Statistical models of a priori information for image processing: Neighboring correlation constraints

A probabilistic formulation of statistical models of a priori source distribution information is presented in terms of global and local correlations of source element strengths. A Bayesian analysis considering both the a priori source distribution probabilistic models and the Poisson statistics of photon detection fluctuations is studied. The Bayesian solution determined by a system of equations that maximizes the a posteriori probability, given the measured data, is presented. A Bayesian image-processing algorithm that obtains the solution iteratively is derived by using an expectation-maximization technique. The iterative Bayesian algorithm is applied to computer-generated ideal data and to experimental phantom imaging data containing Poisson noise. Improvement in image processing with the Bayesian algorithm is demonstrated by comparing the processed images and the convergence performances of objective evaluation test functions obtained by using the Bayesian algorithm with those obtained by using the standard maximum-likelihood algorithm.