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

摘要: The basic mathematical problem behind PET is an inverse problem. Due to the inherent ill-posedness of this problem, reconstructed images will have noise and edge artifacts. A roughness penalty often imposed on solution control stabilize solution, but difficulty avoid smoothing edges. In paper, we propose two new types Bayesian one-step-late reconstruction approaches which utilize different prior regularizations: mean curvature (MC) diffusion function Gauss (GC) function. As they been studied in image processing for removing noise, these regularizations encourage preserving while are smoothed. Moreover, GC constraint can preserve smaller structures cannot be preserved by MC. simulation results show that proposed algorithms outperform quadratic total variation terms edges during emission reconstruction.