The ill posedness of the image reconstruction problem requires approached solution as a regularization of a specific criterion, in general, a penalty is imposed on the solution. The challenge is to avoid the smoothing of edges which are very important attributes of the image when it is regularized. The x-ray Tomography is classified as sensing problems for which we do not know the equipment measurement transfer function so it is considered as an ill posed inverse problem. Many studies have been developed to solve this problem, among them the Bayesian inference which aims at smoothing artifact in image. The problem for Bayesian methods is the edge penalization. In this work, we first present a fuzzy inference model for the edge preservation. Under this condition, we show that it is possible to find the best global solution to the problem by introducing genetic algorithm optimization (GA).