Regular papers

MAP entropy estimation: applications in robust image filtering

¹ Unidad Académica de Ingeniería Eléctrica, Universidad Autónoma de Zacatecas, Antiguo Camino a la Bufa No. 1, Col. Centro. C. P. 98000, Zacatecas, Zac., México
² Instituto Tecnológico Superior de Fresnillo, Av. Tecnológico No. 2000 Col. Solidaridad, C.P. 99010 Fresnillo, Zac., México
³ Facultad de Física, Universidad Autónoma de Zacatecas, Calz. Solidaridad esquina paseo de la Bufa S/N, C. P. 98060, Zacatecas, Zac., México
⁴ École Supérieure d’ Électricité (SUPELEC), Plateau de Moulon, 3 rue Joliot Curie, 91192 Gif-sur-Yvette Cedex, France

^* ismaelrv@ieee.org

Received: 27 May 2013
Accepted: 20 June 2013

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 based on the generalized Gaussian Markov 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 concluding remarks.