Probabilistic Modeling of Photon Interaction Chains in a Silicon Detector

Abstract

Compton camera imaging relies on the positions and energies of multiple photon interactions recorded in the detector. In silicon detectors that resolve individual interactions, these measurements do not directly provide the causal interaction order, and in nuclear medicine applications the photon may also have scattered in the object before entering the detector. We present a probabilistic model for photon interaction chains in a silicon detector and use it for two inference tasks at the event level: interaction order inference and classification of primary versus object-scattered photons. The model combines photon transport based on Compton scattering and attenuation with a detector response model. It is evaluated on Monte Carlo data for monoenergetic point sources at 140~keV and 511~keV, with and without a cylindrical water phantom. For interaction chains of length two to four, the maximum a posteriori order estimate gives high accuracy in the case without a phantom, exceeding 0.95 for all chain lengths at 511~keV, and decreasing with increasing phantom radius. The gap between the two highest posterior order probabilities provides a confidence measure for the ordering estimate and can be used to increase accuracy at the cost of reduced retention. For scatter classification, likelihood-ratio testing yields receiver operating characteristic curves with area under the curve above 0.85 across all phantom radii considered. These results support the use of probabilistic modeling of measured interaction sequences for inference directly at the event level, and show that both interaction ordering and scatter discrimination can be treated within a common framework.