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BACKGROUND: Image reconstruction for realistic medical images under incomplete observation is still one of the core tasks for computed tomography (CT). However, the stair-case artifacts of Total variation (TV) based ones have restricted the usage of the reconstructed images. OBJECTIVE: This work aims to propose and test an accurate and efficient algorithm to improve reconstruction quality under the idea of synergy between local and nonlocal regularizations. METHODS: The total variation combining the nonlocal means filtration is proposed and the alternating direction method of multipliers is utilized to develop an efficient algorithm. The first order approximation of linear expansion at intermediate point is applied to overcome the computation of the huge CT system matrix. RESULTS: The proposed method improves root mean squared error by 25.6% compared to the recent block-matching sparsity regularization (BMSR) on simulation dataset of 19 views. The structure similarities of image of the new method is higher than 0.95, while that of BMSR is about 0.92. Moreover, on real rabbit dataset of 20 views, the peak signal-to-noise ratio (PSNR) of the new method is 36.84, while using other methods PSNR are lower than 35.81. CONCLUSIONS: The proposed method shows advantages on noise suppression and detail preservations over the competing algorithms used in CT image reconstruction.

Spectral computed tomography (CT) based on the photon-counting detection system has the capability to produce energy-discriminative attenuation maps of objects with a single scan. However, the insufficiency of photons collected into the narrow energy bins results in high quantum noise levels causing low image quality. This work aims to improve spectral CT image quality by developing a novel regularization based on framelet tensor prior.First, similar patches are extracted from highly correlated interchannel images in spectral and spatial domains, and stacked to form a third-order tensor after vectorization along the energy channels. Second, the framelet tensor nuclear norm (FTNN) is introduced and applied to construct the regularization to exploit the sparsity embedded in nonlocal similarity of spectral images, and thus the reconstruction problem is modeled as a constrained optimization. Third, an iterative algorithm is proposed by utilizing the alternating direction method of multipliers framework in which efficient solvers are developed for each subproblem.Both numerical simulations and real data verifications were performed to evaluate and validate the proposed FTNN-based method. Compared to the analytic, TV-based, and the state-of-the-art tensor-based methods, the proposed method achieves higher numerical accuracy on both reconstructed CT images and decomposed material maps in the mouse data indicating the capability in noise suppression and detail preservation of the proposed method.A framelet tensor sparsity-based iterative algorithm is proposed for spectral reconstruction. The qualitative and quantitative comparisons show a promising improvement of image quality, indicating its promising potential in spectral CT imaging.

Total variation (TV) regularization-based iterative reconstruction algorithms have an impressive potential to solve limited-angle computed tomography with insufficient sampling projections. The analysis of exact reconstruction sampling conditions for a TV-minimization reconstruction model can determine the minimum number of scanning angle and minimize the scanning range. However, the large-scale matrix operations caused by increased testing phantom size are the computation bottleneck in determining the exact reconstruction sampling conditions in practice. When the size of the testing phantom increases to a certain scale, it is very difficult to analyze quantitatively the exact reconstruction sampling condition using existing methods. In this paper, we propose a fast and efficient algorithm to determine the exact reconstruction sampling condition for large phantoms. Specifically, the sampling condition of a TV minimization model is modeled as a convex optimization problem, which is derived from the sufficient and necessary condition of solution uniqueness for the L1 minimization model. An effective alternating direction minimization algorithm is developed to optimize the objective function by alternatively solving two sub-problems split from the convex problem. The Cholesky decomposition method is used in solving the first sub-problem to reduce computational complexity. Experimental results show that the proposed method can efficiently solve the verification problem of the accurate reconstruction sampling condition. Furthermore, we obtain the lower bounds of scanning angle range for the exact reconstruction of a specific phantom with the larger size.

