This article presents a physics-informed deep learning method for the quantitative estimation of the spatial coordinates of gamma interactions within a monolithic scintillator, with a focus on Positron Emission Tomography (PET) imaging. A Density Neural Network approach is designed to estimate the 2-dimensional gamma photon interaction coordinates in a fast lead tungstate (PbWO4) monolithic scintillator detector. We introduce a custom loss function to estimate the inherent uncertainties associated with the reconstruction process and to incorporate the physical constraints of the detector. This unique combination allows for more robust and reliable position estimations and the obtained results demonstrate the effectiveness of the proposed approach and highlights the significant benefits of the uncertainties estimation. We discuss its potential impact on improving PET imaging quality and show how the results can be used to improve the exploitation of the model, to bring benefits to the application and how to evaluate the validity of the given prediction and the associated uncertainties. Importantly, our proposed methodology extends beyond this specific use case, as it can be generalized to other applications beyond PET imaging.

翻译：本文提出了一种物理信息驱动的深度学习方法，用于定量估计单片闪烁体内伽马相互作用的空间坐标，重点关注正电子发射断层成像（PET）应用。我们设计了一种密度神经网络方法，用于在快速钨酸铅（PbWO4）单片闪烁体探测器中估计二维伽马光子相互作用坐标。引入了一种自定义损失函数，以估计重建过程中固有的不确定性，并融入探测器的物理约束。这种独特的组合使得位置估计更加稳健可靠，实验结果证明了所提出方法的有效性，并突显了不确定性估计的重要优势。我们讨论了该方法对提升PET成像质量的潜在影响，展示了结果如何用于改进模型利用、为应用带来益处，以及如何评估给定预测及其相关不确定性的有效性。重要的是，所提出的方法不仅限于这一特定用例，能够推广到PET成像之外的其他应用。