In this paper, we propose a new method for impulse noise removal from images. It uses the sparsity of images in the Discrete Cosine Transform (DCT) domain. The zeros in this domain give us the exact mathematical equation to reconstruct the pixels tha
t are corrupted by random-value impulse noises. The proposed method can also detect and correct the corrupted pixels. Moreover, in a simpler case that salt and pepper noise is the brightest and darkest pixels in the image, we propose a simpler version of our method. In addition to the proposed method, we suggest a combination of the traditional median filter method with our method to yield better results when the percentage of the corrupted samples is high.
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. Inpainting, the
process of reconstructing lost or deteriorated parts of images or videos, is an interesting application which can be handled by suitably decomposition of an image through combination of overcomplete dictionaries. This paper addresses a novel technique of such a decomposition and investigate that through inpainting of images. Simulations are presented to demonstrate the validation of our approach.
