A new sufficient condition for sparse vector recovery via ℓ1 − ℓ2 local minimization-Reference-Cited by-同舟云学术

A new sufficient condition for sparse vector recovery via ℓ1 − ℓ2 local minimization

Published:2021-04-10 Issue:06 Volume:19 Page:1019-1031
ISSN:0219-5305
Container-title:Analysis and Applications
language:en
Short-container-title:Anal. Appl.

Author:

Bi Ning¹²,Tan Jun¹²,Tang Wai-Shing³

Affiliation:

1. School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China

2. Guangdong Province Key Laboratory of Computational Science, Sun Yat-Sen University, Guangzhou 510275, P. R. China

3. Department of Mathematics, National University of Singapore, Kent Ridge 119076, Republic of Singapore

Abstract

In this paper, we provide a necessary condition and a sufficient condition such that any [Formula: see text]-sparse vector [Formula: see text] can be recovered from [Formula: see text] via [Formula: see text] local minimization. Moreover, we further verify that the sufficient condition is naturally valid when the restricted isometry constant of the measurement matrix [Formula: see text] satisfies [Formula: see text]. Compared with the existing [Formula: see text] local recoverability condition [Formula: see text], this result shows that [Formula: see text] local recoverability contains more measurement matrices.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219530521500068

Reference26 articles.

1. Sharp RIP bound for sparse signal and low-rank matrix recovery

2. Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-Rank Matrices

3. The restricted isometry property and its implications for compressed sensing

4. Decoding by Linear Programming

5. Iteratively reweighted least squares minimization for sparse recovery

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