Sparse Signal Recovery with Temporally Correlated Source Vectors Using Sparse Bayesian Learning

TL;DR

This paper introduces a novel sparse Bayesian learning framework that models temporal correlations in multi-measurement vector problems, significantly improving recovery performance especially with highly correlated sources.

Contribution

It develops two new SBL algorithms that incorporate temporal correlations, outperform existing methods, and analyze their cost functions to ensure sparsity at the global minimum.

Findings

Superior recovery performance with high temporal correlations

Effective in highly underdetermined problems

Global minimum corresponds to the sparsest solution

Abstract

We address the sparse signal recovery problem in the context of multiple measurement vectors (MMV) when elements in each nonzero row of the solution matrix are temporally correlated. Existing algorithms do not consider such temporal correlations and thus their performance degrades significantly with the correlations. In this work, we propose a block sparse Bayesian learning framework which models the temporal correlations. In this framework we derive two sparse Bayesian learning (SBL) algorithms, which have superior recovery performance compared to existing algorithms, especially in the presence of high temporal correlations. Furthermore, our algorithms are better at handling highly underdetermined problems and require less row-sparsity on the solution matrix. We also provide analysis of the global and local minima of their cost function, and show that the SBL cost function has the very desirable property that the global minimum is at the sparsest solution to the MMV problem. Extensive experiments also provide some interesting results that motivate future theoretical research on the MMV model.