基于Tikhonov正则化的扩展Kaczmarz算法  

Extended Kaczmarz algorithm based on Tikhonov regularization

作　　者：高蒙 张建军[1] GAO Meng;ZHANG Jianjun(College of Sciences,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2018年第4期879-890,共12页Communication on Applied Mathematics and Computation

摘　　要：为了更加有效地处理不适定问题,在扩展Kaczmarz算法的思想基础上,提出一种基于Tikhonov正则化的最大残差控制的扩展Kaczmarz算法并证明其收敛性.利用sheep-logan头部图像等进行图像重建实验.数値结果表明,该算法和最大残差控制的扩展Kaczmarz算法(MREK算法)相比,误差更小,图像质量更优.In order to deal with ill-posed problems more effectively,one algo-rithm named the maximum-residual extended Kaczmarz algorithm based on the Tikhonov regularization is proposed and its convergence is proved.Image recon-struction experiments are conducted using images such as the sheep-logan head image,and numerical results show that this algorithm produces a high-quality image with a smaller error,compared with the extended Kaczmarz algorithm.

关 键 词：Kaczmarz算法 TIKHONOV正则化 最大残差控制 

分 类 号：O241.6[理学—计算数学] O176.3[理学—数学]