Hierarchical Bayesian approach for jointly-sparse solution of multiple-measurement vectors

It is well-known that many signals of interest can be well-estimated via just a small number of supports under some specific basis. Here, we consider finding sparse solution for Multiple Measurement Vectors (MMVs) in case of having both jointly sparse and clumpy structure. Most of the previous work for finding such sparse representations are based on greedy and sub-optimal algorithms such as Basis Pursuit (BP), Matching Pursuit (MP), and Orthogonal Matching Pursuit (OMP). In this paper, we first propose a hierarchical Bayesian model to deal with MMVs that have jointly-sparse structure in their solutions. Then, the model is modified to account for clumps of the neighbor supports (block sparsity) in the solution structure, as well. Several examples are considered to illustrate the merit of the proposed hierarchical Bayesian model compared to OMP and a modified version of the OMP algorithm.