Correlation learning on joint support recovery for more sources than measurements

Consider MMV problem Y _{M ×L} = A _M×N X _N×L with X being D-row sparse. In this work, we first we analyze the MSBL algorithm by Wipf and Rao, and provide its limit in the M ≤ D regime. To improve support recovery, we further develop Bayesian methods for learning the correlation structures both temporally or spatially. In particular, we use the Inverse Wishart distribution, the conjugate prior for the covariance matrix of a Gaussian vector, to proceed with the Sparse Bayesian inference on the signal support. Simulation studies show that the method is robust, and it outperforms jointly support SBL families such as MSBL or TSBL under some circumstances.