Bayesian image processing of data from constrained source distributions-I. non-valued, uncorrelated and correlated constraints

A series of Bayesian image processing algorithms which incorporate various classes of a priori source information in treating data which obeys Poisson and Gaussian statistics is derived using maximum entropy considerations. The standard maximum likelihood equations are shown to be a special case of Bayesian image processing when the a priori information about a source distribution φ _j is solely that a non-vanishing probability for each element value φ _j exists only in some finite interval, a _j ≤φ _j ≤φ _j . Bayesian image processing equations for the a priori source information that all φ _j are finite -∞<φ _j <∞ and each φ _j distribution has a defined mean φ _j and a defined variance σ _j are derived. The Bayesian image processing equations are also derived when the a priori source information is that all φ _j ≥0 and that each φ _j distribution has a defined mean φ _j and a defined variance σ _j . The a priori source distribution constraint that a correlation exists among nearby elements is also considered. The results indicate improvement over standard methods.