Improved Impulse Noise Removal with Generalized Median Filter

The median filter is widely used for removing impulse noise in images due to its good denoising property whilst maintaining reasonably edge preservation. When the noise level is large, it can be further improved by combining with a detail-preserving regularization to ensure satisfactory edge recovery. We propose an improvement over a state-of-the-art impulse noise removal method which was demonstrated to cope well with very high impulsive noise levels. We introduce a novel generalized median filter, which is a new perspective based on latest advances in matrix decomposition and allows an explicit noise modelling. We provide comprehensive theoretical justifications for the proposed generalized median filter and demonstrate its effectiveness in recovering noisy images tempered with salt-and-pepper corruptions when combined with detail-preserving regularization over other relevant alternatives.