Rank deficiency and sparsity in partially observed multiple measurement vector models

This paper considers the problem of recovering jointly sparse vectors using partially observed multiple measurement vector (MMV) model, in which only a few entries of the measurement vectors are observed. It is shown that when we have partial observations, seeking only the sparsest solution may not recover the original vectors, even if it succeeds when full observations are available. By simultaneously exploiting the low rank and joint-sparsity, a new reconstruction approach is proposed. Theoretical conditions for perfect recovery are also established. Simulations show that the proposed method outperforms the mixed l1/lq minimization and rank aware sparse reconstruction.