Improving M-SBL for Joint Sparse Recovery Using a Subspace Penalty

Jong Chul Ye, Jong Min Kim, Yoram Bresler

Research output: Contribution to journalArticlepeer-review


A multiple measurement vector problem (MMV) is a generalization of the compressed sensing problem that addresses the recovery of a set of jointly sparse signal vectors. One of the important contributions of this paper is to show that the seemingly least related state-of-the-art MMV joint sparse recovery algorithms-the M-SBL (multiple sparse Bayesian learning) and subspace-based hybrid greedy algorithms-have a very important link. More specifically, we show that replacing the log term in the M-SBL by a rank surrogate that exploits the spark reduction property discovered in the subspace-based joint sparse recovery algorithms provides significant improvements. In particular, if we use the Schatten-p quasi-norm as the corresponding rank surrogate, the global minimizer of the cost function in the proposed algorithm becomes identical to the true solution as p → 0. Furthermore, under regularity conditions, we show that convergence to a local minimizer is guaranteed using an alternating minimization algorithm that has closed form expressions for each of the minimization steps, which are convex. Numerical simulations under a variety of scenarios in terms of SNR and the condition number of the signal amplitude matrix show that the proposed algorithm consistently outperformed the M-SBL and other state-of-the art algorithms.

Original languageEnglish (US)
Article number7244235
Pages (from-to)6595-6605
Number of pages11
JournalIEEE Transactions on Signal Processing
Issue number24
StatePublished - Dec 15 2015


  • Compressed sensing
  • M-SBL
  • Schatten-$p$ norm
  • generalized MUSIC criterion
  • joint sparse recovery
  • multiple measurement vector problem
  • rank surrogate
  • subspace method

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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