Bayesian algorithms for PET image reconstruction with mean curvature and Gauss curvature diffusion regularizations

The basic mathematical problem behind PET is an inverse problem. Due to the inherent ill-posedness of this inverse problem, the reconstructed images will have noise and edge artifacts. A roughness penalty is often imposed on the solution to control noise and stabilize the solution, but the difficulty is to avoid the smoothing of edges. In this paper, we propose two new types of Bayesian one-step-late reconstruction approaches which utilize two...