Abstract
The 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.
Highlights
The use of powerful methods proposed in the seventies under the name of Bayesian estimation [1]–[3], are nowadays essential at least in the cases of image filtering, segmentation and restoration [4]
The idea is based on a robust scheme which could be adapted to reject outliers, tackling situations where noise is present in different forms during the acquisition process [5]–[12]
Some image analysis and processing tasks involve the filtering or image recovery x after it passes by a degradation process giving the observed image y (see Eqs. (1) and (3))
Summary
The use of powerful methods proposed in the seventies under the name of Bayesian estimation [1]–[3], are nowadays essential at least in the cases of image filtering, segmentation and restoration (e.g. image deblurring) [4]. The modellig, when using MRF, takes into account such spatial interaction and it was introduced and formalized by Besag [1], where the powerfulness of these statistical tools is shown (as well as in pioneering works [2, 3, 13, 14]) Combining both kinds of information in an statistical framework, the restoration is led by an estimation procedure given the maximum a posteriori of the true images when the distortion functionals are known. The proposed semi-Huber is compared with respect to the generalized Gaussian MRF introduced in [13, 14], the Welch, and Tukey potential functions with granularity control. The potential function meets all requirements imposed by conditions (8)
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