Analytic separable dictionary learning based on oblique manifold

Sparse representation based on dictionary has gained increasing interest due to its extensive applications. Because of the disadvantages of computational complexity of traditional dictionary learning, we propose an algorithm of analytic separable dictionary learning. Considering the differences of sparse coefficient matrix and dictionary, we divide our algorithm into two phases: 2D sparse coding and dictionary optimization. Then an alternative iteration method is used between these two phases. The algorithm of 2D-OMP (2-dimensional Orthogonal Matching Pursuit) is used in the first phase because of its low complexity. In the second phase, we create a continuous function of the optimization problem, and solve it by the conjugate gradient method on oblique manifold. By employing the separable structure of the optimized dictionary, a competitive result is achieved in our experiments for image de-noising.