The Linearized Bregman Method via Split Feasibility Problems: Analysis and Generalizations

被引：68

作者：

Lorenz, Dirk A. ^{[1
]}

Schoepfer, Frank ^{[2
]}

Wenger, Stephan ^{[3
]}

机构：

[1] TU Braunschweig, Inst Anal & Algebra, D-38092 Braunschweig, Germany

[2] Carl von Ossietzky Univ Oldenburg, Inst Math, D-26111 Oldenburg, Germany

[3] TU Braunschweig, Inst Comp Graph, D-38092 Braunschweig, Germany

来源：

SIAM JOURNAL ON IMAGING SCIENCES | 2014年 / 7卷 / 02期

关键词：

linearized Bregman method; split feasibility problems; Bregman projections; sparse solutions; ITERATIVE ALGORITHMS; EXACT REGULARIZATION; PROJECTION; RECONSTRUCTION; CONVERGENCE; SETS;

D O I：

10.1137/130936269

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The linearized Bregman method is a method to calculate sparse solutions to systems of linear equations. We formulate this problem as a split feasibility problem, propose an algorithmic framework based on Bregman projections, and prove a general convergence result for this framework. Convergence of the linearized Bregman method will be obtained as a special case. Our approach also allows for several generalizations such as other objective functions, incremental iterations, incorporation of non-Gaussian noise models, and box constraints.

引用

页码：1237 / 1262

页数：26

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