We present a method and preliminary results of the image reconstruction in the Jagiellonian PET tomograph. Using GATE (Geant4 Application for Tomographic Emission), interactions of the 511 keV photons with a cylindrical detector were generated. Pairs of such photons, flying back-to-back, originate from e+e- annihilations inside a 1-mm spherical source. Spatial and temporal coordinates of hits were smeared using experimental resolutions of the detector. We incorporated the algorithm of the 3D Filtered Back Projection, implemented in the STIR and TomoPy software packages, which differ in approximation methods. Consistent results for the Point Spread Functions of ~5/7,mm and ~9/20, mm were obtained, using STIR, for transverse and longitudinal directions, respectively, with no time of flight information included.
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