This paper considers block sparse recovery and rank minimization problems from incomplete linear measurements. We study the weighted [Formula: see text] [Formula: see text] norms as a nonconvex metric for recovering block sparse signals and low-rank matrices. Based on the block [Formula: see text]-restricted isometry property (abbreviated as block [Formula: see text]-RIP) and matrix [Formula: see text]-RIP, we prove that the weighted [Formula: see text] 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.
Positive Semidefinite Matrix Factorization: A Connection with Phase Retrieval and Affine Rank Minimization
