensor unit. Additionally, principal component analysis (PCA) is applied to extract latent features from the patches for a robust and efficient similarity measure. Then, low-rank and sparsity decomposition is performed on the produced fourth-order tensor unit, and the weighted nuclear norm and total variation (TV) norm are used to enforce the low-rank and sparsity constraints, respectively. The alternating direction method of multipliers (ADMM) is adopted to optimize the objective function. The experimental results with our proposed FONTSIR demonstrates a superior qualitative and quantitative performance for both simulated and real data sets relative to several state-of-the-art methods, in terms of noise suppression and detail preservation.

Due to the limitations of the data noise and spectrum distortion, accurate multi-material decomposition is a hard problem in spectral CT imaging research. Our group promoted a dynamic dual-energy photon counting detector. Its energy threshold can be dynamically changed at various energy bins during a spectral CT scan. It can provide more spectral information of the materials while keeping the data/image noise in a reasonable level. In this paper, we studied a post-processed multi-material-decomposition method based on this dynamic dual-energy detectors and tensor PRISM reconstruction method. We compared the reconstruction and decomposition results between the traditional static multi-energy CT and this dynamic dual-energy CT. The reconstruction results illustrated that the dynamic dual-energy CT can suppress the noise to a great extent compared to traditional static spectral CT, and can have similar results to reference true value. In the comparisons of decomposition results, some tissues are completely misclassified in the static spectral CT results while the dynamic dual-energy CT results have nearly the same results as the reference true value. Therefore, we conclude that the dynamic dual-energy CT can accurately decompose materials in similar components and have highly feasible in clinical practice.

BACKGROUND Multi-material decomposition is an interesting topic in dual-energy CT (DECT) imaging; however, the accuracy and performance may be limited using the conventional algorithms. PURPOSE In this work, a novel multi-material decomposition network (MMD-Net) is proposed to improve the multi-material decomposition performance of DECT imaging. METHODS To achieve dual-energy multi-material decomposition, a deep neural network, named as MMD-Net, is proposed in this work. In MMD-Net, two specific convolutional neural network modules, Net-I and Net-II, are developed. Specifically, Net-I is used to distinguish the material triangles, while Net-II predicts the effective attenuation coefficients corresponding to the vertices of the material triangles. Subsequently, the material-specific density maps are calculated analytically through matrix inversion. The new method is validated using in-house benchtop DECT imaging experiments with a solution phantom and a pig leg specimen, as well as commercial medical DECT imaging experiments with a human patient. The decomposition accuracy, edge spreading function, and noise power spectrum are quantitatively evaluated. RESULTS Compared to the conventional multiple material decomposition (MMD) algorithm, the proposed MMD-Net method is more effective at suppressing image noise. Additionally, MMD-Net outperforms the iterative MMD approach in maintaining decomposition accuracy, image sharpness, and high-frequency content. Consequently, MMD-Net is capable of generating high-quality material decomposition images. CONCLUSION A high performance multi-material decomposition network is developed for dual-energy CT imaging.

Objective: Dual-energy CT (DECT) strengthens the material characterization and quantification due to its capability of material discrimination. The image-domain multi-material decomposition (MMD) via matrix inversion suffers from serious degradation of the signal-to-noise ratios (SNRs) of the decomposed images, and thus the clinical application of DECT is limited. In this paper, we propose a noise suppression algorithm based on the noise propagation for image-domain MMD. Methods: The noise in the decomposed images only distributes in two perpendicular directions and is suppressed by estimating the center of mass of the same-material pixel group vertically along the principal axis where the noise disturbance is minimal. The proposed method is evaluated using the line-pair and contrast-rod slices of the Catphan©600 phantom and one patient data set. We compared the proposed method with the direct inversion and the block-matching and three-dimensional (BM3D) filtration methods. Results: The results of Catphan©600 phantom and the patient show that the proposed method successfully suppresses the noise of the basis material images by one order of magnitude and preserves the spatial resolution of the decomposed images. Compared with the BM3D filtration method, the proposed method maintains the texture distribution of the decomposed images at the same SNR and the accuracy of the electron density measurement. Conclusion: The algorithm achieves effective noise suppression compared with the BM3D filtration while maintaining the spatial distribution of the decomposed material images. It is, thus, attractive for advanced clinical applications using DECT.

