Low-rank matrix recovery via regularized nuclear norm minimization

In this paper, we theoretically investigate the low-rank matrix recovery problem in context of unconstrained regularized nuclear norm minimization (RNNM) framework. Our theoretical findings show that, RNNM method is able to provide a robust any X (not necessary be exactly low-rank) from its few noisy measurements b=A(X)+n with bounded constraint ‖n‖2≤ϵ, provided that tk-order restricted isometry constant (RIC) A satisfies certain related t>0. Specifically, obtained condition case t>4/3 found same sharp established previously by Cai and Zhang [10] guarantee exact rank-k via constrained method. More importantly, best our knowledge, are first establish RIC based coefficient estimate null space property 0<t≤1.