©Monte Carlo simulation of radiological imaging systems and the recovery of the Poisson distribution
The Monte Carlo (MC) method is impracticable for simulating the physical processes of particle transport in three-dimensional imaging systems without the use of variance reduction (VR) techniques. As a consequence of VR, not photon counts but weights are accumulated which do not generate a Poisson mixture. In this paper, we analyze MC simulated data regarding a) the type of distribution generated, b) the problem of Poisson mixture recovery, c) quantitative MC and d) a stopping criteria for MC simulations. In order to perform this investigation, a MC simulation program which includes photon-specific forced detection/interaction VR techniques is used. By computing generalized linear model estimates and moments of simulated distributions, we found that there exists a scaling factor which scales any uni-variate un-attenuated distribution into a corresponding Poisson distribution. If attenuation is present, we extend the simulated exponential mixture by an un-attenuated population and use the moments of this reference sample to calculate a scaling factor which recovers a complete finite Poisson mixture. The presented results could increase the potential applicability of MC simulations in nuclear medicine by performing quantitative simulations and by reducing computational load by a count-based stopping criteria. As a further result of this investigation, we confirmed that the error introduced by the included VR techniques is marginal for the simulated systems.