Cardiac computed tomography (CT) has emerged as a major imaging modality for the diagnosis and monitoring of cardiovascular diseases. High temporal resolution is essential to ensure diagnostic accuracy. Limited-angle data acquisition can reduce scan time and improve temporal resolution, but typically leads to severe image degradation and motivates for improved reconstruction techniques. In this paper, we propose a novel physics-informed score-based diffusion model (PSDM) for limited-angle reconstruction of cardiac CT. At the sampling time, we combine a data prior from a diffusion model and a model prior obtained via an iterative algorithm and Fourier fusion to further enhance the image quality. Specifically, our approach integrates the primal-dual hybrid gradient (PDHG) algorithm with score-based diffusion models, thereby enabling us to reconstruct high-quality cardiac CT images from limited-angle data. The numerical simulations and real data experiments confirm the effectiveness of our proposed approach.

Sparse-view computed tomography aims to reduce radiation exposure but often suffers from degraded image quality due to insufficient projection data. Traditional methods struggle to balance data fidelity and detail preservation, particularly in high-frequency regions. In this paper, we propose a Cascaded Frequency-Encoded Multi-Scale Neural Fields (Ca-FMNF) framework. We reformulate the reconstruction task as refining high-frequency residuals upon a high-quality low-frequency foundation. It integrates a pre-trained iterative unfolding network for initial low-frequency estimation with a FMNF to represent high-frequency residuals. The FMNF parameters are optimized by minimizing the discrepancy between the measured projections and those estimated through the imaging forward model, thereby refining the residuals based on the initial estimation. This dual-stage strategy enhances data consistency and preserves fine structures. The extensive experiments on simulated and clinical datasets demonstrate that our method achieves the optimal results in both quantitative metrics and visual quality, effectively reducing artifacts and preserving structural details.

Computed tomography (CT) technology reduces radiation exposure to the human body through sparse sampling, but fewer sampling angles pose challenges for image reconstruction. When the projection angles are significantly reduced, the quality of image reconstruction deteriorates. To improve the quality of image reconstruction under sparse angles, an ultra-sparse view CT reconstruction method utilizing multi-scale diffusion models is proposed. This method aims to focus on the global distribution of information while facilitating the reconstruction of local image features in sparse views. Specifically, the proposed model ingeniously combines information from both comprehensive sampling and selective sparse sampling techniques. By precisely adjusting the diffusion model, diverse noise distributions are extracted, enhancing the understanding of the overall image structure and assisting the fully sampled model in recovering image information more effectively. By leveraging the inherent correlations within the projection data, an equidistant mask is designed according to the principles of CT imaging, allowing the model to focus attention more efficiently. Experimental results demonstrate that the multi-scale model approach significantly improves image reconstruction quality under ultra-sparse views and exhibits good generalization across multiple datasets.

X-ray Computed Tomography (CT) is one of the most important diagnostic imaging techniques in clinical applications. Sparse-view CT imaging reduces the number of projection views to a lower radiation dose and alleviates the potential risk of radiation exposure. Most existing deep learning (DL) and deep unfolding sparse-view CT reconstruction methods: 1) do not fully use the projection data; 2) do not always link their architecture designs to a mathematical theory; 3) do not flexibly deal with multi-sparse-view reconstruction assignments. This paper aims to use mathematical ideas and design optimal DL imaging algorithms for sparse-view CT reconstructions. We propose a novel dual-domain unified framework that offers a great deal of flexibility for multi-sparse-view CT reconstruction through a single model. This framework combines the theoretical advantages of model-based methods with the superior reconstruction performance of DL-based methods, resulting in the expected generalizability of DL. We propose a refinement module that utilizes unfolding projection domain to refine full-sparse-view projection errors, as well as an image domain correction module that distills multi-scale geometric error corrections to reconstruct sparse-view CT. This provides us with a new way to explore the potential of projection information and a new perspective on designing network architectures. The multi-scale geometric correction module is end-to-end learnable, and our method could function as a plug-and-play reconstruction technique, adaptable to various applications. Extensive experiments demonstrate that our framework is superior to other existing state-of-the-art methods.

