A Nonconvex Projection Method for Robust PCA
This addresses the problem of matrix decomposition for applications such as image processing and astronomy, offering a novel approach that avoids objective functions or convex relaxations, though it appears incremental in the broader RPCA field.
The paper tackled the robust PCA problem by proposing a nonconvex feasibility reformulation solved with an alternating projection method, demonstrating through experiments on applications like shadow removal and face detection that it matches or outperforms current state-of-the-art methods.
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.