Statistic-based MAP image-reconstruction from Poisson data using Gibbs priors

A statistical method for selecting the Gibbs parameter in MAP image restoration from Poisson data using Gibbs priors is presented. The Gibbs parameter determines the degree to which the prior influences the restoration. The presented method yields a MAP restored image, minimally influenced by the prior, for which a statistic falls within an appropriate confidence interval. The method assumes that a close approximation to the blurring function is known. A simple iterative feedback algorithm is presented to statistically select the parameter as the MAP image restoration is being performed. This algorithm is heuristically based on a model reference control formulation, but it requires only a minimal number of iterations for the parameter to settle to its statistically specified value. The performance of the statistical method for selecting the prior parameter and that of the iterative feedback algorithm are demonstrated using both 2-D and 3-D images