Nonlocal filters for removing multiplicative noise

Abstract

In this paper, we propose nonlocal filters for removing multiplicative noise in images. The considered filters are deduced in a weighted maximum likelihood estimation framework and the occurring weights are defined by a new similarity measure for comparing data corrupted by multiplicative noise. For the deduction of this measure we analyze a probabilistic measure recently proposed for general noise models by Deledalle et al. and study its properties in the presence of additive and multiplicative noise. Since it turns out to have unfavorable properties facing multiplicative noise we propose a new similarity measure consisting of a density specially chosen for this type of noise. The properties of our new measure are examined theoretically as well as by numerical experiments. Afterwards, it is applied to define the weights of our nonlocal filters and different adaptations are proposed to further improve the results. Throughout the paper, our findings are exemplified for multiplicative Gamma noise. Finally, restoration results are presented to demonstrate the good properties of our new filters. © 2012 Springer-Verlag.