  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.
