Markovian Random Fields and Comparison Between Different Convex Criterion

The present work illustrates some recent alternative methods to deal with digital image reconstruction. This collection of methods are inspired on the use of a class of Markov chains best known as Markov Random Fields (MRF). All of these new methodologies are also based on the prior knowledge of some information which will permit more efficiently modeling the image acquisition process. The methods based on the MRF's are proposed and analyzed in a Bayesian framework and their 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. In order to respond to the edge preservation, the use of certain convexity criteria are proposed which will lead to obtain adequate weighting of cost functions (halfquadratic) in cases where discontinuities are remarked and, even better, for cases where such discontinuities are very smooth. The final aim is to apply these methods to problems in optical instrumentation.