Bayesian Filtering and Some Markovian Random Fields for Image Restoration

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. The Bayesian methodology is based on the prior knowledge of some information that allows an e±cient 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. A comparison between the new introduced scheme and other three existent schemes, for the cases of noise ¯ltering and image deblurring, is presented. Results showed a satisfactory performance and the effectiveness of the proposed estimator.