Bayesian reconstructions with PDE image model for emission tomography

The aim of the present study was to investigate a new type of Bayesian reconstruction method which utilizes partial differential equations (PDE) image models as a prior. PDE image models are very popular in image restoration and segmentation. Our method introduces such models to emission tomography reconstruction by using Bayesian one step late (OSL) algorithm and an OS acceleration one. In a PDE based model, the image can be viewed as the solution of an evolutionary differential equation. It can be thought as a descent of an energy function which entitled us to use PDE models in Bayesian reconstruction. In this paper, three different PDE models are studied, two of them are based on anisotropic diffusion model, and another is based on a complex diffusion model. All of them have the properties of edge-preserving and denoising as the latest median root prior (MRP). We validated the effectiveness of the method using a Zubal phantom in numerical experiments and compared it to the classical MLEM and MRP reconstruction. The results show that the proposed PDE model method is better than the MLEM and the MRP reconstruction methods in visualization, bias and variance, and are more suitable for OS acceleration than MRP.