Perturbation analysis of low-rank matrix stable recovery

Abstract

In this paper, we bring forward a completely perturbed nuclear norm minimization method to tackle a formulation of completely perturbed low-rank matrices recovery. In view of the matrix version of the restricted isometry property (RIP) and the Frobenius-robust rank null space property (FRNSP), this paper extends the investigation to a completely perturbed model taking into consideration not only noise but also perturbation, derives sufficient conditions guaranteeing that low-rank matrices can be robustly and stably reconstructed under the completely perturbed scenario, as well as finally presents an upper bound estimation of recovery error. The upper bound estimation can be described by two terms, one concerning the total noise, and another regarding the best [Formula: see text]-approximation error. Specially, we not only improve the condition corresponding with RIP, but also ameliorate the upper bound estimation in case the results reduce to the general case. Furthermore, in the case of [Formula: see text], the obtained conditions are optimal.