Deep Unrolling for Nonconvex Robust Principal Component Analysis

TL;DR

This paper introduces a deep unrolled algorithm for nonconvex Robust Principal Component Analysis that combines neural network benefits with interpretability, automatically learns hyperparameters, and outperforms traditional methods on synthetic and face modeling tasks.

Contribution

It presents a novel deep unrolled approach based on an accelerated alternating projection algorithm for nonconvex RPCA, enhancing performance and interpretability.

Findings

Outperforms traditional RPCA algorithms on synthetic data

Achieves better numerical and visual results in face modeling

Automatically learns hyperparameters through deep unrolling

Abstract

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.