Subspace penalized sparse learning for joint sparse recovery

The 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 reveal that the seemingly least related state-of-art MMV joint sparse recovery algorithms - 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 det(·) term in M-SBL by a log det(·) rank proxy that exploits the spark reduction property discovered in subspace-based joint sparse recovery algorithms, provides significant improvements. Theoretical analysis demonstrates that even thoughM-SBL is often unable to remove all localminimizers, the proposed method can do so under fairly mild conditions, without affecting the global minimizer.