On optimal sparsifying dictionary design with application to image inpainting

This paper deals with the design problem of optimal sparsifying dictionary where the measurement is not directly the sparse signal but disturbed by some linear operators. Similar with traditional dictionary learning problem, the design strategy is divided into two stages. The matching pursuit method is used to calculate the sparse coefficients and a new algorithm based on gradient is proposed to train the sparsifying dictionary. When being applied to image inpainting problem, the dictionary is learnt based on the corrupted image itself and the inpainting process is operated on fully overlapped patches of the image and the resulting image is obtained by averaging the recovered patches. Experiments are done to demonstrate the superiority of the proposed approach for image inpainting application.