High-order block RIP for nonconvex block-sparse compressed sensing-Reference-Cited by-同舟云学术

High-order block RIP for nonconvex block-sparse compressed sensing

Published:2024-04-24 Issue:0 Volume:0 Page:
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Huang Jianwen¹^ORCID,Liu Xinling²,Hou Jingyao³,Wang Jianjun⁴,Zhang Feng⁵,Jia Jinping⁶

Affiliation:

1. School of Mathematical Sciences , Chongqing Normal University , Chongqing 401331; and School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001 , P. R. China

2. College of Mathematics and Information , 56714 China West Normal University , Nanchong 637009 ; and Key Laboratory of Optimization Theory and Applications at China West Normal University of Sichuan Province , P. R. China

3. School of Mathematics and Information , 56714 China West Normal University , Nanchong 637009 , P. R. China

4. School of Mathematics and Statistics , [26463]Southwest University , Chongqing 400715; and School of Mathematics and Information Science, North Minzu University, Yinchuan 750021 , P. R. China

5. School of Mathematics and Statistics , [26463]Southwest University , Chongqing 400715 , P. R. China

6. School of Mathematics and Statistics , 118420 Tianshui Normal University , Tianshui 741001 , P. R. China

Abstract

Abstract This paper concentrates on the recovery of block-sparse signals, which are not only sparse but also nonzero elements are arrayed into some blocks (clusters) rather than being arbitrary distributed all over the vector, from linear measurements. We establish high-order sufficient conditions based on block RIP, which could ensure the exact recovery of every block s-sparse signal in the noiseless case via mixed l 2 / l p

{l_{2}/l_{p}}

minimization method, and the stable and robust recovery in the case that signals are not accurately block-sparse in the presence of noise. Additionally, a lower bound on necessary number of random Gaussian measurements is gained for the condition to be true with overwhelming probability. Furthermore, a series of numerical experiments are conducted to demonstrate the performance of the mixed l 2 / l p

{l_{2}/l_{p}}

minimization. To the best of the authors’ knowledge, the recovery guarantees established in this paper are superior to those currently available.

Funder

National Natural Science Foundation of China

China Postdoctoral Science Foundation

Fundamental Research Funds for the Central Universities

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2022-0017/pdf

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