A Generalized Robust Minimization Framework for Low-Rank Matrix Recovery

Abstract EN

This paper considers the problem of recovering low-rank matrices which are heavily corrupted by outliers or large errors.

To improve the robustness of existing recovery methods, the problem is solved by formulating it as a generalized nonsmooth nonconvex minimization functional via exploiting the Schatten p-norm (0 < p ≤1) and Lq(0 < q ≤1) seminorm.

Two numerical algorithms are provided based on the augmented Lagrange multiplier (ALM) and accelerated proximal gradient (APG) methods as well as efficient root-finder strategies.

Experimental results demonstrate that the proposed generalized approach is more inclusive and effective compared with state-of-the-art methods, either convex or nonconvex.