3D Filtering of Images Corrupted by Additive-Multiplicative Noise

A novel method for filtering images contaminated by mixed (additive-multiplicative) noise is substantiated and implemented for the first time. The method includes several stages: the formation of similar structures in 3D space, homomorphic transformation, a 3D filtering approach based on a sparse representation in the discrete cosine transform space, inverse homomorphic transformation, and final post-processing that involves bilateral filtering and the reconstruction of edges and details. A physical interpretation of the filtering procedure under mixed noise conditions is given, and a filtering block diagram is developed. Numerous experiments based on the developed method have confirmed its superiority in term of conventional criteria, such as the structural similarity index measure and the peak signal-to-noise ratio, as well as in term of visual image quality via human perception.