摘要
Tikhonov正则化是求解线性离散不适定问题的有力工具,然而,针对大规模问题的有效方法仍然缺乏。Kaczmarz方法由于其简单性,是求解大型线性方程组的有效迭代投影算法。因此,本文结合Tikhonov正则化和随机Kaczmarz方法,提出了一种求解大型离散不适定问题的正则化随机扩展Kaczmarz(Regularized randomized extended Kaczmarz,RREK)算法,同时证明了算法的收敛性。数值实验表明,与现有的随机扩展Kaczmarz(Randomized extended Kaczmarz,REK)方法相比,该算法具有更高的精度,图像恢复质量更优。
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.
作者
刘凤鸣
王正盛
杨思雨
徐贵力
LIU Fengming;WANG Zhengsheng;YANG Siyu;XU Guili(College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,P.R.China;College of Automation Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,P.R.China)
基金
supported by the National Natural Science Foundations of China(Nos.11571171,62073161,and 61473148)。