Purpose Dual-energy CT (DECT) has been increasingly used in imaging applications because of its capability for material differentiation. However, material decomposition suffers from magnified noise from two CT images of independent scans, leading to severe degradation of image quality. Existing algorithms exhibit suboptimal decomposition performance because they fail to fully depict the mapping relationship between DECT images and basis materials under noisy conditions. Convolutional neural network exhibits great promise in the modeling of data coupling and has recently become an important technique in medical imaging application. Inspired by its impressive potential, we developed a new Butterfly network to perform the image domain dual material decomposition. Methods The Butterfly network is derived from the model of image domain DECT decomposition by exploring the geometric relationship between the mapping functions of the data model and network components. The network is designed as the double-entry double-out crossover architecture based on the decomposition formulation. It enters a pair of dual-energy images as inputs and defines the ground true decomposed images as each label. The crossover architecture, which plays an important role in material decomposition, is designed to implement the information exchange between the two material generation pathways in the network. The proposed network is further applied on the digital phantom and clinical data to evaluate its performance. Results The qualitative and quantitative evaluations of the material decomposition of digital phantoms and clinical data indicate that the proposed network outperforms its counterparts. For the digital phantom, the proposed network reduces the standard deviation (SD) of noise in tissue, bone, and mixture regions by an average of 95.75% and 86.58% compared with the direct matrix inversion and the conventional iterative method, respectively. The line profiles and image biases of the decomposition results of digital phantom indicate that the proposed network provides the decomposition results closest to the ground truth. The proposed network reduces the SD of the noise in decomposed images of clinical head data by over 90% and 80% compared with the direct matrix inversion and conventional iterative method, respectively. As the modulation transfer function decreases to 50%, the proposed network increases the spatial resolution by average factors of 1.34 and 1.17 compared with the direct matrix inversion and conventional iterative methods, respectively. The proposed network is further applied to the clinical abdomen data. Among the three methods, the proposed method received the highest score from six radiologists in the visual inspection of noise suppression in the clinical data. Conclusions We develop a model-based Butterfly network to perform image domain material decomposition for DECT. The decomposition results of digital phantom validate its capability of decomposing two basis materials from DECT images. The proposed approach also leads to higher decomposition quality in noise suppression on clinical datasets as compared with those using conventional schemes.

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.

Compared with the conventional 1×1 acquisition mode of projection in computed tomography (CT) image reconstruction, the 2×2 acquisition mode improves the collection efficiency of the projection and reduces the x-ray exposure time. However, the collected projection based on the 2×2 acquisition mode has low resolution (LR) and the reconstructed image quality is poor, thus limiting the use of this mode in CT imaging systems. In this study, a novel sinogram-super-resolution (SR) generative adversarial network model is proposed to obtain high-resolution (HR) sinograms from LR sinograms, thereby improving the reconstruction image quality under the 2×2 acquisition mode. The proposed generator is based on the residual network for LR sinogram feature extraction and SR sinogram generation. A relativistic discriminator is designed to render the network capable of obtaining more realistic SR sinograms. Moreover, we combine the cycle consistency loss, sinogram domain loss, and reconstruction image domain loss in the total loss function to supervise SR sinogram generation. Then, a trained model can be obtained by inputting the paired LR/HR sinograms into the network. Finally, the classic filtered-back-projection reconstruction algorithm is used for CT image reconstruction based on the generated SR sinogram. The qualitative and quantitative results of evaluations on digital and real data illustrate that the proposed model not only obtains clean SR sinograms from noisy LR sinograms but also outperforms its counterparts.

Since the excessive radiation dose may induce potential body lesion, the low-dose computed tomography (LDCT) is widely applied for clinical diagnosis and treatment. However, the dose reduction will inevitably cause severe noise and degrade image quality. Most state-of-the-art methods utilize a pre-determined regularizer to account for the prior images, which may be insufficient for the most images acquired in the clinical practice. This study proposed and investigated a joint regularization method combining a data-driven tight frame and total variation (DDTF-TV) to solve this problem. Unlike the existing methods that designed pre-determined sparse transform for image domain, data-driven regularizer introduced a learning strategy to adaptively and iteratively update the framelets of DDTF, which can preferably recover the detailed image structures. The other regularizer, TV term can reconstruct strong edges and suppress noise. The joint term, DDTF-TV, collaboratively affect detail preservation and noise suppression. The proposed new model was efficiently solved by alternating the direction method of the multipliers. Qualitative and quantitative evaluations were carried out in simulation and real data experiments to demonstrate superiority of the proposed DDTF-TV method. Both visual inspection and numerical accuracy analysis show the potential of the proposed method for improving image quality of the LDCT.

