Focuss algorithm for rank aware row-sparse MMV recovery

In this paper we propose a non-convex method for rank aware row-sparse Multiple Measurement Vector (MMV) recovery. Recent studies in row-sparse MMV recovery observed that better results can be achieved when the recovery algorithm takes into account the fact that the MMV matrix to be recovered is low-rank. The proposed non-convex problem requires minimizing the sum of l_2,p-norm and Schatten-q norm subject to data constraints. We derive an algorithm to solve the said problem based on the FOCally Under-determined System Solver (FOCUSS) approach. We compare our proposed method with state-of-the-art methods in rank aware and rank blind row-sparse MMV recovery. Our method always yields the best results in terms of probability of recovery.