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

— 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 correlation and thus their performance degrades significantly with the correlation. In this work, we propose a block sparse Bayesian learning framework which models the temporal correlation. We derive two sparse Bayesian learning (SBL) algorithms, which have superior recovery performance compared to existing algorithms, especially in the presence of high temporal correlation. 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...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Zhilin Zhang, Bhaskar D. Rao
• Keywords: Bayesian Learning, CORR 2011, Education, Solution Matrix, Temporal Correlation