Most scanning schemes of multi-energy computed tomography (MECT) require multiple sets of full-scan measurements under different x-ray spectra, which limits the application of MECT with incomplete scan. To handle this problem, a flexible MECT scanning strategy is proposed in this paper, which divides one half scan into three curves. Also, a novel MECT reconstruction algorithm is developed to relax the requirement of data acquisition of MECT. For MECT, gradient images of CT images at different energies ideally share the same position of zero-value set (Pos-OS) for the same object. Based on this observation, the characteristics of limited-angle artifacts is first explored, and it is found that the limited-angle artifacts in the image domain are closely related to the angle trajectory of the scan. Inspired by this discovery, the Pos-OS of the gradient image from the fusion CT image is extracted, and it is incorporated as prior knowledge into the TV minimization model in the form of equality constraints. The alternating direction method is exploited to solve the improved optimization model iteratively. Based on this, the proposed algorithm is derived to eliminate the limited angle artifacts in the image domain.The experimental results show that the proposed method achieves higher reconstruction quality under the designed scanning configuration than other methods in the literature.

The widespread application of X-ray computed tomography (CT) in clinical diagnosis has led to increasing public concern regarding excessive radiation dose administered to patients. However, reducing the radiation dose will inevitably cause server noise and affect radiologists’ judgment and confidence. Hence, progressive low-dose CT (LDCT) image reconstruction methods must be developed to improve image quality. Over the past two years, deep learning-based approaches have shown impressive performance in noise reduction for LDCT images. Most existing deep learning-based approaches usually require the paired training dataset which the LDCT images correspond to the normal-dose CT (NDCT) images one-to-one, but the acquisition of well-paired datasets requires multiple scans, resulting the increase of radiation dose. Therefore, well-paired datasets are not readily available. To resolve this problem, this paper proposes an unpaired LDCT image denoising network based on cycle generative adversarial networks (CycleGAN) with prior image information which does not require a one-to-one training dataset. In this method, cyclic loss, an important trick in unpaired image-to-image translation, promises to map the distribution from LDCT to NDCT by using unpaired training data. Furthermore, to guarantee the accurate correspondence of the image content between the output and NDCT, the prior information obtained from the result preprocessed using the LDCT image is integrated into the network to supervise the generation of content. Given the map of distribution through the cyclic loss and the supervision of content through the prior image loss, our proposed method can not only reduce the image noise but also retain critical information. Real-data experiments were carried out to test the performance of the proposed method. The peak signal-to-noise ratio (PSNR) improves by more than 3 dB, and the structural similarity (SSIM) increases when compared with the original CycleGAN without prior information. The real LDCT data experiment demonstrates the superiority of the proposed method according to both visual inspection and quantitative evaluation.

The optimization-based method that utilizes the additional sparse prior of region-of-interest (ROI) image, such as total variation, has been the subject of considerable research in problems of interior tomography reconstruction. One challenge for optimization-based iterative ROI image reconstruction is to build the relationship between ROI image and truncated projection data. When the reconstruction support region is smaller than the original object, an unsuitable representation of data fidelity may lead to bright truncation artifacts in the boundary region of field of view. In this work, we aim to develop an iterative reconstruction method to suppress the truncation artifacts and improve the image quality for direct ROI image reconstruction. A novel reconstruction approach is proposed based on an optimization problem involving a two-step filtering-based data fidelity. Data filtering is achieved in two steps: the first takes the derivative of projection data; in the second step, Hilbert filtering is applied in the differentiated data. Numerical simulations and real data reconstructions have been conducted to validate the new reconstruction method. Both qualitative and quantitative results indicate that, as theoretically expected, the proposed method brings reasonable performance in suppressing truncation artifacts and preserving detailed features. The presented local reconstruction method based on the two-step filtering strategy provides a simple and efficient approach for the iterative reconstruction from truncated projections.

With the development of compressive sensing theory, image reconstruction from few-view projections has been paid considerable research attention in the field of computed tomography (CT). Total variation (TV)-based CT image reconstruction has been shown experimentally to be capable of producing accurate reconstructions from sparse-view data. Motivated by the need of solving few-view reconstruction problem with large scale data, a general block distribution reconstruction algorithm based on TV minimization and the alternating direction method (ADM) has been developed in this study. By utilizing the inex- act ADM, which involves linearization and proximal point techniques, the algorithm is relatively simple and hence convenient for the derivation and distributed implementation. And because the data as well as the computation are distributed to individual nodes, an outstanding acceleration factor is achieved. Experimental results demonstrate that the proposed method can accel- erate the alternating direction total variation minimization (ADTVM) algorithm with nearly no loss of accuracy, which means compared with ADTVM, the proposed algorithm has a better accuracy with same running time.

