Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization

CHEN Peng-qing; HUANG Wei

doi:10.21656/1000-0887.370230

Volume 38 Issue 8

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CHEN Peng-qing, HUANG Wei. Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization[J]. Applied Mathematics and Mechanics, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230

Citation:

CHEN Peng-qing, HUANG Wei. Block-Sparse Signal Recovery Based on l₁-l₂Norm Minimization[J]. Applied Mathematics and Mechanics, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230

CHEN Peng-qing, HUANG Wei. Block-Sparse Signal Recovery Based on l1-l2 Norm Minimization[J]. Applied Mathematics and Mechanics, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230

Citation:

CHEN Peng-qing, HUANG Wei. Block-Sparse Signal Recovery Based on l₁-l₂Norm Minimization[J]. Applied Mathematics and Mechanics, 2017, 38(8): 932-942. doi: 10.21656/1000-0887.370230

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Block-Sparse Signal Recovery Based on l₁-l₂Norm Minimization

doi: 10.21656/1000-0887.370230

School of Mathematics, Hefei University of Technology, Hefei 230009, P.R.China

Funds: The Major Research Plan of the National Natural Science Foundation of China(91538112);The National Science Fund for Young Scholars of China（11201450）

Received Date: 2016-07-22
Rev Recd Date: 2017-05-19
Publish Date: 2017-08-15

Abstract

Abstract

Compressed sensing (CS) is a newly developed theoretical framework for information acquisition and processing. Through the solution of non-linear optimization problems, sparse and compressible signals can be recovered from small-scale linear and non-adaptive measurements. Block-sparse signals as typical sparse ones exhibit additional block structures where the non-zero elements occur in blocks (or clusters). Based on the previous l_1-2 norm minimization method given by YIN Peng-hang, LOU Yi-fei, HE Qi, et al. for common sparse signal recovery, the l₁-l₂ minimization recovery algorithm was extended to the block-sparse model, the properties of thel₁-l₂norm were proved and the sufficient condition for block-sparse signal recovery was established. Meanwhile, an iterative method for block-sparsel₁-l₂minimization was presented by means of the DCA (difference of convex functions algorithm) and the ADMM (alternating direction method of multipliers). The numerical simulation results demonstrate that the signal recovery success rate of the proposed algorithm is higher than those of the existing algorithms.
- block-sparse,
- l₁-l₂ norm,
- compressed sensing,
- recovery algorithm

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References(23)

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