Signal recovery for jointly sparse vectors with different sensing matrices

In this paper, we study a sparse multiple measurement vector problem in which we need to recover a set of jointly sparse vectors from incomplete measurements. Most related studies assumed that all these measurements correspond to the same compressed sensing matrix. Differently, we allow that the measurements come from different sensing matrices. To deal with different matrices, we establish an algorithm via applying block coordinate descent and Majorization-Minimization techniques. The numerical examples demonstrate the effectiveness of this new algorithm, which allows us to design different matrices for better recovery performance.