A generalized robust minimization framework for low-rank matrix recovery (Q1718892)

Summary: 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 \((0 < p \leq 1)\) and \(L_q\)\((0 < q \leq 1)\) 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.