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This study introduces the TRIO algorithm, a Bayesian maximum a posteriori inference method for reconstructing images from three-photon events resulting from ortho-positronium decay. By integrating time-based trilateration, energy-based reconstruction, and a physics-informed prior, TRIO significantly enhances image accuracy, achieving a mean position error of 1.62 cm鈥攁pproximately half that of traditional methods. This advancement allows for improved imaging capabilities using standard radionuclides, making it a versatile tool for PET imaging in clinical settings.
TRIO achieves a remarkable reduction in imaging error, enhancing PET diagnostics by leveraging the untapped potential of three-photon annihilation events.
PET provides functional images relying on two-photon coincidences from positron-electron annihilation. In human tissue, about 40\% of annihilations are preceded by Ps formation, of which o-Ps component partially decays into three photons, with the remainder annihilating via pick-off or spin-exchange into two photons. This three-photon channel carries additional information about the surrounding micro-environment, including the three-to-two-photon yield ratio as a potential diagnostic marker. We propose the TRIO algorithm, a novel three-photon event-by-event image reconstruction algorithm formulated as a Bayesian maximum a posteriori inference problem. TRIO unifies time-based trilateration, energy-based reconstruction and, for the first time, a physics-informed prior derived from the QED description of Ps decay within a single probabilistic framework. In contrast to positronium lifetime imaging, which requires a prompt photon and is therefore restricted to specific radionuclides, TRIO relies solely on the three photons and is fully compatible with standard radionuclides such as 18F. Monte Carlo simulation modelled after the Siemens Biograph Quadra scanner demonstrates a mean position error of 1.62~cm, improving by approximately a factor of two over the time-based trilateration (3.05 cm) and by about an order of magnitude over energy-based reconstruction alone (18 cm). More importantly, the proposed Bayesian approach is compatible with existing TOF-PET scanners that can register three-photon annihilation coincidences.
