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In this paper, we consider using the weighted <inline-formula> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> minimization to reconstruct <inline-formula> <tex-math notation="LaTeX">$ {X}$ </tex-math></inline-formula> from <inline-formula> <tex-math notation="LaTeX">$ {Y}= {A} {X}+ {Z}$ </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">$ {X}$ </tex-math></inline-formula> via the weighted <inline-formula> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> minimization. Moreover, a sufficient condition based on the high order RIP is obtained to guarantee the recovery of <inline-formula> <tex-math notation="LaTeX">$ {X}$ </tex-math></inline-formula> via the standard mixed-norm <inline-formula> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> minimization.

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