  This work discusses the problem of sparse signal recovery when there is
correlation among the values of non-zero entries. We examine intra-vector
correlation in the context of the block sparse model and inter-vector
correlation in the context of the multiple measurement vector model, as well as
their combination. Algorithms based on the sparse Bayesian learning are
presented and the benefits of incorporating correlation at the algorithm level
are discussed. The impact of correlation on the limits of support recovery is
also discussed highlighting the different impact intra-vector and inter-vector
correlations have on such limits.
