Sufficient Conditions on Stable Recovery of Sparse Signals With Partial Support Information

Author

Xiaohan Yu ; Seung Jun Baek

Author_Institution

Dept. of Comput. & Commun. Eng., Korea Univ., Seoul, South Korea

Volume

20

Issue

5

fYear

2013

fDate

May-13

Firstpage

539

Lastpage

542

Abstract

In this letter, we study signal reconstruction from compressed sensing measurements. We propose new sufficient conditions for stable recovery when partial support information is available. Weighted l₁-minimization is adopted to recover the original signal under three noise models. The proposed approach is to use Ozeki´s inequality and shifting inequality in order to bound the errors in the associated weighted l₁ -minimization. Our result offers generalized performance bounds on recovery capturing known support information. Improved sufficient conditions for recovery are derived based on our results, even for the cases where the accuracy of prior support information is arbitrarily low.

Keywords

minimisation; signal reconstruction; Ozeki inequality; compressed sensing measurements; generalized performance bounds; noise models; partial support information; shifting inequality; signal reconstruction; sparse signal stable recovery; weighted l₁-minimization; Compressed sensing; Estimation; Noise; Sensors; Sparse matrices; Standards; Vectors; Compressive sensing (CS); partial support information; weighted $ell_{1}$-minimization;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2013.2254712

Filename

6488730