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
International audienceThe present work introduces an alternative method to deal with digital image restoration into a Bayesian framework, particularly, the use of a new half-quadratic function is proposed which performance is satisfactory compared with respect to some other functions in existing literature. The bayesian methodology is based on the prior knowledge of some information that allows an efficient modelling of the image acquisition process. The edge preservation of objects into the image while smoothing noise is necessary in an adequate model. Thus, we use a convexity criteria given by a semi-Huber function to obtain adequate weighting of the cost functions (half-quadratic) to be minimized. The principal objective when using Bayesian methods based on the Markov Random Fields (MRF) in the context of image processing is to eliminate those effects caused by the excessive smoothness on the reconstruction process of image which are rich in contours or edges. A comparison between the new introduced scheme and other three existing schemes, for the cases of noise filtering and image deblurring, is presented. This collection of implemented methods is inspired of course on the use of MRFs such as the semi-Huber, the generalized Gaussian, the Welch, and Tukey potential functions with granularity control. The obtained results showed a satisfactory performance and the effectiveness of the proposed estimator with respect to other three estimators
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