Machine learning methods for subpixel trajectory reconstruction in discretized position detectors

TL;DR

This work demonstrates that transformer-based architectures substantially improve subpixel trajectory reconstruction in discretized detectors for muon tomography, achieving an angular RMSE of $1.14^\\circ$ and a position MAE of $0.24$ cm on Geant4-simulated data, outperforming centroid, CNN, and linear methods by factors up to $2.22\\times$ in angle and $6.33\\times$ in position. The authors introduce a hybrid cell-offset transformer that mirrors the physical localization process and leverage a convolutional stem to process 8×8 energy maps, yielding near-subpixel resolution (about $3.8\\%$ of a pixel width). Comprehensive error analyses show transformer and CNN deliver tighter error distributions, reduced edge biases, and smaller tail effects, translating to more reliable muon trajectory reconstructions for tomography. The study provides a proof-of-concept with simplified geometry, outlining clear paths for experimental validation and extension to multi-plane detectors and other pixelated sensing systems.

Abstract

In this study, we demonstrate that compared with traditional centroid-based methods, machine learning methods (particularly transformer-based architectures) achieve superior subpixel position and therefore angular resolution in discretized particle detectors. Using Geant4 Monte Carlo simulated cosmic ray muon data from an 8x8 segmented scintillator detector array, we compare four reconstruction approaches: transformer neural networks, convolutional neural networks, linear regression, and energy-weighted centroids. The transformer architecture achieves the best angular reconstruction with a root mean square error of 1.14° and a position mean absolute error of 0.24 cm, representing improvements of 2.22x and 6.33x, respectively, over the centroid method. These results enable precise particle trajectory reconstruction for applications in muon tomography and cosmic ray detection.

Figures (7)

• Figure 1: Schematic of the full muon tomography detector simulated in this work. Each plane consists of an $8 \times 8$ pixelated PVT scintillator array. Muons traverse both planes, with trajectories reconstructed from energy depositions in the pixels. The green line represents the muon's trajectory and the grey lines represent scintillation radiation. A blue scale bar that represents 30 cm is included.
• Figure 2: Schematic diagram of the CNN architecture used. The network takes normalized 8×8 energy deposition maps as input and outputs continuous $(x,y)$ coordinates.
• Figure 3: Comparison of performance metrics (RMSE, MAE, and mean error) for the four reconstruction methods. Compared with the linear regression and centroid methods, the transformer and CNN achieve substantially lower errors across all metrics. The centroid method shows the poorest performance.
• Figure 4: Spatial reconstruction accuracy across the detector surface for detector plane 1. The plot compares the four reconstruction methods, showing true muon positions (markers) and reconstructed positions (arrows indicate error vectors). The transformer and CNN methods show tight clustering with minimal systematic bias, whereas the centroid method exhibits larger, spatially correlated errors, particularly near pixel boundaries.
• Figure 5: Spatial reconstruction accuracy across the detector surface for detector plane 2. Similar patterns to plane 1 are observed. ML methods achieve tight spatial accuracy, whereas the centroid method shows systematic geometric biases.