Title: Probabilistic Graphical Modeling approach to dynamic PET direct parametric map estimation and image reconstruction,
Abstract: In the context of dynamic emission tomography, the conventional processing
pipeline consists of independent image reconstruction of single time frames,
followed by the application of a suitable kinetic model to time activity curves
(TACs) at the voxel or region-of-interest level. The relatively new field of 4D
PET direct reconstruction, by contrast, seeks to move beyond this scheme and
incorporate information from multiple time frames within the reconstruction
task. Existing 4D direct models are based on a deterministic description of
voxels' TACs, captured by the chosen kinetic model, considering the photon
counting process the only source of uncertainty. In this work, we introduce a
new probabilistic modeling strategy based on the key assumption that activity
time course would be subject to uncertainty even if the parameters of the
underlying dynamic process were known. This leads to a hierarchical Bayesian
model, which we formulate using the formalism of Probabilistic Graphical
Modeling (PGM). The inference of the joint probability density function arising
from PGM is addressed using a new gradient-based iterative algorithm, which
presents several advantages compared to existing direct methods: it is flexible
to an arbitrary choice of linear and nonlinear kinetic model; it enables the
inclusion of arbitrary (sub)differentiable priors for parametric maps; it is
simpler to implement and suitable to integration in computing frameworks for
machine learning. Computer simulations and an application to real patient scan
showed how the proposed approach allows us to weight the importance of the
kinetic model, providing a bridge between indirect and deterministic direct
methods.