1. Introduction The present chapter illustrates the use of some recent alternative methods to deal with digital image filtering and restoration. This collection of methods is inspired on the use of Markov Random Fields (MRF), which introduces prior knowledge of information that will allow, more efficiently, modeling the image acquisition process. The methods based on the MRF are analyzed and proposed into a Bayesian framework and their principal objective is to eliminate noise and some effects caused by excessive smoothness on the reconstruction process of images which are rich in contours or edges. In order to preserve object edges into the image, the use of certain convexity criteria into the MRF is proposed obtaining adequate weighting of cost functions in cases where discontinuities are remarked and, even better, for cases where such discontinuities are very smooth. Some image analysis and processing tasks involve the filtering or image recovery  x (e.g. restoration) after x passes by a degradation process giving the observed image y (see equation (1)). Such degradation covers the noise perturbations, blurring effects due to focus of the acquisition system lenses or to the bandwidth capacity, and other artifacts that may be added to the correct data. The use of Bayesian methods proposed in the seventies (Besag, 1974; 1986; Geman and Geman, 1984), are nowadays essential at least in the cases of image segmentation and image restoration (Andrews and Hunt, 1977). The basic idea of these methods is to construct a Maximum a posteriori (MAP) estimate of the modes or so called estimator of true images by using MRF into a Bayesian framework. The general approach 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 (Bertaux et al., 2004; Cai et al, 2008; Chan et al., 2006; Durand and Nikolova, 2006a;b; Nikolova, 2006; 2005; Nikolova and Ng, 2005; Pan and Reeves, 2006). The restoration or recuperation of an image to its original condition given a degraded image, passes thus by reverting the effects caused by noise or / and a distortion function. In fact, the degradation characteristic is a crucial source of information and its mathematical A Comparative Study of Some Markov Random Fields and Different Criteria Optimization in Image Restoration José I. De la Rosa, Jesús Villa, Ma. Auxiliadora Araiza, Efrén González and Enrique De la Rosa Laboratorio de Procesamiento Digital de Señales Facultad de Ingeniería Eléctrica, Universidad Autónoma de Zacatecas Mexico 8 www.intechopen.com