Optimized Bayes variational regularization prior for 3D PET images.

A new prior for variational Maximum a Posteriori regularization is proposed to be used in a 3D One-Step-Late (OSL) reconstruction algorithm accounting also for the Point Spread Function (PSF) of the PET system. The new regularization prior strongly smoothes background regions, while preserving transitions. A detectability index is proposed to optimize the prior. The new algorithm has been compared with different reconstruction algorithms such as 3D-OSEM+PSF, 3D-OSEM+PSF+post-filtering and 3D-OSL with a Gauss-Total Variation (GTV) prior. The proposed regularization allows controlling noise, while maintaining good signal recovery; compared to the other algorithms it demonstrates a very good compromise between an improved quantitation and good image quality.