Smoothed rank approximation algorithms for matrix completion

We consider using smooth rank approximation functions to solve the matrix completion problem. Our main contribution in this paper is deriving two robust algorithms using the accelerated proximal gradient (APG) and the alternating direction method of multipliers (ADM). Further, we compare both algorithms against each other and against the iterative reweighted least squares (IRLS-1) algorithm using a variety of noisy images. The experiments show that using ADM achieves approximately 1.5 dB SNR improvement over irls-1, while it needs comparable execution time to IRLS-1. Meanwhile, using APG saves about 50% of IRLS-1's computation time with lower SNR than ADM.