Spectral computed tomography (Spectral CT) is an emerging imaging technology that enhances material differentiation and clinical diagnostic accuracy by acquiring multi-spectral projection data. However, in sparse-angle spectral CT image reconstruction, noise suppression and edge preservation still face challenges. Regularization methods, such as Directional Probabilistic Total Variation (dTV-p) and tight wavelet frame L0, could introduce prior information to improve sparse-angle spectral CT image reconstruction quality. In this study, we propose a dTV-p and tight wavelet frame L0 regularization-based dual-regularization sparse-angle spectral CT image reconstruction algorithm to address noise suppression and edge preservation. We used the fast iterative shrinkage-thresholding algorithm (FISTA) to accelerate the algorithm. First, the dTV-p regularization is solved in the image domain using proximal mapping and FISTA. Next, the L0 regularization is solved in the wavelet domain using iterative hard thresholding. Finally, the dual variables are solved using FISTA acceleration. The experimental results demonstrated the efficacy of the proposed algorithm, revealing superior performance in edge preservation, noise suppression, and quantitative evaluation metrics compared to comparative algorithms.

Cone-beam computed tomography (CT) is inherently limited for high-aspect-ratio objects due to restricted X-ray penetration, whereas cone-beam rotational computed laminography (CL) addresses this issue by tilting the source–detector assembly or the object to maintain consistent transmission across projections. Existing analytical methods typically employ a one-dimensional (1D) ramp filter during projection filtering, which fails to adequately suppress artifacts and may even introduce distortions in the reconstructed object. To improve reconstruction quality, we propose a two-dimensional filtered backprojection (2D-FBP) method based on the point spread function (PSF) for cone-beam rotational CL. The proposed approach first derives an exact expression for the projection process, followed by a modified backprojection process incorporating two weighting factors that yield a more tractable PSF expression. To circumvent the computational burden of three-dimensional (3D)image-space filtering, an approximate transformation is introduced that converts the 3D filtering operation into a 2D filtering operation in the projection space,from which a simple yet effective 2D filter is derived. Experimental results on real data demonstrate that the proposed 2D-FBP method achieves substantially improved reconstruction quality, faithfully preserving structural morphology while enabling reliable detection of void defects, compared with the FDK method.

Cone-beam rotational computed laminography (CL) is a highly effective inspection technique for non-destructive testing of objects with a large aspect ratio, such as printed circuit boards (PCB) and insulated gate bipolar transistors (IGBT). However, when scanning objects with a large aspect ratio, the projection data may become truncated, resulting in region of interest (ROI) artifacts in the reconstructed image and reducing the contrast of the reconstructed image. To address this issue, we have proposed a weighted factor that considers the length of the ray within the reconstructed volume and the distance between the X-ray source and the detector bin position. We have also developed a method called ROI conjugate gradient weighted least squares (ROI-CGWLS) to suppress ROI artifacts and enhance the contrast of the reconstructed image in Cone-beam rotational CL. Both simulation and real PCB experimental results demonstrate the effectiveness of the proposed ROI-CGWLS method in suppressing ROI artifacts and improving image contrast and resolution compared to other classical reconstruction methods.

In industrial computed tomography (CT), using noisy projection data for reconstruction increases the noise in the reconstructed image and reduces the signal-to-noise ratio (SNR). When the quality of projection data is poor, classical denoising and reconstruction algorithms are ineffective in removing the noise. To improve the quality of low signal-to-noise CT reconstructed images, this study proposes a deep learning-based denoising method. The method integrates squeeze-and-excitation blocks into the decoder phase and adaptively adjusts the weights of the channels to better preserve structural details during the denoising process. Experimental results demonstrate that the proposed method significantly reduces the noise and effectively preserves edge details, outperforming other comparative methods in both visual quality and quantitative values.

