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 ofa 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 thea priori information about a source distribution φj is solely that a non-vanishing probability for each element value φj exists only in some finite interval,aj≤φj≤φj. Bayesian image processing equations for thea priori source information that all φj are finite -∞<φj<∞ and each φj distribution has a defined mean φj and a defined variance σj are derived. The Bayesian image processing equations are also derived when thea priori source information is that all φj≥0 and that each φj distribution has a defined mean φj and a defined variance σj. The a priori source distribution constraint that a correlation exists among nearby elements is also considered. The results indicate improvement over standard methods.