  Positron emission tomography (PET) is a classical imaging technique to
reconstruct the mass distribution of a radioactive material. If the mass
distribution is static, this essentially leads to inversion of the X-ray
transform. However, if the mass distribution changes temporally, the
measurement signals received over time (the so-called listmode data) belong to
different spatial configurations. We suggest and analyse a Bayesian approach to
solve this dynamic inverse problem that is based on optimal transport
regularization of the temporally changing mass distribution. Our focus lies on
a rigorous derivation of the Bayesian model and the analysis of its properties,
treating both the continuous as well as the discrete (finitely many detectors
and time binning) setting.
