On the Constrained Minimal Singular Values for Sparse Signal Recovery

被引：9

作者：

Zhang, Hui ^{[1
]}

Cheng, Lizhi ^{[1
]}

机构：

[1] Natl Univ Def Technol, Dept Math & Syst Sci, Coll Sci, Changsha 410073, Hunan, Peoples R China

来源：

IEEE SIGNAL PROCESSING LETTERS | 2012年 / 19卷 / 08期

基金：

美国国家科学基金会;

关键词：

l(1)-constrained minimal singular value; sparse recovery; structured random matrices; width of l(1)-truncated set; CONSTRUCTIONS;

D O I：

10.1109/LSP.2012.2203802

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

The l(1)-constrained minimal singular value (l(1) - CMSV) of the sensing matrix for sparse signal recovery is investigated in this letter. By exploiting certain geometrical properties of the (l(1) - CMSV) we derive new sufficient conditions for the recovery of both exactly and approximately sparse signals. Moreover, we demonstrate that a class of structured random matrices, including the Fourier random matrices and the Hadamard random matrices, can satisfy these sufficient conditions by showing their l(1) - CMSV are bounded away from zero with high probability, as long as the number of measurements is reasonablely large.

引用

页码：499 / 502

页数：4

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