• kinetic modeling
• probabilistic graphical modeling
• image reconstruction
• Dynamic PET
• DCE-MRI
• Bayesian inference

This work is inspired by the search for an answer to two grand challenges affecting 4D emission tomography, namely the solution of the inverse problem of computing the rate of emission in the imaging volume in case of an extreme photon-limited regime, and the estimation of maps of pharmacokinetic parameters.
The strategy to tackle these issues proposed in this thesis is based on the idea that a unified and synergistic approach to the estimation of both dynamic activity time series and parametric maps could provide mutual benefits, by integrating the lack of measured information with predictions made by the chosen model.
Framing emission tomography imaging in the Bayesian framework via probabilistic graphical models, we are able to define a model-based approach to the design of integrated inference algorithms.
From one side, this modeling approach has shown itself able to encompass traditional literature about emission tomography image reconstruction.
From another, it provides a flexible tool to describe causal relationships between variables, and a straightforward strategy to derive inference algorithms from such a combination of graphical and probabilistic representations.
A number of different models are proposed, justified and discussed, in the light of the model-based inference framework proposed in this thesis. A comprehensive description of the phenomenon of image formation allows us to devise unified inference approaches to tackle at once and in a synergistic way the solution of multiple problems that traditionally are dealt with in a sequential way.
At the deeper level, pharmacokinetic models can be used to concisely describe in a mathematical way the physiological interactions between tissues and tracer; these interactions are responsible for determining how the injected radiotracer distributes within tissues, in space, and thus of what we eventually see in the form of images; lastly, the spatial location of radioactive molecules is the source of the measured coincidence photons on which we base our inference.
The formulations presented in this thesis are unifying in several ways, combining in a single model information from multiple domains, and attempting to unify reconstruction and kinetic modeling, tasks usually addressed with a sequential approach.
Moreover, this modeling approach is able to abstract over details that are specific of a certain imaging modality in such a way that the inference strategies developed for PET can be (quite) easily adapted to other imaging modalities that may face similar challenges (like the case of DCE-MRI discussed in this work), requiring just minor changes of the assumptions made during model-design.