Weighted lp−l1 minimization methods for block sparse recovery and rank minimization.

This paper considers block sparse recovery and rank minimization problems from incomplete linear measurements. We study the weighted l p − l 1 (0 < p ≤ 1) norms as a nonconvex metric for recovering block sparse signals and low-rank matrices. Based on the block p -restricted isometry property (abbreviated as block p -RIP) and matrix p -RIP, we prove that the weighted l p − l 1 minimization can guarantee the exact recovery for block sparse signals and low-rank matrices. We also give the stable recovery results for approximately block sparse signals and approximately low-rank matrices in noisy measurements cases. Our results give the theoretical support for block sparse recovery and rank minimization problems. [ABSTRACT FROM AUTHOR]