Accurate 2D Reconstruction for PET Scanners based on the Analytical White Image Model
This work addresses the physical limitations of PET scanners for medical imaging, particularly in small animal studies, by providing a more accurate reconstruction method, though it appears incremental as it modifies an existing algorithm.
The paper tackled the problem of accurate 2D reconstruction for PET scanners by developing a precise mathematical model for crystal-to-crystal response to generate a white image compensation model, resulting in improved performance over non-compensated methods as validated on synthetic and real data.
In this paper, we provide a precise mathematical model of crystal-to-crystal response which is used to generate the white image - a necessary compensation model needed to overcome the physical limitations of the PET scanner. We present a closed-form solution, as well as several accurate approximations, due to the complexity of the exact mathematical expressions. We prove, experimentally and analytically, that the difference between the best approximations and real crystal-to-crystal response is insignificant. The obtained responses are used to generate the white image compensation model. It can be written as a single closed-form expression making it easy to implement in known reconstruction methods. The maximum likelihood expectation maximization (MLEM) algorithm is modified and our white image model is integrated into it. The modified MLEM algorithm is not based on the system matrix, rather it is based on ray-driven projections and back-projections. The compensation model provides all necessary information about the system. Finally, we check our approach on synthetic and real data. For the real-world acquisition, we use the Raytest ClearPET camera for small animals and the NEMA NU 4-2008 phantom. The proposed approach overperforms competitive, non-compensated reconstruction methods.