A preconditioned landweber iteration scheme for the limited-angle image reconstruction

2021 ◽  
pp. 1-19
Author(s):  
Lei Shi ◽  
Gangrong Qu
Keyword(s):  
Image Reconstruction ◽  
Linear System ◽  
Condition Number ◽  
Small Angle ◽  
Practical Importance ◽  
Iteration Scheme ◽  
Normal Equation ◽  
Projection Data ◽  
Reconstruction Problem ◽  
Limited Angle

BACKGROUND: The limited-angle reconstruction problem is of both theoretical and practical importance. Due to the severe ill-posedness of the problem, it is very challenging to get a valid reconstructed result from the known small limited-angle projection data. The theoretical ill-posedness leads the normal equation A T Ax = A T b of the linear system derived by discretizing the Radon transform to be severely ill-posed, which is quantified as the large condition number of A T A. OBJECTIVE: To develop and test a new valid algorithm for improving the limited-angle image reconstruction with the known appropriately small angle range from [ 0 , π 3 ] ∼ [ 0 , π 2 ] . METHODS: We propose a reweighted method of improving the condition number of A T Ax = A T b and the corresponding preconditioned Landweber iteration scheme. The weight means multiplying A T Ax = A T b by a matrix related to A T A, and the weighting process is repeated multiple times. In the experiment, the condition number of the coefficient matrix in the reweighted linear system decreases monotonically to 1 as the weighting times approaches infinity. RESULTS: The numerical experiments showed that the proposed algorithm is significantly superior to other iterative algorithms (Landweber, Cimmino, NWL-a and AEDS) and can reconstruct a valid image from the known appropriately small angle range. CONCLUSIONS: The proposed algorithm is effective for the limited-angle reconstruction problem with the known appropriately small angle range.

Ultra-limited-angle CT image reconstruction algorithm based on reweighting and edge-preserving

2022 ◽  
pp. 1-13
Author(s):  
Lei Shi ◽  
Gangrong Qu ◽  
Yunsong Zhao
Keyword(s):  
Image Reconstruction ◽  
Condition Number ◽  
Reconstruction Algorithm ◽  
Projection Data ◽  
Ct Image ◽  
Reconstruction Algorithms ◽  
Edge Preserving ◽  
Image Reconstruction Algorithm ◽  
Ct Image Reconstruction ◽  
Limited Angle

BACKGROUND: Ultra-limited-angle image reconstruction problem with a limited-angle scanning range less than or equal to π 2 is severely ill-posed. Due to the considerably large condition number of a linear system for image reconstruction, it is extremely challenging to generate a valid reconstructed image by traditional iterative reconstruction algorithms. OBJECTIVE: To develop and test a valid ultra-limited-angle CT image reconstruction algorithm. METHODS: We propose a new optimized reconstruction model and Reweighted Alternating Edge-preserving Diffusion and Smoothing algorithm in which a reweighted method of improving the condition number is incorporated into the idea of AEDS image reconstruction algorithm. The AEDS algorithm utilizes the property of image sparsity to improve partially the results. In experiments, the different algorithms (the Pre-Landweber, AEDS algorithms and our algorithm) are used to reconstruct the Shepp-Logan phantom from the simulated projection data with noises and the flat object with a large ratio between length and width from the real projection data. PSNR and SSIM are used as the quantitative indices to evaluate quality of reconstructed images. RESULTS: Experiment results showed that for simulated projection data, our algorithm improves PSNR and SSIM from 22.46db to 39.38db and from 0.71 to 0.96, respectively. For real projection data, our algorithm yields the highest PSNR and SSIM of 30.89db and 0.88, which obtains a valid reconstructed result. CONCLUSIONS: Our algorithm successfully combines the merits of several image processing and reconstruction algorithms. Thus, our new algorithm outperforms significantly other two algorithms and is valid for ultra-limited-angle CT image reconstruction.

Anisotropic structure property based image reconstruction method for limited-angle computed tomography

2021 ◽  
pp. 1-24
Author(s):  
Changcheng Gong ◽  
Li Zeng
Keyword(s):  
Computed Tomography ◽  
Image Reconstruction ◽  
Projection Data ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Anisotropic Structure ◽  
Structure Property ◽  
Image Reconstruction Method ◽  
Ct Data ◽  
Limited Angle

Limited-angle computed tomography (CT) may appear in restricted CT scans. Since the available projection data is incomplete, the images reconstructed by filtered back-projection (FBP) or algebraic reconstruction technique (ART) often encounter shading artifacts. However, using the anisotropy property of the shading artifacts that coincide with the characteristic of limited-angle CT images can reduce the shading artifacts. Considering this concept, we combine the anisotropy property of the shading artifacts with the anisotropic structure property of an image to develop a new algorithm for image reconstruction. Specifically, we propose an image reconstruction method based on adaptive weighted anisotropic total variation (AwATV). This method, termed as AwATV method for short, is designed to preserve image structures and then remove the shading artifacts. It characterizes both of above properties. The anisotropy property of the shading artifacts accounts for reducing artifacts, and the anisotropic structure property of an image accounts for preserving structures. In order to evaluate the performance of AwATV, we use the simulation projection data of FORBILD head phantom and real CT data for image reconstruction. Experimental results show that AwATV can always reconstruct images with higher SSIM and PSNR, and smaller RMSE, which means that AwATV enables to reconstruct images with higher quality in term of artifact reduction and structure preservation.