Objective.Sparse-view computed tomography (SVCT), which can reduce the radiation doses administered to patients and hasten data acquisition, has become an area of particular interest to researchers. Most existing deep learning-based image reconstruction methods are based on convolutional neural networks (CNNs). Due to the locality of convolution and continuous sampling operations, existing approaches cannot fully model global context feature dependencies, which makes the CNN-based approaches less efficient in modeling the computed tomography (CT) images with various structural information. Approach. To overcome the above challenges, this paper develops a novel multi-domain optimization network based on convolution and swin transformer (MDST). MDST uses swin transformer block as the main building block in both projection (residual) domain and image (residual) domain sub-networks, which models global and local features of the projections and reconstructed images. MDST consists of two modules for initial reconstruction and residual-assisted reconstruction, respectively. The sparse sinogram is first expanded in the initial reconstruction module with a projection domain sub-network. Then, the sparse-view artifacts are effectively suppressed by an image domain sub-network. Finally, the residual assisted reconstruction module to correct the inconsistency of the initial reconstruction, further preserving image details. Main results. Extensive experiments on CT lymph node datasets and real walnut datasets show that MDST can effectively alleviate the loss of fine details caused by information attenuation and improve the reconstruction quality of medical images. Significance. MDST network is robust and can effectively reconstruct images with different noise level projections. Different from the current prevalent CNN-based networks, MDST uses transformer as the main backbone, which proves the potential of transformer in SVCT reconstruction.

Sparse-view CT reconstruction represents a prototypical ill-posed inverse problem. The implementation of deep learning solutions has proven to be highly successful in this field. The dual-domain reconstruction network achieves a favorable trade-off between reconstruction performance and computational cost by leveraging the powerful mapping capability of deep learning and the domain-transform relying on analytical reconstruction algorithms. However, further research is required to enhance the domain-transform in this field. Inspired by the successful utilization of low-rank prior in various medical imaging tasks, we proposed an end-to-end one-shot dual-domain network for sparse-view CT reconstruction. The domain-transform was designed as a high-fidelity multi-channel parallel back-projection in proposed network. In this way, feature maps between channels in the image domain imply strong low-rank priors. We implemented the singular value thresholding algorithm as a network layer, learning parameters and thresholds in a data-driven manner, fully leveraging the low-rank prior across channels to greatly reduce information loss and distortion during domain-transform. Moreover, we constructed a projection completion network based on dual attention mechanism that synthesizes missing view projections by effectively utilizing potential local correlation among projection domains during fan-beam scanning. In the image domain, a refine subnetwork based on Vision Transformer utilizes mix-scale features to implement two-dimensional filtering belonging to the back-projection filter algorithm. Extensive experiments on two clinically relevant datasets have demonstrated that the proposed network achieves competing performance on both quantitative metrics and visual quality.

The inherent spectral properties of photon-counting computed tomography (PCCT) allow detailed material identification through decomposition techniques, but these methods often amplify image noise and artifacts. Current denoising approaches mainly focus on improving already degraded images, ignoring the fundamental noise caused by random variations in photon detection. To tackle these issues, we combine a physics-based noise analysis with deep learning to control noise during the material decomposition process. Our work has three key parts: (1) A noise analysis model that explains how random photon-count variations in the detector affect the noise levels in different materials after decomposition. This model connects the Poisson-distributed detector noise to material-specific noise patterns. (2) A self-supervised training method that combines the noise model with neural networks using probability-based optimization, allowing the system to learn from limited training data without needing high-quality data. (3) A flexible image improvement system that adapts to different body structures and noise conditions, ensuring reliable results across various scanning scenarios. Tests using real patient scan data show our method better preserves material accuracy and produces cleaner virtual monochromatic images compared to traditional approaches. Importantly, our solution works effectively with small training datasets and can be practically used in hospital settings without slowing down workflows. This research bridges the gap between theoretical noise analysis and clinical medical imaging needs, offering a balanced approach to improving PCCT technology.

