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In this paper, we provide a precise mathematical model of crystal-to-crystalresponse which is used to generate the white image - a necessary compensationmodel needed to overcome the physical limitations of the PET scanner. Wepresent a closed-form solution, as well as several accurate approximations, dueto the complexity of the exact mathematical expressions. We prove,experimentally and analytically, that the difference between the bestapproximations and real crystal-to-crystal response is insignificant. Theobtained responses are used to generate the white image compensation model. Itcan be written as a single closed-form expression making it easy to implementin known reconstruction methods. The maximum likelihood expectationmaximization (MLEM) algorithm is modified and our white image model isintegrated into it. The modified MLEM algorithm is not based on the systemmatrix, rather it is based on ray-driven projections and back-projections. Thecompensation model provides all necessary information about the system.Finally, we check our approach on synthetic and real data. For the real-worldacquisition, we use the Raytest ClearPET camera for small animals and the NEMANU 4-2008 phantom. The proposed approach overperforms competitive,non-compensated reconstruction methods.

Accurate 2D Reconstruction for PET Scanners based on the Analytical White Image Model