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Volume 38, Issue 3
Enhanced Block-Sparse Signal Recovery Performance via Truncated $ℓ_2/ℓ_{1−2}$ Minimization

Weichao Kong, Jianjun Wang, Wendong Wang & Feng Zhang

DOI: 10.4208/jcm.1811-m2017-0275

J. Comp. Math., 38 (2020), pp. 437-451.

Published online: 2020-03

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  • Abstract

In this paper, we investigate truncated $ℓ_2/ℓ_{1−2}$ minimization and its associated alternating direction method of multipliers (ADMM) algorithm for recovering the block sparse signals. Based on the block restricted isometry property (Block-RIP), a theoretical analysis is presented to guarantee the validity of proposed method. Our theoretical results not only show a less error upper bound, but also promote the former recovery condition of truncated ℓ1−2 method for sparse signal recovery. Besides, the algorithm has been compared with some state-of-the-art algorithms and numerical experiments have shown excellent performances on recovering the block sparse signals.

  • Keywords

Compressed sensing, Block-sparse, Truncated $ℓ_2/ℓ_{1−2}$ minimization method, ADMM.

  • AMS Subject Headings

68W40, 68P30, 94A08, 94A12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

15870430035@163.com (Weichao Kong)

wjj@swu.edu.cn (Jianjun Wang)

wdwang@swu.edu.cn (Wendong Wang)

zhangf@email.swu.edu.cn (Feng Zhang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-38-437, author = {Kong , WeichaoWang , JianjunWang , Wendong and Zhang , Feng}, title = {Enhanced Block-Sparse Signal Recovery Performance via Truncated $ℓ_2/ℓ_{1−2}$ Minimization}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {38}, number = {3}, pages = {437--451}, abstract = {

In this paper, we investigate truncated $ℓ_2/ℓ_{1−2}$ minimization and its associated alternating direction method of multipliers (ADMM) algorithm for recovering the block sparse signals. Based on the block restricted isometry property (Block-RIP), a theoretical analysis is presented to guarantee the validity of proposed method. Our theoretical results not only show a less error upper bound, but also promote the former recovery condition of truncated ℓ1−2 method for sparse signal recovery. Besides, the algorithm has been compared with some state-of-the-art algorithms and numerical experiments have shown excellent performances on recovering the block sparse signals.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1811-m2017-0275}, url = {http://global-sci.org/intro/article_detail/jcm/15794.html} }
TY - JOUR T1 - Enhanced Block-Sparse Signal Recovery Performance via Truncated $ℓ_2/ℓ_{1−2}$ Minimization AU - Kong , Weichao AU - Wang , Jianjun AU - Wang , Wendong AU - Zhang , Feng JO - Journal of Computational Mathematics VL - 3 SP - 437 EP - 451 PY - 2020 DA - 2020/03 SN - 38 DO - http://doi.org/10.4208/jcm.1811-m2017-0275 UR - https://global-sci.org/intro/article_detail/jcm/15794.html KW - Compressed sensing, Block-sparse, Truncated $ℓ_2/ℓ_{1−2}$ minimization method, ADMM. AB -

In this paper, we investigate truncated $ℓ_2/ℓ_{1−2}$ minimization and its associated alternating direction method of multipliers (ADMM) algorithm for recovering the block sparse signals. Based on the block restricted isometry property (Block-RIP), a theoretical analysis is presented to guarantee the validity of proposed method. Our theoretical results not only show a less error upper bound, but also promote the former recovery condition of truncated ℓ1−2 method for sparse signal recovery. Besides, the algorithm has been compared with some state-of-the-art algorithms and numerical experiments have shown excellent performances on recovering the block sparse signals.

Kong , WeichaoWang , JianjunWang , Wendong and Zhang , Feng. (2020). Enhanced Block-Sparse Signal Recovery Performance via Truncated $ℓ_2/ℓ_{1−2}$ Minimization. Journal of Computational Mathematics. 38 (3). 437-451. doi:10.4208/jcm.1811-m2017-0275
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