Support agnostic Bayesian recovery of jointly sparse signals

A matching pursuit method using a Bayesian approach is introduced for recovering a set of sparse signals with common support from a set of their measurements. This method performs Bayesian estimates of joint-sparse signals even when the distribution of active elements is not known. It utilizes only the a priori statistics of noise and the sparsity rate of the signal, which are estimated without user intervention. The method utilizes a greedy approach to determine the approximate MMSE estimate of the joint-sparse signals. Simulation results demonstrate the superiority of the proposed estimator.