A Nonconvex Projection Method for Robust PCA

  • Aritra Dutta King Abdullah University of Science and Technology
  • Filip Hanzely King Abdullah University of Science and Technology
  • Peter Richtàrik King Abdullah University of Science and Technology

Abstract

Robust principal component analysis (RPCA) is a well-studied problem whose goal is to decompose 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, this is the first paper proposing 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.

Published
2019-07-17
Section
AAAI Technical Track: Constraint Satisfaction and Optimization