基于邻近算子的RPCA问题快速优化算法

An Efficient Optimization Method for RPCA Based on the Proximity Operator

鲁棒主成分分析(RPCA)问题用于恢复某些元素被严重破坏的低秩矩阵,在视频去噪、背景建模、推荐系统等领域具有广泛的应用.考虑到RPCA问题的非凸性,设计求解RPCA问题的快速凸优化算法是近年来的一个研究热点.本文以邻近算子为工具,提出一种求解RPCA问题的快速有效且能简单证明其收敛性的不动点凸优化算法.通过与两种经典方法比较,本文提出的算法在计算效率上具有明显的优势.

Robust Principal Component Analysis(RPCA),used to restore low-rank matrices where some elements are severely damaged,has been widely applied in video denoising,background modeling and recommendation systems.Considering the non-convexity of RPCA problem,the design of a fast convex optimization algorithm for RPCA problem is a hot topic in recent years.Taking adjacent operators as tools,this paper proposes a new fixed point convex optimization algorithm to solve RPCA problem,which is fast,effective and simple to prove its convergence.Compared with the two classical methods,the algorithm presented in this paper has obvious advantages in computational efficiency.