Regularization over-complete dictionary learning with application to image denoising

In recent years there has been a growing interest in the study of sparse representation of image signals. The sparse representation may represent efficiently the geometrical characteristics of the images with the redundancy of over-complete dictionary. The paper proposes a dictionary-learning method that can optimize it with regularized technique. Firstly the method uses the orthogonal-matching pursuit algorithm to obtain the sparse representation solutions of image patches. Secondly the solutions are used to train the dictionary with regularized optimization. Then the alternating minimizations are kept between above two steps until the difference between the sparse representations and the image satisfied a convergence criterion. The maximum posteriori probability is used to realize global optimization for image de-noising through the prior of sparse representation base the learned dictionary. Experiments results show the effect of the method.