MAP entropy estimation: applications in robust image filtering

Abstract

International audienceWe introduce a new approach for image filtering in a Bayesian framework. In this case the probability density function (pdf) of thelikelihood function is approximated using the concept of non-parametric or kernel estimation. The method is based on the generalizedGaussian Markov random fields (GGMRF), a class of Markov random fields which are used as prior information into the Bayesian rule, whichprincipal objective is to eliminate those effects caused by the excessive smoothness on the reconstruction process of images which arerich 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 thelikelihood term. The previous idea leads to the construction of Maximum a posteriori (MAP) robust estimators, since the real systems arealways exposed to continuous perturbations of unknown nature. Some promising results of three new MAP entropy estimators (MAPEE) forimage filtering are presented, together with some concluding remarks