A probabilistic framework for uncertainty quantification in positron emission particle tracking

Positron Emission Particle Tracking (PEPT) is an imaging method for the visualization of fluid motion, capable reconstructing three-dimensional trajectories small tracer particles suspended in nearly any medium, including fluids that are opaque or contained within vessels. The labeled radioactively, and their positions reconstructed from detection pairs back-to-back photons emitted by positron annihilation. Current reconstruction algorithms heuristic typically based on minimizing distance between so-called lines response (LoRs) joining points, while accounting spurious LoRs generated scattering. Here we develop a probabilistic framework Bayesian inference uncertainty quantification particle PEPT data. We formulate likelihood describing emission noisy as Poisson process space LoRs. derive formulas corresponding rate case cylindrical detectors, both undetected scattered photons. illustrate formulation quantifying position single circular path data state-of-the-art Monte Carlo simulations. results show how observation time $\Delta t$ can be chosen optimally to balance need large number with requirement displacement imposed assumption static over t$. further this relaxed inferring jointly velocity particle, clear benefits accuracy reconstruction.