Restricted p-isometry properties of nonconvex block-sparse compressed sensing

被引：44

作者：

Wang, Yao ^{[1
]}

Wang, Jianjun ^{[2
]}

Xu, Zongben ^{[1
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Peoples R China

[2] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

SIGNAL PROCESSING | 2014年 / 104卷

关键词：

Compressed sensing; Block-sparse signal recovery; Mixed l(2)/l(p)-minimization; Restricted p-isometry properties; Gaussian measurements; SIGNALS; RECOVERY; RECONSTRUCTION;

D O I：

10.1016/j.sigpro.2014.03.040

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：

In this paper, by generalizing the notion of restricted p-isometry constant (0 < p <= 1) defined by Chartrand and Staneva [1] to the setting of block-sparse signal recovery, we establish a general restricted p-isometry property (p-RIP) condition for recovery of (nearly) block-sparse signals via mixed l(2)/l(p)-minimization. Moreover, we derive a lower bound on the necessary number of Gaussian measurements for the p-RIP condition to hold with high probability, which shows clearly that fewer measurements with smaller p are needed for exact recovery of block-sparse signals via mixed l(2)/l(p)-minimization than when p=1. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：188 / 196

页数：9

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