Deep Learning reconstruction with uncertainty estimation for $γ$ photon interaction in fast scintillator detectors

TL;DR

This work tackles 2D gamma interaction localization in a PbWO4 monolithic scintillator for PET and adds event-specific uncertainty estimates via a Density Neural Network. By modeling the outputs with a truncated Gaussian likelihood, the method respects detector boundaries and provides per-event uncertainties, which are then leveraged (via weighting) to improve reconstruction precision, especially near edges. Across grid and uniform test datasets, the approach outperforms baseline physics-based methods and conventional MSE in terms of robust edge recovery and calibrated uncertainty, with potential to enhance PET image quality and ToF-PET performance. The methodology is generalizable to other sensor-domain regression tasks and can be extended to include depth, energy, and time reconstruction, offering a framework for uncertainty-aware event-level imaging improvements.

Abstract

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.

Figures (11)

• Figure 1: Left: Schematic diagram of the ClearMind detection module. A 511 keV gamma-ray interaction in the crystal produces scintillation and Cherenkov photons that are converted by the photocathode to photoelectrons. These photoelectrons are then multiplied by the MCP-PMT and induce signals on the transmission lines (TLs). Signals from the left and right ends of each TL are amplified by 40 dB amplifiers and digitized by a SAMPIC module. Right: Transmission lines Printed Circuit Board (PCB). The axis $x$ and $y$ corresponds to the coordinate system that we use to locate the interaction position.
• Figure 2: Set of pulses as registered by the SAMPIC waveshape recorder for a 511 keV energy deposit. For clarity purpose, only the pulses registered on one side of the transmission lines are shown (half of the set).
• Figure 3: Waveforms registered on one trigered line $l$. Red and green lines are the left $F_{l,\mathrm{Left}}(t_{j})$ and right $F_{l,\mathrm{Right}}(t_{j})$, time shifted, registered pulses shapes. Black line shows the time difference waveform $F_{l,\mathrm{Left}}(t_{j}) - F_{l,\mathrm{Right}}(t_{j})$. We identify on this line three pulses clusters at 4.6 ns, 6 ns and 8.5 ns. For each of them, the time difference curve shows a bipolar shape, correlated to the position of each photoelectron charge induction along the readout line.
• Figure 4: Simulated sources - Expected positions
• Figure 5: Grid reconstruction by the different methods