Complex noise suppression using a sparse representation and 3D filtering of images

A novel method for the filtering of images corrupted by complex noise composed of randomly distributed impulses and additive Gaussian noise has been substantiated for the first time. The method consists of three main stages: the detection and filtering of pixels corrupted by impulsive noise, the subsequent image processing to suppress the additive noise based on 3D filtering and a sparse representation of signals in a basis of wavelets, and the concluding image processing procedure to clean the final image of the errors emerged at the previous stages. A physical interpretation of the filtering method under complex noise conditions is given. A filtering block diagram has been developed in accordance with the novel approach. Simulations of the novel image filtering method have shown an advantage of the proposed filtering scheme in terms of generally recognized criteria, such as the structural similarity index measure and the peak signal-to-noise ratio, and when visually comparing the filtered images.