Bayesian Entropy Estimation: Applications in Robust Image Filtering

Abstract

We introduce a new approach for image filtering in a Bayesian framework, in this case the probability density function (pdf) of the likelihood function is approximated using the concept of non-parametric or kernel estimation. The method is also based on generalized Gaussian Márkov random fields (GGMRF), a class of Markov random fields which are used as prior information into the Bayesian rule, which principal objective is to eliminate those effects caused by the excessive smoothness on the reconstruction process of images which are rich in contours or edges. Accordingly to the hypothesis made for the present work, it is assumed a limited knowledge of the noise pdf, so the idea is to use a non-parametric estimator to estimate such a pdf and then apply the entropy to construct the cost function for the likelihood term. The previous idea leads to the construction of Maximum a posteriori (MAP) robust estimators, since the real systems are always exposed to continuous perturbations of unknown nature. Some promising results of three new MAP entropy estimators (MAPEE) for image filtering are presented, together with some partial concluding remarks.