New Bounds Based on RIP for the Sparse Matrix Recovery via the Weighted <inline-formula> <tex-math notation="LaTeX">$\ell_{2,1}$ </tex-math></inline-formula> Minimization

Abstract

In this paper, we consider using the weighted ℓ2,1 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 ℓ2,1 minimization. Moreover, a sufficient condition based on the high order RIP is obtained to guarantee the recovery of X via the standard mixed-norm ℓ2,1 minimization.

Keywords

• Multiple measurement vector
• restricted isometry property
• the weighted ℓ₁,₂ minimization