X-Ray Transform in Asymptotically Conic Spaces

TL;DR

This paper investigates the geodesic X-ray transform in asymptotically conic spaces, establishing injectivity under specific geometric conditions and exploring related inverse problems involving lens data.

Contribution

It introduces new injectivity results for the X-ray transform in asymptotically conic geometries and defines a lens data framework for inverse problems.

Findings

Injectivity of the X-ray transform under non-trapping and no conjugate point conditions.

Definition and analysis of lens data for asymptotically conic metrics.

Insights into inverse problems related to geodesic data in such spaces.

Abstract

In this article, we study the properties of the geodesic X-ray transform for asymptotically Euclidean or conic Riemannian metrics and show injectivity under non-trapping and no conjugate point assumptions. We also define a notion of lens data for such metrics and study the associated inverse problem.