Objective.low-dose computed tomography (LDCT) images suffer from severe noise due to reduced radiation exposure. Most existing deep learning-based denoising methods require supervised learning with paired training data that is difficult to obtain. To address this limitation, we aim to develop a denoising method that does not rely on paired normal-dose computed tomography data.Approach.we propose a self-supervised denoising method based on guided image filtering (GIF) that requires only LDCT images for training. The method first applies GIF to generate pseudo-labels from LDCT images, enabling the network to learn noise distributions between inputs and pseudo-labels for denoising, without paired data. Then, an attention gate (AG) mechanism is embedded in the decoder stage of a residual network to further enhance denoising performance.Main results.experimental results demonstrate that the proposed method achieves superior performance compared to state-of-the-art unsupervised denoising networks, transformer-based denoising model and post-processing methods, in terms of both visual quality and quantitative metrics. Furthermore, ablation studies are conducted to analyze the impact of different attention mechanisms and the number of AG mechanisms, showing that the proposed network architecture achieves optimal performance.Significance.this work leverages self-supervised learning with GIF to generate pseudo-labels, enabling LDCT denoising without paired data. The embedded AG mechanism, supported by detailed ablation analysis, further enhances denoising performance by improving feature focus and structural preservation.

Computed tomography is a highly effective inspection methodology for non-destructive testing, however, it faces challenges with objects that have a significant aspect ratio. In such scenarios, computed laminography (CL) serves as a viable alternative. The unique geometric configuration of cone-beam rotary CL makes the classical FDK reconstruction algorithm unsuitable. To address this inverse problem, we proposed an approximate analytical reconstruction method inspired by the core idea of the FDK algorithm. Firstly, we addressed the cone-beam rotary CL reconstruction problem by approximating it as a series of fan-beam reconstruction tasks, and deriving the geometric relationships between the original coordinate system and the fan-beam coordinates. Secondly, the fan-beam reconstruction formula within the fan-beam coordinate system is derived. Finally, disregarding the fact that the projection data come from different planes based on the idea of the Feldkamp–Davis–Kress algorithm, an approximate analytical reconstruction algorithm is derived based on the geometric relationships between the original coordinate system and the detector coordinates. The effectiveness of our method is demonstrated through simulations and real data experiments. The results demonstrate that the proposed method mitigates the superimposition artifacts and enhances the fine structural details to a certain extent compared to the CL-filtered backprojection method, while preserving the object boundaries.

BACKGROUND:Due to the incomplete projection data collected by limited-angle computed tomography (CT), severe artifacts are present in the reconstructed image. Classical regularization methods such as total variation (TV) minimization, ℓ0 minimization, are unable to suppress artifacts at the edges perfectly. Most existing regularization methods are single-objective optimization approaches, stemming from scalarization methods for multiobjective optimization problems (MOP). OBJECTIVE:To further suppress the artifacts and effectively preserve the edge structures of the reconstructed image. METHOD:This study presents a multiobjective optimization model incorporates both data fidelity term and ℓ0-norm of the image gradient as objective functions. It employs an iterative approach different from traditional scalarization methods, using the maximization of structural similarity (SSIM) values to guide optimization rather than minimizing the objective function.The iterative method involves two steps, firstly, simultaneous algebraic reconstruction technique (SART) optimizes the data fidelity term using SSIM and the Simulated Annealing (SA) algorithm for guidance. The degradation solution is accepted in the form of probability, and guided image filtering (GIF) is introduced to further preserve the image edge when the degradation solution is rejected. Secondly, the result from the first step is integrated into the second objective function as a constraint, we use ℓ0 minimization to optimize ℓ0-norm of the image gradient, and the SSIM, SA algorithm and GIF are introduced to guide optimization process by improving SSIM value like the first step. RESULTS:With visual inspection, the peak signal-to-noise ratio (PSNR), root mean square error (RMSE), and SSIM values indicate that our approach outperforms other traditional methods. CONCLUSIONS:The experiments demonstrate the effectiveness of our method and its superiority over other classical methods in artifact suppression and edge detail restoration.

In X-ray CT imaging, there are some cases where the obtained CT images have serious ring artifacts and noise, and these degraded CT images seriously affect the quality of clinical diagnosis. Thus, developing an effective method that can simultaneously suppress ring artifacts and noise is of great importance. Total variation (TV) is a famous prior regularization for image denoising in the image processing field, however, for degraded CT images, it can suppress the noise but fail to reduce the ring artifacts. To address this issue, the L-0 smoothing filter is incorporated with TV prior for CT ring artifacts and noise removal problem where the problem is transformed into several optimization sub-problems which are iteratively solved. The experiments demonstrate that the ring artifacts and noise presented in the CT image can be effectively suppressed by the proposed method and meanwhile the detailed features such as edge structure can be well preserved. As the superiority of TV and L-0 smoothing filters are fully utilized, the performance of the proposed method is better than the existing methods such as the TV-based method and L-0-based method.

