ALTERNATING DIRECTION METHOD OF MULTIPLIERS FOR LINEAR INVERSE PROBLEMS

被引：34

作者：

Jiao, Yuling ^{[1
]}

Jin, Qinian ^{[2
]}

Lu, Xiliang ^{[3
,4
]}

Wang, Weijie ^{[3
]}

机构：

[1] Zhongnan Univ Econ & Law, Sch Math & Stat, Wuhan 430063, Peoples R China

[2] Australian Natl Univ, Inst Math Sci, Canberra, ACT 2601, Australia

[3] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[4] Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Peoples R China

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2016年 / 54卷 / 04期

基金：

中国国家自然科学基金; 澳大利亚研究理事会;

关键词：

linear inverse problems; alternating direction method of multipliers; Bregman distance; convergence; regularization property; RACHFORD SPLITTING METHOD; REGULARIZATION; ALGORITHMS;

D O I：

10.1137/15M1029308

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we propose an iterative method using alternating direction method of multipliers (ADMM) strategy to solve linear inverse problems in Hilbert spaces with a general convex penalty term. When the data is given exactly, we give a convergence analysis of our ADMM algorithm without assuming the existence of a Lagrange multiplier. In case the data contains noise, we show that our method is a regularization method as long as it is terminated by a suitable stopping rule. Various numerical simulations are performed to test the efficiency of the method.

引用

页码：2114 / 2137

页数：24

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