Deep Learning reconstruction with uncertainty estimation for $γ$
  photon interaction in fast scintillator detectors
Geoffrey Daniel Mohamed Bahi Yahiaoui Claude Comtat Sebastien Jan Olga Kochebina Jean-Marc Martinez Viktoriya Sergeyeva Viatcheslav Sharyy Chi-Hsun Sung Dominique Yvon
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.