The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proof...The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proofs are given.Thomas Strohmer and Roman Vershynin introduced a randomized version of the Kaczmarz method for consistent,and over-determined linear systems and proved whose rate does not depend on the number of equations in the systems in 2009.In this paper,we apply this method to computed tomography(CT)image reconstruction and compared images generated by the sequential Kaczmarz method and the randomized Kaczmarz method.Experiments demonstrates the feasibility of the randomized Kaczmarz algorithm in CT image reconstruction and its exponential curve convergence.展开更多
Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This ...Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is associated with many interesting challenges encoun- tered in the image restoration and image reconstruction fields. We developed a splitting primal-dual proximity algorithm to solve this problem. Furthermore, we propose a preconditioned method~ of which the iterative parameters are obtained without the need to know some particular operator norm in advance. Theoretical convergence theorems are presented. We then apply the proposed methods to solve a total variation regularization model, in which the L2 data error function is added to the L1 data error function. The main advantageous feature of this model is its capability to combine different loss functions. The numerical results obtained for computed tomography （CT） image recon- struction demonstrated the ability of the proposed algorithm to reconstruct an image with few and sparse projection views while maintaining the image quality.展开更多
基金National Natural Science Foundation of China(No.61171179,No.61171178)Natural Science Foundation of Shanxi Province(No.2010011002-1,No.2010011002-2and No.2012021011-2)
文摘The order of the projection in the algebraic reconstruction technique(ART)method has great influence on the rate of the convergence.Although many scholars have studied the order of the projection,few theoretical proofs are given.Thomas Strohmer and Roman Vershynin introduced a randomized version of the Kaczmarz method for consistent,and over-determined linear systems and proved whose rate does not depend on the number of equations in the systems in 2009.In this paper,we apply this method to computed tomography(CT)image reconstruction and compared images generated by the sequential Kaczmarz method and the randomized Kaczmarz method.Experiments demonstrates the feasibility of the randomized Kaczmarz algorithm in CT image reconstruction and its exponential curve convergence.
基金Supported by the NSFC(Grant Nos.11201216,11401293,11461046 and 11661056)the National Basic Research Program of China(Grant No.2013CB329404)the NSF of Jiangxi Province(Grant Nos.20151BAB211010and 20142BAB211016)
文摘Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is associated with many interesting challenges encoun- tered in the image restoration and image reconstruction fields. We developed a splitting primal-dual proximity algorithm to solve this problem. Furthermore, we propose a preconditioned method~ of which the iterative parameters are obtained without the need to know some particular operator norm in advance. Theoretical convergence theorems are presented. We then apply the proposed methods to solve a total variation regularization model, in which the L2 data error function is added to the L1 data error function. The main advantageous feature of this model is its capability to combine different loss functions. The numerical results obtained for computed tomography （CT） image recon- struction demonstrated the ability of the proposed algorithm to reconstruct an image with few and sparse projection views while maintaining the image quality.