Objective. Limited-angle x-ray computed tomography (CT) is a typical ill-posed inverse problem, leading to artifacts in the reconstructed image due to the incomplete projection data. Most iteration CT reconstruction methods involve optimization for a single object. This paper explores a multi-objective optimization model and an interactive method based on multi-objective optimization to suppress the artifacts of limited-angle CT. Approach. The model includes two objective functions on the dual domain within the data consistency constraint. In the interactive method, the structural similarity index measure (SSIM) is regarded as the value function of the decision maker (DM) firstly. Secondly, the DM arranges the objective functions of the multi-objective optimization model to be optimized according to their absolute importance. Finally, the SSIM and the simulated annealing (SA) method help the DM choose the desirable reconstruction image by improving the SSIM value during the iteration process. Main results. Simulation and real data experiments demonstrate that the artifacts can be suppressed by the proposed method, and the results were superior to those reconstructed by the other three reconstruction methods in preserving the edge structure of the image. Significance. The proposed interactive method based on multi-objective optimization shows some potential advantages over classical single object optimization methods.

In some computed tomography (CT) practical applications, the projection data is incom-plete, which makes some limited-angle artifacts presented in the reconstructed image. To-tal variation (TV) regularization method is used to suppress the artifacts, but the edge of reconstructed image is distorted or some tiny details are missed. To preserve the edge of reconstructed image, a cascading t 0 regularization-based reconstruction model in nonsub-sampled contourlet transform (NSCT) domain is proposed, which considers both the direc-tional peculiarity of artifacts and the smooth of low frequency of the reconstructed image. In the proposed reconstruction model, a t 0 regularization term in the high frequency is used to suppress the artifacts and noise, and a t 0 regularization of gradient image in low frequency is used to suppress the limited-angle artifacts, to preserve the edge of object and to smooth the reconstructed image. To solve the proposed model, a proximal alternating linearized Peaceman-Rachford splitting method (PAL-PRSM) is proposed, which uses the Peaceman-Rachford splitting method that updates the Lagrange multiplier twice, one after each minimization of the subproblem, to deal with the optimization problem firstly, and then the proximal linearization is used to avoid computing the inverse of a huge system matrix. In addition, to compensate the proximal linearization, we add an additional term into Lagrange multiplier updating. Real data experiments are investigated to demonstrate the effectiveness of PAL-PRSM method, and the results show that the proposed method outperforms two other CT reconstruction methods on preserving the edge of reconstructed image. On the whole, the proposed method is a compromise between denoising and pre-serving the edge of reconstructed image.(c) 2023 Elsevier Inc. All rights reserved.

This paper proposes a fast regularized method for limited angle CT, the preconditioning matrix, which includes a weighting matrix and a filtering matrix, is utilized to improve the convergence speed. The projection and back-projection in the iteration process are replaced by the analytic operators to accelerate the computation speed. In addition, a Hamming window function is added to further suppress the noise and artifacts. Real data experiments show that the proposed method outperforms the other three methods in preserving the edge, convergence speed and computing speed.

BACKGROUNDThe Mueller, Siddon and Joseph weighting algorithms are frequently used for projection and back-projection, which are relatively complicated when they are implemented in computer code.OBJECTIVEThis study aims to reduce the actual complexity of the projection and back-projection.METHODSFirst, we neglect the exact shape of the pixel, so that its shadow is a rectangle projecting precisely to a detector bin, which implies that all the pixel weights are exactly 1 for each ray through them, otherwise are exactly 0. Next, a one-to-one reversible image rotation algorithm (RIRA) is proposed to compute the projection and back-projection, where two one-to-one mapping lists namely, U and V, are used to store the coordinates of a rotated pixel and its corresponding new coordinates, respectively. For each 2D projection, the projection is simply the column sum in each orientation according to the lists U and V. For each 2D back-projection, it is simply to arrange the projection to the corresponding column element according to the lists U and V. Thus, there is no need for an interpolation in the projection and back-projection. Last, a rotating image computed tomography (RICT) based on RIRA is proposed to reconstruct the image.RESULTSExperiments show the RICT reconstructs a good image that is close to the result of filtered back-projection (FBP) method according to the RMSE, PSNR and MSSIM values. What's more, our weight, projection and back-projection are much easier to be implemented in computer code than the FBP method.CONCLUSIONThis study demonstrates that the RIRA method has potential to be used to simplify many computed tomography image reconstruction algorithms.

