Stable Recovery of Low Rank Matrices From Nuclear Norm Minimization

作     者：Hui-min WANG Song LI 

作者机构：Department of Mathematics Shaoxing University Department of Mathematics Zhejiang University 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2015年第31卷第1期

页      面：247-260页

核心收录：

学科分类：080802[工学-电力系统及其自动化] 0808[工学-电气工程] 07[理学] 08[工学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(No.11171299) 

主　　题：restricted isometry constants nuclear norm minimization low rank matrices 

摘      要：Low rank matrix recovery is a new topic drawing the attention of many researchers which addresses the problem of recovering an unknown low rank matrix from few linear measurements. The matrix Dantzig selector and the matrix Lasso are two important algorithms based on nuclear norm minimization. In this paper, we first prove some decay properties of restricted isometry constants, then we discuss the recovery errors of these two algorithms and give a new bound of restricted isometry constant to guarantee stable recovery, which improves the results of [11].