Incident Photon Direction Calculation Using Bayesian Estimation for High Energy Photon Detector Systems with 3D Positioning Capability

We are developing high resolution PET systems comprising detectors that can position photon interactions in three dimensions and distinguish between individual interactions for single photons entering the system. Having these interaction locations and energies, algorithms can be employed to gain more information about the photon before interaction, including the incident direction and energy. We have developed a maximum likelihood algorithm using Bayesian methods to estimate a single photon's incident angle and interaction location, provided that it produced more than one detectable interaction. Both the phi (Phi) and theta (thetas) angle are calculated in this algorithm. The forward model was simulated using Geant4 Application for Tomographic Emission (GATE). The probabilities were calculated for a system comprised of 1 mm times 1 mm times 3 mm LSO arrays coupled to position-sensitive avalanche photodiodes with 12% energy and 2 ns coincidence time resolution. A training set of ~20,000 single photon events were used per angle to calculate the likelihood and prior probabilities for all angles in the range detected by the system (nearly 180 degrees in theta and phi). A test set of singles for particular angles produced an incoming photon angular estimation with a ~16 degrees root mean squared (RMS) deviation in both thetas and Phi.