New Bounds Based on RIP for the Sparse Matrix Recovery via the Weighted $\ell_{2,1}$ Minimization

In this paper, we consider using the weighted ℓ
_2,1
minimization to reconstruct X from Y = AX + Z. This method has been applied to recover multichannel signal in resent years since it exploits both the interchannel correlation and multisource prior. We show improved sufficient conditions based on the restricted isometry property (RIP) for the exact and stable recovery of X via the weighted ℓ
_2,1
minimization. Moreover, a sufficient condition based on the high order RIP is obtained to guarantee the recovery of X via the standard mixed-norm ℓ
_2,1
minimization.