A Unified Approach to Weighted L2,1 Minimization for Joint Sparse Recovery

A unified view of the area of joint sparse recovery is presented for the weighted L-2,L-1 minimization. The support invariance transformation (SIT) is discussed to insure that the proposed scheme does not change the support of the sparse signal. The proposed weighted L-2,L-1 minimization framework utilizes a support-related weighted matrix to differentiate each potential position, resulting in a favorable situation that larger weights are assigned at those positions where indices of the corresponding bases are more likely to be outside of the row support so that the solution at those positions are close to zero. Therefore, the weighted L-2,L-1 minimization prefers to allot the received energy to those positions where indices of the corresponding bases are inside of the row support, which further improves the sparseness of the solution. The simulations demonstrate that the weighted L-2,L-1 minimization reaches the strong recover threshold with lower SNR and fewer measurements.