A Variational Bayesian inference method for parametric imaging of PET data.

In dynamic Positron Emission Tomography (PET) studies, compartmental models provide the richest information on the tracer kinetics of the tissue. Inverting such models at the voxel level is however quite challenging due to the low signal-to-noise ratio of the time activity curves. In this study, we propose the use of a Variational Bayesian (VB) approach to efficiently solve this issue and thus obtain robust quantitative parametric maps. VB was adapted to the non-uniform noise distribution of PET data. Moreover, we propose a novel hierarchical scheme to define the model parameter priors directly from the images in case such information are not available from the literature, as often happens with new PET tracers. VB was initially tested on synthetic data generated using compartmental models of increasing complexity, providing accurate (%bias<2%±2%, root mean square error<15%±5%) parameter estimates. When applied to real data on a paradigmatic set of PET tracers (L-[1-11C]leucine, [11C]WAY100635 and [18F]FDG), VB was able to generate reliable parametric maps even in presence of high noise in the data (unreliable estimates<11%±5%).