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We are developing cadmium zinc telluride detectors with three-dimensional photon positioning capabilities for high-resolution PET imaging. These detectors exhibit high spatial resolution (1 mm), energy resolution (2.5% full width at half maximum for 511 keV photons), and the ability to resolve individual Compton interactions within the detector. Using these measurements, non-coincident single photons can be reconstructed by estimating the incoming direction of the photon using the kinematics of Compton scatter within the detector. In this paper, we investigated image reconstruction methods for combining two different types of measurements: conventional coincidence photon events and non-coincident single photon events. We introduce a new image reconstruction method that uses a Bayesian projector function. Using Monte Carlo simulated data generated by GATE (Geant4), we showed that this new approach has the potential to improve contrast and resolution with comparable signal-to-noise ratio.