A Nonconvex Projection Method for Robust PCA

TL;DR

This paper introduces a novel nonconvex projection method for robust PCA that avoids convex relaxations, demonstrating superior performance across multiple applications through extensive experiments.

Contribution

It presents the first nonconvex feasibility reformulation and alternating projection approach for RPCA, bypassing traditional convex relaxations.

Findings

Outperforms state-of-the-art methods in various applications

Effective in shadow removal, background estimation, face detection, galaxy evolution

Matches or exceeds existing techniques in accuracy and efficiency

Abstract

Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and apply an alternating projection method to solve it. To the best of our knowledge, we are the first to propose a method that solves RPCA problem without considering any objective function, convex relaxation, or surrogate convex constraints. We demonstrate through extensive numerical experiments on a variety of applications, including shadow removal, background estimation, face detection, and galaxy evolution, that our approach matches and often significantly outperforms current state-of-the-art in various ways.