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.
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