In medical imaging many conventional regularization methods, such as total variation or total generalized variation, impose strong prior assumptions which can only account for very limited classes of images. A more reasonable sparse representation frame for images is still badly needed. Visually understandable images contain meaningful patterns, and combinations or collections of these patterns can be utilized to form some sparse and redundant representations which promise to facilitate image reconstructions. In this work, we propose and study block matching sparsity regularization (BMSR) and devise an optimization program using BMSR for computed tomography (CT) image reconstruction for an incomplete projection set. The program is built as a constrained optimization, minimizing the L1-norm of the coefficients of the image in the transformed domain subject to data observation and positivity of the image itself. To solve the program efficiently, a practical method based on the proximal point algorithm is developed and analyzed. In order to accelerate the convergence rate, a practical strategy for tuning the BMSR parameter is proposed and applied. The experimental results for various settings, including real CT scanning, have verified the proposed reconstruction method showing promising capabilities over conventional regularization.

Purpose Low-dose computed tomography (CT) imaging has been widely explored because it can reduce the radiation risk to human bodies. This presents challenges in improving the image quality because low radiation dose with reduced tube current and pulse duration introduces severe noise. In this study, we investigate block-matching sparsity regularization (BMSR) and devise an optimization problem for low-dose image reconstruction. Method The objective function of the program is built by combining the sparse coding of BMSR and analysis error, which is subject to physical data measurement. A practical reconstruction algorithm using hard thresholding and projection-onto-convex-set for fast and stable performance is developed. An efficient scheme for the choices of regularization parameters is analyzed and designed. Results In the experiments, the proposed method is compared with a conventional edge preservation method and adaptive dictionary-based iterative reconstruction. Experiments with clinical images and real CT data indicate that the obtained results show promising capabilities in noise suppression and edge preservation compared with the competing methods. Conclusions A block-matching-based reconstruction method for low-dose CT is proposed. Improvements in image quality are verified by quantitative metrics and visual comparisons, thereby indicating the potential of the proposed method for real-life applications.

Iterative reconstruction algorithms for computed tomography (CT) through total variation (TV) regularization can provide accurate and stable reconstruction results. TV minimization is the L1-norm of gradient-magnitude images and can be regarded as a convex relaxation method to replace the L0 norm. In this study, a fast and efficient algorithm, which is named a weighted difference of L1 and L2 (L1 - αL2) on the gradient minimization, was proposed and investigated. The new algorithm provides a better description of sparsity for the optimization-based algorithms than TV minimization algorithms. The alternating direction method is an efficient method to solve the proposed model, which is utilized in this study. Both simulations and real CT projections were tested to verify the performances of the proposed algorithm. In the simulation experiments, the reconstructions from the proposed method provided better image quality than TV minimization algorithms with only 7 views in 180 degrees, which is also computationally faster. Meanwhile, the new algorithm enabled to achieve the final solution with less iteration numbers.

Nowadays, diversities of task-specific applications for computed tomography (CT) have already proposed multiple challenges for algorithm design of image reconstructions. Consequently, efficient algorithm design tool is necessary to be established. A fast and efficient algorithm design framework for CT image reconstruction, which is based on alternating direction method (ADM) with ordered subsets (OS), is proposed, termed as OS-ADM. The general ideas of ADM and OS have been abstractly introduced and then they are combined for solving convex optimizations in CT image reconstruction. Standard procedures are concluded for algorithm design which contain 1) model mapping, 2) sub-problem dividing and 3) solving, 4) OS level setting and 5) algorithm evaluation. Typical reconstruction problems are modeled as convex optimizations, including (non-negative) least-square, constrained L1 minimization, constrained total variation (TV) minimization and TV minimizations with different data fidelity terms. Efficient working algorithms for these problems are derived with detailed derivations by the proposed framework. In addition, both simulations and real CT projections are tested to verify the performances of two TV-based algorithms. Experimental investigations indicate that these algorithms are of the state-of-the-art performances. The algorithm instances show that the proposed OS-ADM framework is promising for practical applications.

