Recovery of corrupted low-rank matrices via half-quadratic based nonconvex minimization

Recovering arbitrarily corrupted low-rank matrices arises in computer vision applications, including bioinformatic data analysis and visual tracking. The methods used involve minimizing a combination of nuclear norm and l¹ norm. We show that by replacing the l¹ norm on error items with nonconvex M-estimators, exact recovery of densely corrupted low-rank matrices is possible. The robustness of the proposed method is guaranteed by the M-estimator theory. The multiplicative form of half-quadratic optimization is used to simplify the nonconvex optimization problem so that it can be efficiently solved by iterative regularization scheme. Simulation results corroborate our claims and demonstrate the efficiency of our proposed method under tough conditions.