Synthesis and analysis prior algorithms for joint-sparse recovery

This paper proposes a Majorization-Minimization approach for solving the synthesis and analysis prior joint-sparse multiple measurement vector reconstruction problem. The proposed synthesis prior algorithm yielded the same results as the Spectral Projected Gradient (SPG) method. The analysis prior algorithm is the first to be proposed for this problem. It yielded considerably better results than the proposed synthesis prior algorithm. For problems of a given size, the run times for our proposed algorithms are fixed; unlike SPG where the reconstruction time also depends on the support size of the vectors.