  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.
