Institute of Information Science, Academia Sinica

In recent years, sparse coding has been widely used in many applications ranging from image processing to pattern recognition. Most existing sparse coding based applications require solving a class of challenging non-smooth and non-convex optimization problems. Despite the fact that many numerical methods have been developed for solving these problems, it remains an open problem to find a numerical method which is not only empirically fast, but also has mathematically guaranteed strong convergence property. In this talk, I will present proposed an alternating scheme for solving the optimization problems arising from sparse coding based applications. A rigorous convergence analysis shows that the proposed method has global convergence property, i.e. the whole sequence is convergent and converges to a critical point. Besides the theoretical soundness, the practical benefit of the proposed method is tested in the applications of image restoration and recognition. The experiments showed that the proposed method is also faster than some widely used method with comparable performance, e.g., the K-SVD method.