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
收藏
页码：2114 / 2137
页数：24
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