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 be effective noise suppression, while also maintaining sharp edges without oscillations. This feature makes it particularly attractive for the reconstruction of positron emission tomography (PET) where the aim is to identify the shape of objects 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 has been tested on simulated, real phantom data. Comparison studies with conventional filtered backprojection (FBP) method and Huber prior clearly demonstrate that the proposed GG-Prior performs better in lowering the noise, preserving the image edge and in higher signal noise ratio (SNR) condition.