On the Schatten p-quasi-norm minimization for low-rank matrix recovery

摘要

The first part of the paper proves the conjectures on inequalities in the Schatten p-quasi-norm of matrices. The second part of the paper uses the inequalities for proving a sufficient condition when the Schatten p-quasi-norm minimization can be used for low rank matrix recovery. More precisely, when the restricted isometry constant delta(2s) 1, there exists a real number p(0) 1 such that any solution of the p minimization is the minimal rank solution for any p = p(0). In addition, in the noisy setting, the estimate of the difference parallel to X - X-0 parallel to is also given which is useful for applications. (c) 2020 Published by Elsevier Inc.