Radiation is harmful to the human body, which is coupled with the fact that scanning conditions pose a number of restrictions. As a result, the projection data of a scanned object are generally acquired within a limited-angle range in practical computed tomography (CT) applications. Under this circumstance, classical image reconstruction methods cannot obtain high-quality images, and limited-angle artifacts appear in the reconstructed image. In recent years, the l1 norm of a gradient image-based total variation minimization (TVL1) image reconstruction method has often been used to deal with the image reconstruction problem from undersampling projection data, but limited-angle artifacts have been encountered near the edges for limited-angle CT. The l0 norm of a gradient image-based total variation minimization (TVL0) image reconstruction method can better preserve the edges, but it cannot obtain acceptable results when the scanning angle range is further reduced. Inspired by the advantages of guided image filtering (GIF), which can better smooth an image and preserve its structure, we used it to improve the reconstructed image quality for limited-angle CT by transferring reconstructed results of the TVL1 method to those of the TVL0 method. Simulation experiments show that the proposed method can better preserve structures and suppress limited-angle artifacts and noise than several related reconstruction methods.

Abstract Limited-angle computed tomography (CT) reconstruction problem arises in some practical applications due to restrictions in the scanning environment or CT imaging device. Some artifacts will be presented in image reconstructed by conventional analytical algorithms. Although some regularization strategies have been proposed to suppress the artifacts, such as total variation (TV) minimization, there is still distortion in some edge portions of image. Guided image filtering (GIF) has the advantage of smoothing the image as well as preserving the edge. To further improve the image quality and protect the edge of image, we propose a coupling method, that combines ℓ0{\ell_{0}} gradient minimization and GIF. An intermediate result obtained by ℓ0{\ell_{0}} gradient minimization is regarded as a guidance image of GIF, then GIF is used to filter the result reconstructed by simultaneous algebraic reconstruction technique (SART) with nonnegative constraint. It should be stressed that the guidance image is dynamically updated as the iteration process, which can transfer the edge to the filtered image. Some simulation and real data experiments are used to evaluate the proposed method. Experimental results show that our method owns some advantages in suppressing the artifacts of limited angle CT and in preserving the edge of image.

Low-dose computed tomography (LdCT) imaging can greatly reduce the radiation dose imposed to patient, however it leads to the low signal-to-noise ratio (SNR) measured projection data. Using conventional analytical reconstruction method (e.g., filtered back-projection method), the reconstruction results usually suffer from serious noise in LdCT. To obtain high-quality CT images, iterative reconstruction method combined with prior knowledge of the object is of great importance. In this work, both structural group sparsity and gradient prior sparsity are jointed as a novel regularization constraint in the proposed CT reconstruction model. To solve the optimization-based CT reconstruction problem, original problem was transformed into a series of sub-problems based on alternating direction method of multipliers framework. The merit of the proposed joint regularization method is that global and local sparsity are both utilized. To valid the performance of proposed reconstruction algorithm, we did simulated experiments with different noise levels and real data studies. The qualitative and quantitative analyses show that the proposed reconstruction algorithm has better performance than other iterative reconstruction algorithms. What's more, compared to the existing iterative reconstruction methods, the proposed reconstruction algorithm can well reconstructed important structure features and effectively suppress the noise and artifacts. (c) 2020 Published by Elsevier B.V.

Photoacoustic tomography (PAT) is an emerging and effective imaging technique, which offers high spatial resolution with high contrast. In particular, the acquired data is incomplete due to geometrical limitations or accelerating data acquisition by undersampling technology, thus some artifacts will be presented in the reconstructed image. To deal with limited-view PAT, we introduce a [Formula: see text] regularization scheme into PAT and propose a three-stage method. We first use the gradient descent method to obtain an initial solution, then project it onto a constrain set, and finally a proximal mapping scheme is used to further improve the reconstruction quality. Our simulation experiments on homogeneous medium are utilized to validate the effectiveness of the proposed method, and a discussion on the parameters of the proposed method is given. The experimental results reveal that the proposed method outperforms other classical methods, and it can further improve the reconstruction quality in terms of suppressing the noise and artifacts, and preserving the edge.

