Raw-Hit Muon Tomography: A Measurement-Domain Formulation for Cosmic-Ray Muon Imaging

Abstract

Cosmic-ray muon tomography records only a few detector-plane crossings per particle, while material information enters through stochastic scattering and energy loss along the path. Most pipelines first compress these hits to a per-muon scattering summary and assign a nominal momentum, moving the inverse problem away from the raw measurements. We introduce Raw-Hit Muon Tomography (RHMT), a measurement-domain formulation built directly on detector hits. RHMT-S projects out the unknown straight track and evaluates the remaining hit contrast with a Fermi--Eyges covariance; marginalizing the unknown scattering scale gives a blank-calibrated Student-$t$-type likelihood. RHMT-E fits the hits in a six-plane magnetic spectrometer to estimate each muon's log momentum loss and models it as a Bethe--Bloch line integral of the electron-density-related contrast $ρZ/A$. In a controlled Geant4 benchmark, RHMT-S improves the mean ROC-AUC over four-plane scattering baselines ($0.84$--$0.86$ versus $0.81$ for ASR), and RHMT-E provides a separate energy-loss contrast for aluminium, where scattering contrast is weak.