A Proximal Method for Dictionary Updating in Sparse Representations

In this paper, we propose a new dictionary updating method for sparse dictionary learning. Our method imposes the ℓ₀ norm constraint on coefficients as well as a proximity regularization on the distance of dictionary modifications in the dictionary updating process. We show that the derived dictionary updating rule is a generalization of the K-SVD method. We study the convergence and the complexity of the proposed method. We also compare its performance with that of other methods.