# Compton scattering tomography in translational geometries

## TL;DR

This paper introduces new mathematical results on the injectivity of Compton scattering tomography in translational geometries, with potential applications in security screening and threat detection.

## Contribution

It provides explicit inversion formulas for novel 2-D and 3-D Radon transforms related to CST in translational geometries, expanding the theoretical understanding of these imaging modalities.

## Key findings

- Proved $L^2$ injectivity for new CST geometries
- Derived explicit inversion formulas for 2-D and 3-D Radon transforms
- Generalized injectivity results to surfaces of revolution of $C^1$ curves

## Abstract

Here we present new $L^2$ injectivity results for 2-D and 3-D Compton scattering tomography (CST) problems in translational geometries. The results are proven through the explicit inversion of a new toric section and apple Radon transform, which describe novel 2-D and 3-D acquisition geometries in CST. The geometry considered has potential applications in airport baggage screening and threat detection. We also present a generalization of our injectivity results in 3-D to Radon transforms which describe the integrals of the charge density over the surfaces of revolution of a class of $C^1$ curves.