Low rank matrix recovery via augmented lagrange multiplier with nonconvex minimization

In recovery problem, nuclear norm as a convex envelope of rank function is widely used. However, nuclear norm minimization problem tends not to identify optimal solution, so recently, other heuristic surrogate functions such as nonconvex logdet are utilized to recover sparser signal. In this paper, to handle nonconvex optimation problem, a modified Augmented Lagrange Multiplier Method (ALMM) is developed using weighted nuclear norm instead of nuclear norm which conventional ALMM treats for convex optimization. We experiment on real images in Matrix Completion problem with diverse nonconvex, and show that instead of solving a simple convex problem, nonconvex optimization problem can reconstruct a low rank matrix more accurately and the convergence rate is faster with having higher average PSNR.