论文标题
非凸低矩阵稳健恢复的扰动分析
The perturbation analysis of nonconvex low-rank matrix robust recovery
论文作者
论文摘要
在本文中，我们提出了一个完全干扰的非convex schatten $ p $毫米化，以解决完全干扰的低级矩阵恢复的模型。基于限制的等轴测属性的论文将调查推广到一个完全扰动模型对噪声的思考，而且还具有扰动性，提供了受限的等轴测属性条件，可确保低级别矩阵的恢复和相应的重建误差绑定。特别是，对结果的分析表明，在$ p $的情况下，$ 0 $和$ a> 1 $对于完整的扰动和低级矩阵，该条件是最佳的足够条件$δ_{2R} <1 $ \ cite {recht et al 2010}。进行数值实验是为了显示出更好的性能，并提供了非凸schatten $ p $ - 毫米化方法的表现，该方法与凸核范围最小化方法相比，在完全干扰的情况下。
In this paper, we bring forward a completely perturbed nonconvex Schatten $p$-minimization to address a model of completely perturbed low-rank matrix recovery. The paper that based on the restricted isometry property generalizes the investigation to a complete perturbation model thinking over not only noise but also perturbation, gives the restricted isometry property condition that guarantees the recovery of low-rank matrix and the corresponding reconstruction error bound. In particular, the analysis of the result reveals that in the case that $p$ decreases $0$ and $a>1$ for the complete perturbation and low-rank matrix, the condition is the optimal sufficient condition $δ_{2r}<1$ \cite{Recht et al 2010}. The numerical experiments are conducted to show better performance, and provides outperformance of the nonconvex Schatten $p$-minimization method comparing with the convex nuclear norm minimization approach in the completely perturbed scenario.
