Bayesian image reconstruction using a high-order interacting MRF model

Abstract

We propose a Markov Random Field image model formulated using both low-order and high-order interactions of the pixels for piecewise smooth image reconstruction. We discuss and compare the applications of two Bayes estimators, namely the Maximum a Posteriori (MAP) estimator and the Minimum Mean Squares Error (MMSE) estimator, to Positron Emission Tomography (PET) imaging. The usefulness of the high-order interactions is demonstrated especially in the reconstruction of noisy image regions with small supports. The MAP and MMSE estimates are obtained in an efficient way by making use of the noise properties of the images obtained using the Filtered Backprojection (FBP) algorithm. We illustrate the efficacy of our overall approach by simulation experiments.