General Mathematics


Low-Rank Matrix Recovery Via Regularized Nuclear Norm Minimization

Authors: Wendong Wang, Feng Zhang, Jianjun Wang

In this paper, we theoretically investigate the low-rank matrix recovery problem in the context of the unconstrained regularized nuclear norm minimization (RNNM) framework. Our theoretical findings show that, one can robustly recover any matrix X from its few noisy measurements b=A(X)+n with a bounded constraint ||n||_{2}<ε via the RNNM, if the linear map A satisfies restricted isometry property (RIP) with δ_{tk}<√(t-1)/t for certain fixed t>1. Recently, this condition with t≥4/3 has been proved by Cai and Zhang (2014) to be sharp for exactly recovering any rank-k matrices via the constrained nuclear norm minimization (NNM). To the best of our knowledge, our work first extends nontrivially this recovery condition for the constrained NNM to that for its unconstrained counterpart. Furthermore, it will be shown that similar recovery condition also holds for regularized l_{1}-norm minimization, which sometimes is also called Basis Pursuit DeNoising (BPDN).

Comments: 10 Pages.

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[v1] 2018-10-08 22:09:22

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