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For the design of a high resolution PET detector based on PSPMTs (position-sensitive PMT), the insensitive area at the edge of the PSPMT normally prevents close packing of the scintillator crystals directly on the entire front face of the PSPMT. This edge-resolving problem is particularly severe for a high resolution PET system with multiple detector rings since it would cause gaps between detector rings and may lead to severe image artifacts. We have proposed a new method to solve this edge resolving problem by a dual scintillator detection method: it optically couples one scintillator at the insensitive edge of the PSPMT to another scintillator at the adjacent sensitive area; these two scintillators have different decay times. With this method, a gamma ray interaction that happens inside either scintillator can be detected, and the identification of which scintillator can be achieved by differentiating pulse shapes between the two scintillators. The feasibility of the method has been demonstrated with experiments measurements. Also, the artifacts from the missing data due to the gaps among detector rings has been investigated preliminarily with PET System Monte Carlo simulations.