论文标题
强大的低级矩阵恢复的最佳条件
An Optimal Condition of Robust Low-rank Matrices Recovery
论文作者
论文摘要
在本文中，我们研究了低级别基质恢复的核标准最小化的重建条件。我们获得了足够的条件$δ_{tr} <t/（4-t）$，$ 0 <t <4/3 $保证了强大的重建$（z \ neq0）$或所有等级$ r $ r $ r $ r $ r $ r $ r $ r $ r $ x \ in \ mathbb in \ mathbb {r}^r}^r}^r}^r}^r}^r}^r}^r}^r} n} $ b = \ Mathcal {a}（x）+z $通过核标准最小化。此外，我们不仅表明当$ t = 1 $时，$δ_r<1/3 $的上限与CAI和Zhang \ cite {Cai和Zhang}的结果相同，而且还证明了有关恢复误差的上限更好。此外，我们证明了限制的等轴测特性条件很清晰。此外，还进行了数值实验以揭示核标准最小化方法稳定且可靠，可用于恢复低级别基质。
In this paper we investigate the reconstruction conditions of nuclear norm minimization for low-rank matrix recovery. We obtain sufficient conditions $δ_{tr}<t/(4-t)$ with $0<t<4/3$ to guarantee the robust reconstruction $(z\neq0)$ or exact reconstruction $(z=0)$ 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 $δ_r<1/3$ 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. Moreover, we prove that the restricted isometry property condition is sharp. Besides, the numerical experiments are conducted to reveal the nuclear norm minimization method is stable and robust for the recovery of low-rank matrix.
