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Volume 37, Issue 1
The High Order Block RIP Condition for Signal Recovery

Yaling Li & Wengu Chen

DOI: 10.4208/jcm.1710-m2017-0175

J. Comp. Math., 37 (2019), pp. 61-75.

Published online: 2018-08

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  • Abstract

In this paper, we consider the recovery of block sparse signals, whose nonzero entries appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from incomplete linear measurements. A high order sufficient condition based on block RIP is obtained to guarantee the stable recovery of all block sparse signals in the presence of noise, and robust recovery when signals are not exactly block sparse via mixed $l_2/l_1$ minimization. Moreover, a concrete example is established to ensure the condition is sharp. The significance of the results presented in this paper lies in the fact that recovery may be possible under more general conditions by exploiting the block structure of the sparsity pattern instead of the conventional sparsity pattern.

  • Keywords

Block sparsity, Block restricted isometry property, Compressed sensing, Mixed $l_2/l_1$ minimization.

  • AMS Subject Headings

90C59, 94A12, 94A20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

leeyaling@126.com (Yaling Li)

chenwg@iapcm.ac.cn (Wengu Chen)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-61, author = {Li , Yaling and Chen , Wengu}, title = {The High Order Block RIP Condition for Signal Recovery}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {1}, pages = {61--75}, abstract = {

In this paper, we consider the recovery of block sparse signals, whose nonzero entries appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from incomplete linear measurements. A high order sufficient condition based on block RIP is obtained to guarantee the stable recovery of all block sparse signals in the presence of noise, and robust recovery when signals are not exactly block sparse via mixed $l_2/l_1$ minimization. Moreover, a concrete example is established to ensure the condition is sharp. The significance of the results presented in this paper lies in the fact that recovery may be possible under more general conditions by exploiting the block structure of the sparsity pattern instead of the conventional sparsity pattern.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1710-m2017-0175}, url = {http://global-sci.org/intro/article_detail/jcm/12649.html} }
TY - JOUR T1 - The High Order Block RIP Condition for Signal Recovery AU - Li , Yaling AU - Chen , Wengu JO - Journal of Computational Mathematics VL - 1 SP - 61 EP - 75 PY - 2018 DA - 2018/08 SN - 37 DO - http://doi.org/10.4208/jcm.1710-m2017-0175 UR - https://global-sci.org/intro/article_detail/jcm/12649.html KW - Block sparsity, Block restricted isometry property, Compressed sensing, Mixed $l_2/l_1$ minimization. AB -

In this paper, we consider the recovery of block sparse signals, whose nonzero entries appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from incomplete linear measurements. A high order sufficient condition based on block RIP is obtained to guarantee the stable recovery of all block sparse signals in the presence of noise, and robust recovery when signals are not exactly block sparse via mixed $l_2/l_1$ minimization. Moreover, a concrete example is established to ensure the condition is sharp. The significance of the results presented in this paper lies in the fact that recovery may be possible under more general conditions by exploiting the block structure of the sparsity pattern instead of the conventional sparsity pattern.

Li , Yaling and Chen , Wengu. (2018). The High Order Block RIP Condition for Signal Recovery. Journal of Computational Mathematics. 37 (1). 61-75. doi:10.4208/jcm.1710-m2017-0175
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