A new approach in decomposition over multiple-overcomplete dictionaries with application to image inpainting

Recently, great attention was intended toward overcomplete dictionaries and the sparse representations they can provide. In a wide variety of signal processing problems, sparsity serves a crucial property leading to high performance. Decomposition of a given signal over two or more dictionaries with sparse coefficients is investigated in this paper. This kind of decomposition is useful in many applications such as inpainting, denoising, demosaicing, speech source separation, high-quality zooming and so on. This paper addresses a novel technique of such a decomposition and investigates this idea through inpainting of images which is the process of reconstructing lost or deteriorated parts of images or videos.When samples are missed in an image, the the original sparsity level in representing coefficients is changed, so with an iterative method we can estimate the original level. Simulations are presented to demonstrate the validation of our approach.