Improved online dictionary learning for sparse signal representation

In this paper a new dictionary learning algorithm is proposed. Similar to many dictionary learning algorithms, the proposed algorithm alternates between two stages. First, sparse coding stage uses the current dictionary to obtain the sparse representation coefficients. Herein, the orthogonal matching pursuit algorithm is used for sparse coding. Second, a dictionary update stage that employs the calculated coefficients to update the dictionary and is based on iterative least squares method. The autocorrelation and the cross correlation between the sparse coding coefficients and the training data are estimated recursively by applying a forgetting factor. The variable step size which depends on the forgetting factor and autocorrelation function is derived. The simulation results indicate that representation ability of dictionaries designed by the proposed method has improved SNR compared to those designed with existing state of the art algorithms with faster convergence. Preliminary results for single image super-resolution are promising.