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

Abstract The first part of the paper proves the conjectures on an 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 δ 2 s 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 ‖ X − X 0 ‖ is also given which is useful for applications.