Linear scan computed tomography (CT) is a promising imaging configuration with high scanning efficiency while the data set is under-sampled and angularly limited for which high quality image reconstruction is challenging. In this work, an edge guided total variation minimization reconstruction (EGTVM) algorithm is developed in dealing with this problem. The proposed method is modeled on the combination of total variation (TV) regularization and iterative edge detection strategy. In the proposed method, the edge weights of intermediate reconstructions are incorporated into the TV objective function. The optimization is efficiently solved by applying alternating direction method of multipliers. A prudential and conservative edge detection strategy proposed in this paper can obtain the true edges while restricting the errors within an acceptable degree. Based on the comparison on both simulation studies and real CT data set reconstructions, EGTVM provides comparable or even better quality compared to the non-edge guided reconstruction and adaptive steepest descent-projection onto convex sets method. With the utilization of weighted alternating direction TV minimization and edge detection, EGTVM achieves fast and robust convergence and reconstructs high quality image when applied in linear scan CT with under-sampled data set.

Region-of-interest (ROI) and interior reconstructions for computed tomography (CT) have drawn much attention and can be of practical value for potential applications in reducing radiation dose and hardware cost. The conventional wisdom is that the exact reconstruction of an interior ROI is very difficult to be obtained by only using data associated with lines through the ROI. In this study, we propose and investigate optimization-based methods for ROI and interior reconstructions based on total variation (TV) and data derivative. Objective functions are built by the image TV term plus the data finite difference term. Different data terms in the forms of L1-norm, L2-norm, and Kullback-Leibler divergence are incorporated and investigated in the optimizations. Efficient algorithms are developed using the proximal alternating direction method of multipliers (ADMM) for each program. All sub-problems of ADMM are solved by using closed-form solutions with high efficiency. The customized optimizations and algorithms based on the TV and derivative-based data terms can serve as a powerful tool for interior reconstructions. Simulations and real-data experiments indicate that the proposed methods can be of practical value for CT imaging applications.

Total generalized variation (TGV)-based computed tomography (CT) image reconstruction, which utilizes high-order image derivatives, is superior to total variation-based methods in terms of the preservation of edge information and the suppression of unfavorable staircase effects. However, conventional TGV regularization employs l1-based form, which is not the most direct method for maximizing sparsity prior. In this study, we propose a total generalized p-variation (TGpV) regularization model to improve the sparsity exploitation of TGV and offer efficient solutions to few-view CT image reconstruction problems. To solve the nonconvex optimization problem of the TGpV minimization model, we then present an efficient iterative algorithm based on the alternating minimization of augmented Lagrangian function. All of the resulting subproblems decoupled by variable splitting admit explicit solutions by applying alternating minimization method and generalized p-shrinkage mapping. In addition, approximate solutions that can be easily performed and quickly calculated through fast Fourier transform are derived using the proximal point method to reduce the cost of inner subproblems. The accuracy and efficiency of the simulated and real data are qualitatively and quantitatively evaluated to validate the efficiency and feasibility of the proposed method. Overall, the proposed method exhibits reasonable performance and outperforms the original TGV-based method when applied to few-view problems.

Total variation (TV)-based CT image reconstruction, employing the image gradient sparsity, has shown to be experimentally capable of reducing the X-ray sampling rate and removing the unwanted artifacts, yet may cause unfavorable over-smoothing and staircase effects by the piecewise constant assumption. In this paper, we present a total generalized p-variation (TGpV) regularization model to adaptively preserve the edge information while avoiding the staircase effect. The new model is solved by splitting variables with an efficient alternating minimization scheme. With the utilization of generalized p-shrinkage mappings and partial Fourier transform, all the subproblems have closed solutions. The proposed method shows excellent properties of edge preserving as well as the smoothness features by the consideration of high order derivatives. Experimental results indicate that the proposed method could avoid the mentioned effects and reconstruct more accurately than both the TV and TGV minimization algorithms when applied to a few-view problem.

