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.
Highlights
The image restoration approaches or recuperation of an image to its original condition given a degraded image, passes by reverting the effects caused by a distortion functional which in some cases is known or must be estimated
The filtering results are promising for non-Gaussian noise, the obtained results for the Beta noise filtering confirm the robustness of the proposed approach, where the PSNR depicted in Table 2 shows the obtained improvement
The selection among the three different kernel options, permits the performance improvement of the MAP entropy estimators (MAPEE) estimators which could be classified in terms of simplicity and in terms of filtering quality
Summary
The image restoration approaches or recuperation of an image to its original condition given a degraded image, passes by reverting the effects caused by a distortion functional which in some cases is known or must be estimated. In the case of classical MAP filters, usually the additive Gaussian noise is considered, in some applications this noise is non-Gaussian [1] or unknown (with some partial knowledge) This is a source of information which imposes a key rule in the image processing context (the contextual or spatial information), that represents the likelihood function or correlation between the intensity values of a well specified neighborhood of pixels. This comparison shows the performance and the improvement of estimation results when one takes into account the influence of the bandwidth parameter h used by the classical kernel estimators, and when it is discarded by using two other nonparametric procedures.
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