CONVERGENCE OF THE LINEARIZED BREGMAN ITERATION FOR l1-NORM MINIMIZATION

被引：130

作者：

Cai, Jian-Feng ^{[1
]}

Osher, Stanley ^{[2
]}

Shen, Zuowei ^{[3
]}

机构：

[1] Natl Univ Singapore, Temasek Labs, Singapore 117543, Singapore

[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[3] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

来源：

MATHEMATICS OF COMPUTATION | 2009年 / 78卷 / 268期

关键词：

ROBUST UNCERTAINTY PRINCIPLES; THRESHOLDING ALGORITHM; SIGNAL RECONSTRUCTION; INVERSE PROBLEMS; RECOVERY;

D O I：

10.1090/S0025-5718-09-02242-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

One of the key steps in compressed sensing is to solve the basis pursuit problem min(u is an element of Rn){parallel to u parallel to(1) : Au = f}. Bregman iteration was very successfully used to solve this problem in [40]. Also, a simple and fast iterative algorithm based on linearized Bregman iteration was proposed in [40], which is described in detail with numerical simulations in [35]. A convergence analysis of the smoothed version of this algorithm was given in [11]. The purpose of this paper is to prove that the linearized Bregman iteration proposed in [40] for the basis pursuit problem indeed converges.

引用

页码：2127 / 2136

页数：10

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