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

Abstract

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 $\log \det (\cdot )$ term in M-SBL by a rank proxy that exploits the spark reduction property discovered in subspace-based joint sparse recovery algorithms, provides significant improvements. In particular, if we use the Schatten-$p$ quasi-norm as the corresponding rank proxy, the global minimiser of the proposed algorithm becomes identical to the true solution as $p\to 0$. Furthermore, under the same regularity conditions, we show that the convergence to a local minimiser 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 condition number of the signal amplitude matrix demonstrate that the proposed algorithm consistently outperforms M-SBL and other state-of-the art algorithms.

References in corpus (1)

• Reduce and Boost: Recovering Arbitrary Sets of Jointly Sparse Vectors

Cited by in corpus (4)

• Performance Limits for Noisy Multi-Measurement Vector Problems
• Performance Limits with Additive Error Metrics in Noisy Multi-Measurement Vector Problem
• Statistical Physics and Information Theory Perspectives on Linear Inverse Problems
• On Collaborative Compressive Sensing Systems: The Framework, Design and Algorithm