Joint Bayesian PET reconstruction algorithm using a quadratic hybrid multi-order prior

To overcome the ill-posed problem of image reconstruction with noisy detected data in PET reconstruction, Bayesian reconstruction or maximum a posteriori (MAP) method has its superiority over others with regard to image quality and convergence. Based on Markov Random Fields (MRF) and Bayesian reconstruction theory, quadratic membrane (QM) prior and quadratic plate (QP) prior function differently for different objective surfaces with different properties. It is reasonable to believe that a hybrid prior which combines the two quadratic prior can work better than just using one prior alone. In this paper, a MRF quadratic hybrid prior multi-order model is proposed. A threshold estimation method based on statistical classification is devised to facilitate a selectively utilization of QM prior, QP prior in the quadratic hybrid multi-order QHM) prior. Application of the proposed QHM prior in PET reconstruction with joint estimation algorithm is also given. Visional and quantitative comparisons of the results of experiments prove the new hybrid prior's good performance in lowering noise effect and preserving edges for PET reconstruction.