Stable Recovery of Sparse Signals and an Oracle Inequality

被引：115

作者：

Cai, Tony Tony ^{[1
]}

Wang, Lie ^{[2
]}

Xu, Guangwu ^{[3
]}

机构：

[1] Univ Penn, Wharton Sch, Dept Stat, Philadelphia, PA 19104 USA

[2] MIT, Dept Math, Cambridge, MA 02139 USA

[3] Univ Wisconsin, Dept Elect Engn & Comp Sci, Milwaukee, WI 53211 USA

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2010年 / 56卷 / 07期

关键词：

l(1) minimization; compressed sensing; mutual incoherence; oracle inequality; sparse recovery; RESTRICTED ISOMETRY PROPERTY; OVERCOMPLETE REPRESENTATIONS;

D O I：

10.1109/TIT.2010.2048506

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This article considers sparse signal recovery in the presence of noise. A mutual incoherence condition which was previously used for exact recovery in the noiseless case is shown to be sufficient for stable recovery in the noisy case. Furthermore, the condition is proved to be sharp. A specific counterexample is given. In addition, an oracle inequality is derived under the mutual incoherence condition in the case of Gaussian noise.

引用

页码：3516 / 3522

页数：7

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