Abstract

Sparse coding and dictionary learning have seen their applications in many vision tasks, which usually is formu-lated as a non-convex optimization problem. Many iterative methods have been proposed to tackle such an optimiza-tion problem. However, it remains an open problem to have a method that is not only practically fast but also is glob-ally convergent. In this paper, we proposed a fast proximal method for solving `0 norm based dictionary learning problems, and we proved that the whole sequence generated bythe proposed method converges to a stationary point with sub-linear convergence rate. The benefit of having a fast and convergent dictionary learning method is demonstratedin the applications of image recovery and face recognition.