Smoothing Technique and Fast Alternating Direction Method for Robust PCA

The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision. In this paper, smoothing technique is used to smooth the non-smooth terms in the objective function, and we develop the fast alternating direction method for solving RPCA. Moving object detection experiments and numerical results on impulsive sparse matrix data show that our algorithms are competitive to current state-of-the-art solvers for RPCA in terms of speed.