A block-sparse music algorithm for the localization and the identification of directive sources

We introduce a generalization of the MUSIC algorithm to treat block-sparse signals in a multi-measurement vector framework. We show, through theoretical analysis and numerical experiments, that the requirements in terms of number of snapshots and number of measurements depend not only on the sparsity and on the size of the blocks, but also on the rank of the matrices of coefficients for each block. We apply this algorithm to the localization of directive sources, which can be modeled by block-sparsity in a dictionary of multipoles, and show that it compares favorably to a greedy approach based on the same model.