Hanming Zhang

Edge guided image reconstruction in linear scan CT by weighted alternating direction TV minimization.

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.

Constrained Total Generalized p-Variation Minimization for Few-View X-Ray Computed Tomography Image Reconstruction

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.

High performance parallel backprojection on multi-GPU

The speed of image reconstruction is an important indicator of the three-dimensional Computed Tomography (CT) imaging systems. GPU has become a focus of the research in CT reconstruction due to its characteristic of parallel computing. In this paper, the acceleration of backprojection, which is the most time consuming step of reconstruction, was implemented on multi-GPU hardware and OpenCL platform. The optimization techniques of parallelization strategy and memory management were explored and studied. The experimental results showed that the method obtained a considerable speedup, and the calculation times of total backprojection using 2 GPUs that were 1.67 times faster than using a single GPU. The method may be taken as the useful reference for researchers working on GPU applications and high-performance applications.

Computed Tomography Sinogram Inpainting With Compound Prior Modelling Both Sinogram and Image Sparsity

The presence of metal objects remains a challenge in x-ray computed tomography (CT) imaging. Sinograms passing through metals, called metal trace, usually provide uncorrected information and are considered missing in CT image reconstruction. The sparse prior of an image in some appropriate transform domains, defined implicit sparsity, is often used in sinogram inpainting methods for metal trace recovery. However, conventional inpainting methods only employ the implicit sparsity of a sinogram and often result in several artifacts in the reconstructed images. In this paper, we propose a sinogram inpainting model with implicit sparsity exploitation for both sinogram and image. A newly added regularization term, which minimizes the sparse representation of image objects, is utilized to reduce unwanted artifacts and preserve fine structures. To solve the proposed model, we then present an efficient iterative algorithm based on the Chambolle-Pock optimization approach. The results for both digital phantom and actual CT data indicate that the new inpainting method exhibits reasonable performance and outperforms the conventional methods when applied to metal artifact reduction problems.

Efficient and robust 3D CT image reconstruction based on total generalized variation regularization using the alternating direction method.

Iterative reconstruction algorithms for computed tomography (CT) through total variation regularization based on piecewise constant assumption can produce accurate, robust, and stable results. Nonetheless, this approach is often subject to staircase artefacts and the loss of fine details. To overcome these shortcomings, we introduce a family of novel image regularization penalties called total generalized variation (TGV) for the effective production of high-quality images from incomplete or noisy projection data for 3D reconstruction. We propose a new, fast alternating direction minimization algorithm to solve CT image reconstruction problems through TGV regularization. Based on the theory of sparse-view image reconstruction and the framework of augmented Lagrange function method, the TGV regularization term has been introduced in the computed tomography and is transformed into three independent variables of the optimization problem by introducing auxiliary variables. This new algorithm applies a local linearization and proximity technique to make the FFT-based calculation of the analytical solutions in the frequency domain feasible, thereby significantly reducing the complexity of the algorithm. Experiments with various 3D datasets corresponding to incomplete projection data demonstrate the advantage of our proposed algorithm in terms of preserving fine details and overcoming the staircase effect. The computation cost also suggests that the proposed algorithm is applicable to and is effective for CBCT imaging. Theoretical and technical optimization should be investigated carefully in terms of both computation efficiency and high resolution of this algorithm in application-oriented research.

System matrix analysis for sparse-view iterative image reconstruction in X-ray CT

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.

Distributed reconstruction via alternating direction method.

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.

Distributed CT image reconstruction algorithm based on the alternating direction method

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 inexact 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 accelerate 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.

3D alternating direction TV-based cone-beam CT reconstruction with efficient GPU implementation.

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 of 256 × 256 × 256 and 36 projections of the size of 512 × 512.

A two-step filtering-based iterative image reconstruction method for interior tomography

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.