Bayesian nonparametric mrf and entropy estimation for robust image filtering

Abstract

We introduce an 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 complemented using Márkov random fields, for instance the Semi-Huber Markov random field (SHMRF), which is used as prior information into the Bayesian rule, and the principal objective of it is to eliminate those effects caused by the excessive smoothness on the reconstruction process of signals which are rich in discontinuities. Accordingly to the hypothesis made for the present work, it is assumed a limited knowl- edge 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 new Maximum a posteriori (MAP) robust estimators, and considering that real systems are always exposed to continuous perturbations of unknown nature. Some promising results have been obtained from two new MAP entropy estimators (MAPEE) for the case of robust image filtering, where such results have been compared with respect to the classical median image filter.