We design algorithms for Robust Principal Component Analysis (RPCA) which
consists in decomposing a matrix into the sum of a low rank matrix and a sparse
matrix. We propose a deep unrolled algorithm based on an accelerated
alternating projection algorithm which aims to solve RPCA in its nonconvex
form. The proposed procedure combines benefits of deep neural networks and the
interpretability of the original algorithm and it automatically learns
hyperparameters. We demonstrate the unrolled algorithm's effectiveness on
synthetic datasets and also on a face modeling problem, where it leads to both
better numerical and visual performances.

提出了一种基于加速交替投影算法的深度展开算法，旨在解决矩阵分解问题中的 Robust Principal Component Analysis (RPCA) 问题，并自学习超参数。通过在合成数据集和面部建模问题上的效果展示出其在数值和视觉上的效能。

非凸健壮主成分分析的深度展开

Deep Unrolling for Nonconvex Robust Principal Component Analysis

We demonstrate necessary and sufficient conditions of the local convergence
of the alternating projection algorithm to a unique solution up to a global
phase factor. Additionally, for the ptychography imaging problem, we discuss
phase synchronization and graph connection Laplacian, and show how to construct
an accurate initial guess to accelerate convergence speed to handle the big
imaging data in the coming new light source era.

本文研究交替投影算法的本地收敛性必要条件和充分条件，并探讨凝聚相位和图连接拉普拉斯的问题，以展示如何构建准确的初始猜测来加速收敛速度，以处理即将到来的新光源时代的大型成像数据。