Sparse representation and dictionary learning based on alternating parallel coordinate descent

Recently, sparse representations via an overcomplete dictionary has become a major field of research in signal processing. Much efforts have been focused on the development of dictionary learning algorithms so that the sparse representation of signals can be efficiently performed. In this paper, we propose a method for learning a signal dependent overcomplete dictionary. This is accomplished by posing the sparse representation of signals as a problem of matrix factorization with a sparsity constraint. By generalizing the conventional coordinate descent method, we develop a so-called sparse alternating parallel coordinate descent (SAPCD) algorithm, which is structured by iteratively solving the two optimal problems, the learning process of the dictionary and the estimating process of the coefficients for constructing the signals. Numerical experiments demonstrate that the proposed algorithm performs better than the famous K-SVD algorithm and several other algorithms for comparison.