Deep Unrolling for Nonconvex Robust Principal Component Analysis
This work addresses RPCA for applications like face modeling, but it is incremental as it combines existing deep learning and optimization techniques without introducing a fundamentally new approach.
The authors tackled Robust Principal Component Analysis (RPCA) by proposing a deep unrolled algorithm based on accelerated alternating projection to decompose matrices into low-rank and sparse components, demonstrating effectiveness on synthetic datasets and a face modeling problem with improved numerical and visual performance.
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.