Inverse source problems in transport via attenuated tensor tomography

TL;DR

This paper investigates inverse source problems in transport theory, establishing injectivity results for the attenuated X-ray transform on tensor fields in simple geometries, with implications for imaging and tomography.

Contribution

It provides new injectivity results and explicit inversion methods for the attenuated X-ray transform on tensor fields in variable index of refraction geometries.

Findings

Injectivity modulo gauge established for certain inverse problems

Constructive results for inversion of the attenuated X-ray transform

Connections made to explicit inversion on simple Riemannian surfaces

Abstract

We establish results for the injectivity and injectivity modulo gauge of certain inverse source problems in transport on a simply connected domain with variable index of refraction inducing a 'simple geometry'. The model given by radiative transfer involves a scattering kernel with finite harmonic content in the deviation angle. The results on injectivity are constructive, and they are connected to the explicit inversion (modulo kernel) of the attenuated X-ray transform on tensor fields on simple Riemannian surfaces.