The High Order Block RIP Condition for Signal Recovery

The High Order Block RIP Condition for Signal Recovery

Year:    2019

Author:    Yaling Li, Wengu Chen

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1710-m2017-0175

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 1 : pp. 61–75

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

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

Author Details

Yaling Li

Wengu Chen

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