Objective. Photon-counting CT (PCCT) has better dose efficiency and spectral resolution than energy-integrating CT, which is advantageous for material decomposition. Unfortunately, the accuracy of PCCT-based material decomposition is limited due to spectral distortions in the photon-counting detector (PCD). Approach. In this work, we demonstrate a deep learning (DL) approach that compensates for spectral distortions in the PCD and improves accuracy in material decomposition by using decomposition maps provided by high-dose multi-energy-integrating detector (EID) data as training labels. We use a 3D U-net architecture and compare networks with PCD filtered back projection (FBP) reconstruction (FBP2Decomp), PCD iterative reconstruction (Iter2Decomp), and PCD decomposition (Decomp2Decomp) as the input. Main results. We found that our Iter2Decomp approach performs best, but DL outperforms matrix inversion decomposition regardless of the input. Compared to PCD matrix inversion decomposition, Iter2Decomp gives 27.50% lower root mean squared error (RMSE) in the iodine (I) map and 59.87% lower RMSE in the photoelectric effect (PE) map. In addition, it increases the structural similarity (SSIM) by 1.92%, 6.05%, and 9.33% in the I, Compton scattering (CS), and PE maps, respectively. When taking measurements from iodine and calcium vials, Iter2Decomp provides excellent agreement with multi-EID decomposition. One limitation is some blurring caused by our DL approach, with a decrease from 1.98 line pairs/mm at 50% modulation transfer function (MTF) with PCD matrix inversion decomposition to 1.75 line pairs/mm at 50% MTF when using Iter2Decomp. Significance. Overall, this work demonstrates that our DL approach with high-dose multi-EID derived decomposition labels is effective at generating more accurate material maps from PCD data. More accurate preclinical spectral PCCT imaging such as this could serve for developing nanoparticles that show promise in the field of theranostics (therapy and diagnostics).

In computed tomography (CT), although sparse sampling of projections effectively mitigates radiation problems, the quality of CT images is severely compromised. Recovering high-quality CT images from sparsely sampled data is a challenging task. Recently, “Iterative Theory + Deep Learning” schemes have shown promising results in CT reconstruction tasks. In this paper, we propose an Iterative Reconstruction Network Model based on learnable projection operators (LIR-NET). Unlike existing image domain iteration schemes that fuse information from the projection domain, LIR-Net achieves joint optimization and iteration of dual-domain data. The dual-domain subnetwork uses a replaceable and lightweight U-net. We propose an Enhanced Aligned Loss (EAL) scheme to speed up convergence in the projection domain subnet. A designed last-iteration Sparse Truth Bootstrap (STB) module improves data distortion, while Bit-plane Codec (BC) is combined to enhance the noise discovery and removal capability of the image domain subnet. Extensive experiments based on the dataset from the “Low Dose CT Image and Projection Data (LDCT-and-Projection data)” show that our approach outperforms the best available solutions in both quantitative and qualitative evaluations. Moreover, the robustness of the proposed scheme has been tested and validated on an additional dataset.

Magnetic particle imaging (MPI) is a novel tomographic imaging modality that scans the distribution of superparamagnetic iron oxide nanoparticles. However, it is time‐consuming to scan multiview two‐dimensional (2D) projections for three‐dimensional (3D) reconstruction in projection MPI, such as computed tomography (CT). An intuitive idea is to use the sparse‐view projections for reconstruction to improve the temporal resolution. Tremendous progress has been made toward addressing the sparse‐view problem in CT, because of the availability of large data sets. For the novel tomography of MPI, to the best of our knowledge, studies on the sparse‐view problem have not yet been reported.

Score-based generative model (SGM) has risen to prominence in sparse-view CT reconstruction due to its impressive generation capability. The consistency of data is crucial in guiding the reconstruction process in SGM-based reconstruction methods. However, the existing data consistency policy exhibits certain limitations. Firstly, it employs partial data from the reconstructed image of the iteration process for image updates, which leads to secondary artifacts with compromising image quality. Moreover, the updates to the SGM and data consistency are considered as distinct stages, disregarding their interdependent relationship. Additionally, the reference image used to compute gradients in the reconstruction process is derived from the intermediate result rather than ground truth. Motivated by the fact that a typical SGM yields distinct outcomes with different random noise inputs, we propose a Multi-channel Optimization Generative Model (MOGM) for stable ultra-sparse-view CT reconstruction by integrating a novel data consistency term into the stochastic differential equation model. Notably, the unique aspect of this data consistency component is its exclusive reliance on original data for effectively confining generation outcomes. Furthermore, we pioneer an inference strategy that traces back from the current iteration result to ground truth, enhancing reconstruction stability through foundational theoretical support. We also establish a multi-channel optimization reconstruction framework, where conventional iterative techniques are employed to seek the reconstruction solution. Quantitative and qualitative assessments on 23 views datasets from numerical simulation, clinical cardiac and sheep’s lung underscore the superiority of MOGM over alternative methods. Reconstructing from just 10 and 7 views, our method consistently demonstrates exceptional performance.

Sparse‐view CT shortens scan time and reduces radiation dose but results in severe streak artifacts due to insufficient sampling data. Deep learning methods can now suppress these artifacts and improve image quality in sparse‐view CT reconstruction.