南京航空航天大学学报（英文版）2020，Vol.37Issue(5)：787-795,9.
一种求解大型离散不适定问题的正则化随机Kaczmarz算法
A Regularized Randomized Kaczmarz Algorithm for Large Discrete Ill?Posed Problems
摘要
Abstract
Tikhonov regularization is a powerful tool for solving linear discrete ill?posed problems. However,effective methods for dealing with large?scale ill?posed problems are still lacking. The Kaczmarz method is an effective iterative projection algorithm for solving large linear equations due to its simplicity. We propose a regularized randomized extended Kaczmarz (RREK)algorithm for solving large discrete ill?posed problems via combining the Tikhonov regularization and the randomized Kaczmarz method. The convergence of the algorithm is proved. Numerical experiments illustrate that the proposed algorithm has higher accuracy and better image restoration quality compared with the existing randomized extended Kaczmarz(REK)method.关键词
不适定问题/Tikhonov正则化/随机扩展Kaczmarz算法/图像恢复Key words
ill⁃posed problem/Tikhonov regularization/randomized extended Kaczmarz(REK)algorithm/imagerestoration分类
数理科学引用本文复制引用
刘凤鸣,王正盛,杨思雨,徐贵力..一种求解大型离散不适定问题的正则化随机Kaczmarz算法[J].南京航空航天大学学报（英文版）,2020,37(5):787-795,9.基金项目
This work was supported by the Na?tional Natural Science Foundations of China(Nos.11571171,62073161,and 61473148). （Nos.11571171,62073161,and 61473148）
