Bayesian reconstruction for positron emission tomography using MRF quadratic hybrid multi-order prior

Many methods have been considered to suppress noise effects in reconstructed images in positron emission tomography (PET) image reconstruction. Among all the methods, bayesian reconstruction, or maximum a posteriori (MAP) method, has proved its superiority over others in the regard of quality of reconstructed image. This article proposed a new type of MRF (Markov random fields) hybrid multi-order prior for Bayesian reconstruction, which combines quadratic smoothness priors of different orders. Based on the different intrinsic properties of the smoothness priors of different orders, the design of the new prior aims to make an adaptive use of the smoothness priors. The hybrid prior is able to maintain the convexity of the prior energy functional, thus guaranteeing the concavity of the whole objective posterior energy functional. Simulation experiments and comparisons proved that for PET reconstruction the new hybrid prior performs well in both lowering noise effect and preserving edges.