Comparison of Two Image Denoising Approaches Based on Compressive Sensing Principles

Starting from the realistic assumption that digital images are highly concentrated in the domain of the two-dimensional discrete cosine transform (2D-DCT), we have exploited principles from the compressive sensing (CS) theory to build up a blind denoising framework for the detection and removal of outliers. Namely, we have developed two techniques, both of which use the fact that pixels are linear combinations of sparse coefficients, and that the disturbances degrade the concentration of the image. One of the techniques directly uses minimization of concentration measure of the image to detect the positions of corrupted pixels, which is followed by compressive sensing reconstruction. The second technique uses RANSAC-based automatic selection of pixels that are likely not corrupted, and are further considered as available measurements. The selection is performed based on the CS principles. In this paper, we present a short comparative analysis of these techniques based on numerical experiments.