... This paper presents the theory of the pixon, the fundamental unit of picture information, and its application to Bayesian image reconstruction. Examples of the applications of these methods to artificial and real data are presented. These examples demonstrate that pixon-based methods produce results superior to both pure Goodness-of-Fit (i.e. Maximum Likelihood) methods and the best examples of Maximum Entropy methods. Keywords: Bayesian Methods, Pixons, Image Modeling . Introduction . ...