Artificial Intelligence


New Sufficient Conditions of Robust Recovery for Low-Rank Matrices

Authors: Jianwen Huang, Jianjun Wang, Feng Zhang, Wendong Wang

In this paper we investigate the reconstruction conditions of nuclear norm minimization for low-rank matrix recovery from a given linear system of equality constraints. Sufficient conditions are derived to guarantee the robust reconstruction in bounded $l_2$ and Dantzig selector noise settings $(\epsilon\neq0)$ or exactly reconstruction in the noiseless context $(\epsilon=0)$ of all rank $r$ matrices $X\in\mathbb{R}^{m\times n}$ from $b=\mathcal{A}(X)+z$ via nuclear norm minimization. Furthermore, we not only show that when $t=1$, the upper bound of $\delta_r$ is the same as the result of Cai and Zhang \cite{Cai and Zhang}, but also demonstrate that the gained upper bounds concerning the recovery error are better. Finally, we prove that the restricted isometry property condition is sharp.

Comments: 18 Pages.

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Submission history

[v1] 2018-06-28 03:27:39

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