Stochastic greedy algorithms for multiple measurement vectors

Jing Qin, Shuang Li, Deanna Needell, Anna Ma, Rachel Grotheer, Chenxi Huang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Sparse representation of a single measurement vector (SMV) has been explored in a variety of compressive sensing applications. Recently, SMV models have been extended to solve multiple measurement vectors (MMV) problems, where the underlying signal is assumed to have joint sparse struc-tures. To circumvent the NP-hardness of the ℓ0 minimization problem, many deterministic MMV algorithms solve the convex relaxed models with limited ef-ficiency. In this paper, we develop stochastic greedy algorithms for solving the joint sparse MMV reconstruction problem. In particular, we propose the MMV Stochastic Iterative Hard Thresholding (MStoIHT) and MMV Stochastic Gradient Matching Pursuit (MStoGradMP) algorithms, and we also utilize the mini-batching technique to further improve their performance. Convergence analysis indicates that the proposed algorithms are able to converge faster than their SMV counterparts, i.e., concatenated StoIHT and StoGradMP, under certain conditions. Numerical experiments have illustrated the superior effectiveness of the proposed algorithms over their SMV counterparts.

Original languageEnglish
Pages (from-to)79-107
Number of pages29
JournalInverse Problems and Imaging
Issue number1
StatePublished - Feb 2021

Bibliographical note

Publisher Copyright:
© 2021, American Institute of Mathematical Sciences. All rights reserved.


  • Compressive sensing
  • Joint sparsity
  • Multiple measurement vectors
  • Signal recovery
  • Stochastic opti-mization
  • Video recovery

ASJC Scopus subject areas

  • Analysis
  • Modeling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization


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