Uncertainty-aware gamma interaction localization and reconstruction in PET.

Abstract

Background: Precise localization of gamma-ray interactions inside scintillation detectors is essential for high-resolution positron emission tomography (PET) imaging. Although machine learning methods have demonstrated strong performance in gamma interaction positioning, most existing approaches do not quantify event-level uncertainty, leaving valuable information unused.

Purpose: This study quantifies event-wise positional uncertainties in gamma interaction localization and demonstrates its utility for improving PET image quality through uncertainty-aware filtering and weighting.

Methods: We employ machine learning to perform gamma interaction positioning in a semi-monolithic scintillation detector block with overall dimensions of $48.4\times 48.3\times 10{\mathrm{mm}}^3$ , corresponding to the planar-segmented, planar-monolithic, and depth-of-interaction (DOI) directions. We train multilayer perceptrons (MLPs) and convolutional neural networks (CNNs) using silicon photomultiplier (SiPM) light spread measurements as network inputs. Regression models were trained using a Gaussian negative log-likelihood to jointly estimate gamma interaction coordinates and event-wise positional variance. Classifiers were evaluated, which inferred event-level uncertainty from the variance of the predicted spatial probability distribution. These uncertainty estimates primarily reflect variability in detector response and photon statistics, corresponding to aleatoric uncertainty. Regression and classification objectives were explored through task-specific hyperparameter optimizations. All 24 semi-monolithic detectors of a proof-of-concept PET system were calibrated in the segmented, monolithic, and depth-of-interaction (DOI) dimensions using collimated fan-beam irradiations of each detector. For each detector, a dataset of 880,000 events per spatial dimension was acquired and randomly split into 60% training, 20% validation, and 20% test sets, with models trained and evaluated independently across seven detectors. The resulting calibration models were then applied to reprocess measurements of imaging phantoms. Performance was evaluated using the mean absolute error (MAE) on the fan-beam dataset and the median distance between reconstructed lines of response (LORs) and known point-source locations measured within the scanner. Predicted variances were further integrated into the time-of-flight ordered-subsets expectation maximization (TOF-OSEM) reconstruction via event-level filtering and LOR weighting to assess spatial resolution and noise propagation.

Results: Across architectures, uncertainty-aware models achieved high positioning accuracy. CNN classifiers provided the best planar performance, while CNN regressors performed best for depth-of-interaction (DOI) estimation. Variance- and energy-based filtering substantially improved positioning accuracy, reducing the MAE to $0.47\mathrm{mm}$ in the monolithic and $0.83\mathrm{mm}$ in the DOI dimension. Variance- and energy-aware filtering also improved the LOR precision, reducing the median LOR distance to as low as $0.98\mathrm{mm}$ . In image reconstruction, filtering and weighting improved image quality, with filtering providing the strongest gains and enabling visualization of $0.8\mathrm{mm}$ rods with a peak-to-valley ratio (PVR) of 1.184. These approaches increased the signal-to-noise ratio (SNR) but also the coefficient of variation (COV), consistent with reduced effective sensitivity and amplified Poisson noise.

Conclusions: Event-level uncertainty estimation enables meaningful filtering and weighting strategies that improve interaction positioning and reconstructed PET image quality. Despite the trade-off between enhanced spatial resolution and increased noise, the uncertainty-aware framework introduces a new reconstruction parameter that can be exploited to improve image quality and potentially support more reliable quantitative PET imaging.