Iterative image reconstruction (IIR) with sparsity-exploiting methods, such as total variation (TV) minimization, used for investigations in compressive sensing (CS) claim potentially large reductions in sampling requirements. Quantifying this claim for computed tomography (CT) is non-trivial, as both the singularity of undersampled reconstruction and the sufficient view number for sparse-view reconstruction are ill-defined. In this paper, the singular value decomposition method is used to study the condition number and singularity of the system matrix and the regularized matrix. An estimation method of the empirical lower bound is proposed, which is helpful for estimating the number of projection views required for exact reconstruction. Simulation studies show that the singularity of the system matrices for different projection views is effectively reduced by regularization. Computing the condition number of a regularized matrix is necessary to provide a reference for evaluating the singularity and recovery potential of reconstruction algorithms using regularization. The empirical lower bound is helpful for estimating the projections view number with a sparse reconstruction algorithm.

Sparse-view imaging is a promising scanning method which can reduce the radiation dose in X-ray computed tomography (CT). Reconstruction algorithm for sparse-view imaging system is of significant importance. The adoption of the spatial iterative algorithm for CT image reconstruction has a low operation efficiency and high computation requirement. A novel Fourier-based iterative reconstruction technique that utilizes nonuniform fast Fourier transform is presented in this study along with the advanced total variation (TV) regularization for sparse-view CT. Combined with the alternating direction method, the proposed approach shows excellent efficiency and rapid convergence property. Numerical simulations and real data experiments are performed on a parallel beam CT. Experimental results validate that the proposed method has higher computational efficiency and better reconstruction quality than the conventional algorithms, such as simultaneous algebraic reconstruction technique using TV method and the alternating direction total variation minimization approach, with the same time duration. The proposed method appears to have extensive applications in X-ray CT imaging.

An efficient iterative algorithm, based on recent work in non-convex optimization and generalized p-shrinkage mappings, is proposed for volume image reconstruction from circular cone-beam scans. Conventional total variation regularization makes use of L1 norm of gradient magnitude images (GMI). However, this paper utilizes a generalized penalty function, induced by p-shrinkage, of GMI which is proven to be a better measurement of its sparsity. The reconstruction model is formed using generalized total p-variation (TpV) minimization, which differs with the state of the art methods, with the constraint that the estimated projection data is within a specified tolerance of the available data and that the values of the volume image are non-negative. Theoretically, the proximal mapping for penalty functions induced by p-shrinkage has an exact and closed-form expression; thus, the constrained optimization can be stably and efficiently solved by the alternating direction minimization (ADM) scheme. Each sub-problem decoupled by variable splitting is minimized by explicit and easy-to-implement formulas developed by ADM. The proposed algorithm is efficiently implemented using a graphics processing unit and is referred to as "TpV-ADM." This method is robust and accurate even for very few view reconstruction datasets. Verifications and comparisons performed using various datasets (including ideal, noisy, and real projections) illustrate that the proposed method is effective and promising.

Iterative image reconstruction (IIR) with sparsity-exploiting methods, such as total variation (TV) minimization, claims potentially large reductions in sampling requirements. However, the computation complexity becomes a heavy burden, especially in 3D reconstruction situations. In order to improve the performance for iterative reconstruction, an efficient IIR algorithm for cone-beam computed tomography (CBCT) with GPU implementation has been proposed in this paper. In the first place, an algorithm based on alternating direction total variation using local linearization and proximity technique is proposed for CBCT reconstruction. The applied proximal technique avoids the horrible pseudoinverse computation of big matrix which makes the proposed algorithm applicable and efficient for CBCT imaging. The iteration for this algorithm is simple but convergent. The simulation and real CT data reconstruction results indicate that the proposed algorithm is both fast and accurate. The GPU implementation shows an excellent acceleration ratio of more than 100 compared with CPU computation without losing numerical accuracy. The runtime for the new 3D algorithm is about 6.8 seconds per loop with the image size of256×256×256and 36 projections of the size of512×512.

With the development of compressive sensing theory, image reconstruction from few-view projections has received considerable research attentions in the field of computed tomography (CT). Total-variation- (TV-) based CT image reconstruction has been shown to be experimentally capable of producing accurate reconstructions from sparse-view data. In this study, a distributed reconstruction algorithm based on TV minimization has been developed. This algorithm is very simple as it uses the alternating direction method. The proposed method can accelerate the alternating direction total variation minimization (ADTVM) algorithm without losing accuracy.