•A nonconvex and nonsmooth optimization model is investigated for limited-angle CT imaging.•The proposed method can avoid computing the inverse of a large system matrix.•We show that each bounded sequence generated by our method globally converges to a critical point.•The results by our method are shown superior than some classical CT reconstruction methods by real data experiments.

In the real applications of computed tomography (CT) imaging, the projection data of the scanned objects are usually acquired within a limited-angle range because of the limitation of the scanning condition. Under these circumstances, conventional analytical algorithms, such as filtered back-projection (FBP), do not work because the projection data are incomplete. The regularization method has proven to be effective for tomographic reconstruction from under-sampled measurements. To deal with the limited-angle CT reconstruction problem, the regularization method is commonly used, but it is difficult to find a generic regularization term and choose the regularization parameters. Moreover, in some cases, the quality of reconstructed images is less than satisfactory. To solve this problem, we developed an alternating direction method of multipliers (ADMM)-based deep reconstruction (ADMMBDR) algorithm for limited-angle CT. First, we used the ADMM algorithm to decompose a regularization reconstruction model. Then, we utilized a deep convolutional neural network (CNN) to replace a part of the ADMM algorithm to reduce artifacts and avoid the choice of the regularization term and the regularization parameter. Furthermore, we conducted some numerical experiments to evaluate the feasibility and the advantages of the proposed algorithm. The results showed that the proposed algorithm had a better performance than several state-of-the-art algorithms; with respect to structure preservation and artifact reduction.

Restricted by the scanning environment and the radiation exposure of computed tomography (CT), the obtained projection data are sometimes incomplete, which results in an ill-posed problem, such as a limited-angle image reconstruction. In such circumstance, the commonly used analytic and iterative algorithms, such as filtered back-projection and simultaneous algebraic reconstruction technique (SART), will not work well. Nowadays, a popular iterative image reconstruction algorithm (\({\hbox {SART}}+{\hbox {TV}}\)) solving the optimization model based on the minimization of total variation (TV) of the image applies to the sparse-view reconstruction problem well; it is not effective on small limited-angle reconstruction problem, especially in aspect of suppressing slope artifacts when the limited-angle projection views are severely reduced. In this work, we develop a reconstruction model based on the Mumford–Shah-like model and wavelet tight frames that applies to limited-angle CT; and the corresponding iterative method is given. Numerical experiments and quantitative analysis demonstrate that our method outperforms SART and \({\hbox {SART}}+{\hbox {TV}}\) in suppressing slope artifacts when the limited-angle projection views are severely decreased.

Computed tomography (CT) has its irreplaceable function in nondestructive testing and medical diagnosis. In some practical CT imaging applications, the limited-angle scanning is common due to X-ray's potential harm to human and the limitation of the scanning conditions. Under these circumstances, analytic reconstruction algorithms, like filtered backprojection (FBP), will not obtain satisfactory results because of lacking the projection data. Iterative reconstruction (IR) methods that can incorporate prior knowledge have attracted attention in many fields, and wavelet frame-based regularization reconstruction algorithms have proven to be a useful means to reduce slope artifacts and noise for limited-angle CT. However, with the obtained projection data of the scanned object further reduces, the edge structures and the details of the reconstructed image worsen. For the sake of improving the quality of the reconstructed image from the limited-angle projection data, a guided image filtering (GIF)-based limited-angle CT reconstruction algorithm using wavelet frame was proposed. In each iteration of the proposed algorithm, the reconstructed result constrained by the wavelet frame was used as the guidance image to transfer the important features it contains to the reconstructed result of SART method by GIF. Furthermore, some simulated experiments and real data tests were conducted to evaluate the feasibility and validity of the proposed algorithm, and the qualitative and quantitative indexes indicated that the proposed algorithm was superior to other iterative reconstruction algorithms in artifacts reduction, noise suppression, and structure preservation.