Sparse recovery of multiple measurement vectors in impulsive noise: A smooth block successive minimization algorithm

Zhen Qing He, Zhi Ping Shi, Lei Huang, Hongbin Li, H. C. So

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

This paper considers the sparse recovery problem of multiple measurement vector (MMV) model corrupted in impulsive noise. To ensure outlier-robust sparse recovery, we formulate an MMV problem that includes the generalized ℓp-norm (1 < p < 2) divergence data-fidelity term added to the ℓ2,0 joint sparsity-promoting regularizer. The joint sparse penalty, however, is non-continuous and hence non-differentiable, which inevitably raises difficulty in optimization when using a gradient-based method. To address this, we build a smooth approximation for the ℓ2,0-based sparse metric via the log-sum based sparse-encouraging surrogate function. Then, we propose a block successive upper-bound minimization algorithm for the smooth MMV problem by solving a series of subproblems based on the block coordinate descent (BCD) method. Furthermore, local convergence of the proposed algorithm to a stationary point of the smooth problem is proved. Experiments demonstrate its efficiency and robust recovery performance for suppressing impulsive noise.

Original languageEnglish
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
Pages4543-4547
Number of pages5
ISBN (Electronic)9781479999880
DOIs
StatePublished - 18 May 2016
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China
Duration: 20 Mar 201625 Mar 2016

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2016-May
ISSN (Print)1520-6149

Conference

Conference41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Country/TerritoryChina
CityShanghai
Period20/03/1625/03/16

Keywords

  • Compressed sensing
  • impulsive noise
  • multiple measurement vectors
  • sparse signal recovery

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