A Novel Nonlocal QuadraticMRF Prior Model for Positron Emission Tomography

Bayesian approaches, or maximum a posteriori (MAP) methods, have been accepted as an effective solution to overcome the ill-posed problem of such image reconstructions as positron emission tomography (PET) image reconstruction. Based on Bayesian theory, prior information of the objective image is imposed on image reconstruction to suppress noise. Generally, the information in most of prior models is from a simply weighted differences between the pixel densities in a small local neighborhood, so it can only provide limit prior information for reconstruction. In this paper, a novel nonlocal Markov random fields (MRF) prior, which is able to exploit global information in image using large neighborhoods and a new weighting method, is proposed. Relevant experiments about the proposed prior´s application in PET are illustrated. Results and comparisons with other priors proved the proposed nonlocal prior´s good performance in both lowering noise effect and preserving edges