Generalized Gibbs priors based positron emission tomography reconstruction

Bayesian methods have been widely applied to the ill-posed problem of image reconstruction. Typically the prior information of the objective image is needed to produce reasonable reconstructions. In this paper, we propose a novel generalized Gibbs prior (GG-Prior), which exploits the basic affinity structure information in an image. The motivation for using the GG-Prior is that it has been shown to suppress noise effectively while capturing sharp edges without oscillations. This feature makes it particularly attractive for those applications of Positron Emission Tomographic (PET) where the objective is to identify the shape of objects (e.g.tumors) that are distinguished from the background by sharp edges. We show that the standard paraboloidal surrogate coordinate ascent (PSCA) algorithm can be modified to incorporate the GG-Prior using a local linearized scheme in each iteration process. The proposed GG-Prior MAP reconstruction algorithm based on PSCA algorithm has been tested on simulated, real phantom data. Comparisons the GG-Prior model with other existing prior model clearly demonstrate that the proposed GG-Prior performs better in lowering the noise, and preserving the edge and detail in the image.