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We define a modified time-of-flight (TOF) filtered back projection (FBP) image reconstruction method, proposed for the Jagiellonian PET (J-PET) scanners of high temporal resolution. It is shown that TOF FBP could be represented as a sum of single-event reconstructions, each performed within a small volume in image space around the most likely position (MLP) of positronium annihilation, using TOF and filtering kernels. Such an approach, which resembles spherically-symmetric kernel density estimation (KDE), is highly scalable with the perspective of being employed for real time imaging. Using GATE (Geant4 Application for Tomographic Emission), we simulated the experiment conducted earlier for 1-mm spherical source put inside 3-layer 50-cm long J-PET prototype, eventually comparing the results. Estimated transverse spatial resolution of about 5-8 mm was achieved using TOF FBP for both simulations and real data, which is similar or better than obtained by KDE and non-TOF FBP from STIR software package. Axial resolution of similar to 20 mm was estimated for the simulations using all reconstruction methods, which is consistent with temporal properties of tube photomultipliers utilised for the readout. Substantially worse result (similar to 35 mm in axial direction for TOF FBP), obtained for the experiment, could be explained by unoptimised setup, data pre-selection and/or calibration issues.

Estimation of Spatial Resolution for 3-layer J-PET Scanner Using TOF FBP Based on Event-by-Event Approach