  Poisson distributed measurements in inverse problems often stem from Poisson
point processes that are observed through discretized or finite-resolution
detectors, one of the most prominent examples being positron emission
tomography (PET). These inverse problems are typically reconstructed via
Bayesian methods. A natural question then is whether and how the reconstruction
converges as the signal-to-noise ratio tends to infinity and how this
convergence interacts with other parameters such as the detector size. In this
article we carry out a corresponding variational analysis for the exemplary
Bayesian reconstruction functional from [arXiv:2311.17784,arXiv:1902.07521],
which considers dynamic PET imaging (i.e.\ the object to be reconstructed
changes over time) and uses an optimal transport regularization.
