DocumentCode
1517006
Title
Stable Recovery of Sparse Signals and an Oracle Inequality
Author
Cai, Tony Tony ; Wang, Lie ; Xu, Guangwu
Author_Institution
Dept. of Stat., Univ. of Pennsylvania, Philadelphia, PA, USA
Volume
56
Issue
7
fYear
2010
fDate
7/1/2010 12:00:00 AM
Firstpage
3516
Lastpage
3522
Abstract
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.
Keywords
Gaussian noise; signal processing; Gaussian noise; oracle inequality; sparse signal recovery; stable recovery; Compressed sensing; Dictionaries; Gaussian noise; Image reconstruction; Mathematics; Noise level; Signal processing; Sparse matrices; Statistics; Vectors; $ell _{1}$ minimization; compressed sensing; mutual incoherence; oracle inequality; sparse recovery;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.2010.2048506
Filename
5484999
Link To Document