An Evolutionary Algorithm for CT Image Reconstruction

2000 ◽  
Vol 12 (4) ◽  
pp. 466-473 ◽  
Author(s):  
Fathelalem F. Ali ◽  
◽  
Kazunori Matsuo ◽  
Zensho Nakao ◽  
Yen-Wei Chen ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Evolutionary Algorithm ◽  
Ct Images ◽  
Evolutionary Approach ◽  
Projection Data ◽  
Ct Image ◽  
Reconstruction Problem ◽  
Genetic Operators ◽  
Ct Image Reconstruction ◽  
Algebraic Reconstruction Techniques

Presented in this paper is an evolutionary approach to the problem of CT image reconstruction: an evolutionary algorithm (EA) is used to reconstruct CT images from a limited number of projection data, where conventional methods (e.g. Algebraic Reconstruction Techniques ART) solution tends to be unsatisfactory. We use traditional as well as adapted genetic operators in our evolutionary approach to the CT image reconstruction problem. The evolutionary algorithm yielded good results that challenge the conventional ART.

scholarly journals Weighting Algorithm and Relaxation Strategies of the Landweber Method for Image Reconstruction

2018 ◽  
Vol 2018 ◽  
pp. 1-19 ◽  
Author(s):  
Guanghui Han ◽  
Gangrong Qu ◽  
Qian Wang
Keyword(s):  
Image Reconstruction ◽  
Iterative Algorithms ◽  
Projection Data ◽  
High Quality ◽  
Ill Posed ◽  
High Resolution Images ◽  
Landweber Method ◽  
Weighting Methods ◽  
Limited Angle

The iterative approach is important for image reconstruction with ill-posed problem, especially for limited angle reconstruction. Most of iterative algorithms can be written in the general Landweber scheme. In this context, appropriate relaxation strategies and appropriately chosen weights are critical to yield reconstructed images of high quality. In this paper, based on reducing the condition number of matrix ATA, we find one method of weighting matrices for the general Landweber method to improve the reconstructed results. For high resolution images, the approximate iterative matrix is derived. And the new weighting matrices and corresponding relaxation strategies are proposed for the general Landweber method with large dimensional number. Numerical simulations show that the proposed weighting methods are effective in improving the quality of reconstructed image for both complete projection data and limited angle projection data.

A non-smooth and non-convex regularization method for limited-angle CT image reconstruction

2018 ◽  
Vol 26 (6) ◽  
pp. 799-820 ◽  
Author(s):  
Lingli Zhang ◽  
Li Zeng ◽  
Chengxiang Wang ◽  
Yumeng Guo
Keyword(s):  
Regularization Method ◽  
State Of The Art ◽  
Projection Data ◽  
Reconstruction Algorithms ◽  
Reconstruction Problem ◽  
Practical Applications ◽  
Splitting Technique ◽  
Ill Posed ◽  
Convex Regularization ◽  
Limited Angle

Abstract Restricted by the practical applications and radiation exposure of computed tomography (CT), the obtained projection data is usually incomplete, which may lead to a limited-angle reconstruction problem. Whereas reconstructing an object from limited-angle projection views is a challenging and ill-posed inverse problem. Fortunately, the regularization methods offer an effective way to deal with that. Recently, several researchers are absorbed in {\ell_{1}} regularization to address such problem, but it has some problems for suppressing the limited-angle slope artifacts around edges due to incomplete projection data. In this paper, in order to surmount the ill-posedness, a non-smooth and non-convex method that is based on {\ell_{0}} and {\ell_{1}} regularization is presented to better deal with the limited-angle problem. Firstly, the splitting technique is utilized to deal with the presented approach called LWPC-ST-IHT. Afterwards, some propositions and convergence analysis of the presented approach are established. Numerical implementations show that our approach is more capable of suppressing the slope artifacts compared with the classical and state of the art iterative reconstruction algorithms.

scholarly journals Wavelet tight frame and prior image-based image reconstruction from limited-angle projection data

2017 ◽  
Vol 11 (6) ◽  
pp. 917-948 ◽  
Author(s):  
Chengxiang Wang ◽  
◽  
Li Zeng ◽  
Yumeng Guo ◽  
Lingli Zhang ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Tight Frame ◽  
Projection Data ◽  
Limited Angle
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