Application of the Wasserstein Distance to identify inter-crystal scatter in a light-sharing depth-encoding PET detector

In finely-pixelated PET detectors, Compton-scatter of the incident annihilation photon generates a spatial blurring known as inter-crystal scatter (ICS). This blurring is particularly exacerbated in light-sharing depth-encoding detectors - a design that is otherwise an excellent candidate for cost-effective high-resolution imaging. Accurate identification of ICS in these detectors is crucial to establishing their viability as a high-performance imaging platform. We therefore developed a pair of data-driven ICS identification algorithms - a contour-based method that utilizes only the centroid position of the event and a Wasserstein distanced-based method that incorporates the full dimensionality of the detector response pattern. As a proof-of-concept, both algorithms were tested on experimental calibration data acquired from the Prism-PET brain scanner, and each event was classified as ICS or photoelectric (PE). Results of the classification were evaluated by inspecting distributions of the energy and the DOI estimation parameter (w) for both ICS and PE-classified events. Excellent classification performance was demonstrated by both methods via suppression of high-energy components of the energy distribution and shaping of the DOI-parameter distribution to align with expectations from the Beer-Lambert relation. However, the Wasserstein-based classification outperformed the contour method, indicating the importance of utilizing the full dimensionality of the input detector response data.