Machine Learning-Based Uncertainty Estimation for PET Gamma Interaction Localization

Abstract

Signal patterns recorded by SiPM arrays in PET scintillation detectors exhibit a highly nonlinear dependency on the gamma-ray interaction position. Effects such as Compton scattering, reflections at detector boundaries, and crystal inhomogeneities increase the uncertainty of position estimation. In this work, we propose a neural network-based approach that predicts the 3D interaction position and associated event-wise variance. Fully connected and convolutional models are trained on fan-beam data of finely segmented semi-monolithic LYSO slab detectors. Training is performed per detector and spatial dimension to accommodate detector-specific response characteristics. Uncertainty estimates are obtained via Gaussian negative log-likelihood loss in regression, where the model explicitly predicts positional variances, and are derived in classification from the variance of the predicted softmax distribution. We introduce filtering strategies that reject lines of response with high predicted variance and compare them to conventional energy-based filtering. Variance filtering reduces mean absolute errors from 1.43 mm to$0.49 ~\text{mm}, 1.13 ~\text{mm}$to 0.63 mm, and 1.15 mm to 0.93 mm in the segmented, monolithic, and DOI dimensions, respectively, at 50% retention. Integrating this filtering into the reconstruction pipeline improves image quality, with PSNR increasing from 16.412 dB (no filtering) to 16.704 dB (combined variance and energy filtering), as demonstrated in HotRod phantom reconstructions. Predicted uncertainties also reveal correlations with deposited photon energy and enable new strategies for event weighting and probabilistic modelling. These findings establish variance prediction as a meaningful uncertainty proxy for PET and open up paths toward uncertaintyaware, data-driven reconstruction.

Authors 4

1. Julian Thull Aachen Institute of Imaging & Computer Vision

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute of Imaging and Computer Vision,Aachen,North Rhine-Westphalia,Germany

2. J. Remennik Aachen Institute of Imaging & Computer Vision

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute of Imaging and Computer Vision,Aachen,North Rhine-Westphalia,Germany

3. Yannick Kuhl Aachen Institute of Imaging & Computer Vision

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute of Imaging and Computer Vision,Aachen,North Rhine-Westphalia,Germany

4. Volkmar Schulz Aachen Institute of Imaging & Computer Vision

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute of Imaging and Computer Vision,Aachen,North Rhine-Westphalia,Germany