Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

$μ$-Net: ConvNext-Based U-Nets for Cosmic Muon Tomography

Li Xin Jed Lim, Ziming Qiu

TL;DR

μ-Net addresses the ill-posed 3D muon tomography problem by a two-stage deep learning pipeline that uses an MLP to predict muon trajectories and a ConvNeXt-based U-Net to map scattering points to voxel densities, trained on Geant4-simulated data. The approach achieves state-of-the-art PSNR of $17.14$ at $1024$ muons and shows robustness to momentum error and detector resolution, outperforming traditional PoCA and MLEM methods. A large-scale voxelized dataset mapping muon detections to voxels is publicly released to enable systematic benchmarking. The results indicate that deep learning can substantially improve reconstruction quality and speed for muon tomography, with practical implications for nuclear non-proliferation and archaeology.

Abstract

Muon scattering tomography utilises muons, typically originating from cosmic rays to image the interiors of dense objects. However, due to the low flux of cosmic ray muons at sea-level and the highly complex interactions that muons display when travelling through matter, existing reconstruction algorithms often suffer from low resolution and high noise. In this work, we develop a novel two-stage deep learning algorithm, $μ$-Net, consisting of an MLP to predict the muon trajectory and a ConvNeXt-based U-Net to convert the scattering points into voxels. $μ$-Net achieves a state-of-the-art performance of 17.14 PSNR at the dosage of 1024 muons, outperforming traditional reconstruction algorithms such as the point of closest approach algorithm and maximum likelihood and expectation maximisation algorithm. Furthermore, we find that our method is robust to various corruptions such as inaccuracies in the muon momentum or a limited detector resolution. We also generate and publicly release the first large-scale dataset that maps muon detections to voxels. We hope that our research will spark further investigations into the potential of deep learning to revolutionise this field.

$μ$-Net: ConvNext-Based U-Nets for Cosmic Muon Tomography

TL;DR

μ-Net addresses the ill-posed 3D muon tomography problem by a two-stage deep learning pipeline that uses an MLP to predict muon trajectories and a ConvNeXt-based U-Net to map scattering points to voxel densities, trained on Geant4-simulated data. The approach achieves state-of-the-art PSNR of at muons and shows robustness to momentum error and detector resolution, outperforming traditional PoCA and MLEM methods. A large-scale voxelized dataset mapping muon detections to voxels is publicly released to enable systematic benchmarking. The results indicate that deep learning can substantially improve reconstruction quality and speed for muon tomography, with practical implications for nuclear non-proliferation and archaeology.

Abstract

Muon scattering tomography utilises muons, typically originating from cosmic rays to image the interiors of dense objects. However, due to the low flux of cosmic ray muons at sea-level and the highly complex interactions that muons display when travelling through matter, existing reconstruction algorithms often suffer from low resolution and high noise. In this work, we develop a novel two-stage deep learning algorithm, -Net, consisting of an MLP to predict the muon trajectory and a ConvNeXt-based U-Net to convert the scattering points into voxels. -Net achieves a state-of-the-art performance of 17.14 PSNR at the dosage of 1024 muons, outperforming traditional reconstruction algorithms such as the point of closest approach algorithm and maximum likelihood and expectation maximisation algorithm. Furthermore, we find that our method is robust to various corruptions such as inaccuracies in the muon momentum or a limited detector resolution. We also generate and publicly release the first large-scale dataset that maps muon detections to voxels. We hope that our research will spark further investigations into the potential of deep learning to revolutionise this field.
Paper Structure (51 sections, 3 theorems, 14 equations, 14 figures, 4 tables, 1 algorithm)

This paper contains 51 sections, 3 theorems, 14 equations, 14 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Physical Background
  4. Problem Statement
  5. Motivation
  6. Related Work
  7. Deep Learning Methods
  8. Point Clouds.
  9. U-Net.
  10. ConvNext.
  11. IEEE BigData 2023 Cup.
  12. Traditional Algorithms
  13. Point of Closest Approach.
  14. Maximum Likelihood Expectation Maximization.
  15. Methods
  16. ...and 36 more sections

Key Result

Theorem 4.1

Suppose $f: \chi\rightarrow\mathbb{R}^p$ is a continuous set function w.r.t $d_H(\cdot,\cdot)$, such that for all $\epsilon > 0$, there exists some configuration of the model parameters $\theta$ for sufficiently large $p$or$\phi(\eta(x_i))=J_{p\times d}$ (i.e. the indicator function maps to every po where $\gamma_\theta:\mathbb{R}^{p\times c}\rightarrow\mathbb{R}^p$ is any continuous function, $h_

Figures (14)

  • Figure 1: A weakness of PoCA. Since the muon scatters more than once, the computed PoCA is not within any object.
  • Figure 2: First stage of $\boldsymbol{\mu}$-Net. The muon features (initial position, initial momentum, etc.) are passed through an MLP and placed at PoCA scattering points within a 3D volume. If they overlap, the average is taken.
  • Figure 3: Simulation setup. A scale diagram (except the voxels) illustrating the simulation setup within Geant4.
  • Figure 4: Model scaling has little impact. The PSNR of the different model sizes plotted against dosage levels. We see that for low dosages, the model size has little impact. However, at larger dosages, the impact of model size is greater.
  • Figure 5: $\boldsymbol{\mu}$-Net outperforms PoCA. The PSNR of $\mu$-Net and PoCA plotted against dosage levels. $\mu$-Net consistently outperforms PoCA over all dosages and all model sizes.
  • ...and 9 more figures

Theorems & Definitions (5)

  • Theorem 4.1
  • Theorem 1.1
  • proof
  • Theorem 1.2
  • proof