A Bayesian approach to PET reconstruction using image-modeling Gibbs priors: implementation and comparison

We demonstrate that (i) classical methods of image reconstruction from projections can be improved upon by considering the output of such a method as a distorted version of the original image and applying a Bayesian approach to estimate from it the original image (based on a model of distortion and on a Gibbs distribution as the prior) and (ii) by selecting an “image-modeling” prior distribution (i.e., one which is such that it is likely that a random sample from it shares important characteristics of the images of the application area) one can improve over another Gibbs prior formulated using only pairwise interactions. We illustrate our approach using simulated positron emission tomography (PET) data from realistic brain phantoms. Since algorithm performance ultimately depends on the diagnostic task being performed. We examine a number of different medically relevant figures of merit to give a fair comparison. Based on a training-and-testing evaluation strategy, we demonstrate that statistically significant improvements can be obtained using the proposed approach. We also present a statistical verification of the normality condition required for the above statistical claim