仅用TOF-PET数据同步重建活性与衰减图，无需额外扫描。
An efficient approach with theoretical guarantees to simultaneously reconstruct activity and attenuation sinogram for TOF-PET
- 基于最大似然建立联合重建模型，利用衰减因子的指数特性。
- 数值实验显示方法收敛且抗噪，精度和效率优于现有方法。
- 适合需要避免额外扫描的临床PET成像场景。
正电子发射断层成像（PET）中，为获得体内放射性示踪剂分布的定量准确图像，必须进行衰减校正。通常依赖于计算机断层成像或磁共振成像获取的衰减图。然而，该方法不仅引入了校正因子误差，还因额外扫描带来辐射剂量增加、检查时间延长，以及两次扫描间因运动导致的严重配准偏差。为此，本文基于最大似然估计，提出一种仅使用时间飞行（TOF）PET发射数据同时重建活性与衰减投影数据的新数学模型。特别地，充分利用衰减校正因子的指数形式，并在模型中引入特定掩膜区域内活性总量的约束。进一步证明了该模型的适定性，包括解的存在性、唯一性和稳定性。设计交替更新算法求解该模型，并分析其收敛性。最后，多种TOF-PET发射数据的数值实验表明，所提方法具有数值收敛性与强抗噪能力，在精度与效率上优于若干先进方法，具备自主衰减校正能力。
原文摘要 · Abstract (English)
In positron emission tomography (PET), it is indispensable to perform attenuation correction in order to obtain the quantitatively accurate activity map (tracer distribution) in the body. Generally, this is carried out based on the estimated attenuation map obtained from computed tomography or magnetic resonance imaging. However, except for errors in the attenuation correction factors obtained, the additional scan not only brings in new radiation doses and/or increases the scanning time but also leads to severe misalignment induced by various motions during and between the two sequential scans. To address these issues, based on maximum likelihood estimation, we propose a new mathematical model for simultaneously reconstructing the activity and attenuation sinogram from the time-of-flight (TOF)-PET emission data only. Particularly, we make full use of the exclusively exponential form for the attenuation correction factors, and consider the constraint of a total amount of the activity in some mask region in the proposed model. Furthermore, we prove its well-posedness, including the existence, uniqueness and stability of the solution. We propose an alternating update algorithm to solve the model, and also analyze its convergence. Finally, numerical experiments with various TOF-PET emission data demonstrate that the proposed method is of numerical convergence and robust to noise, and outperforms some state-of-the-art methods in terms of accuracy and efficiency, and has the capability of autonomous attenuation correction.
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