A semiclassical approach to geometric X-ray transforms in the presence of convexity

TL;DR

This paper introduces a semiclassical method for inverting geometric X-ray transforms that simplifies previous approaches by removing the need for small domains and layer stripping under natural geometric conditions.

Contribution

The paper presents a novel semiclassical approach to invert geometric X-ray transforms, improving stability and injectivity results without domain size restrictions.

Findings

Eliminates the need for small domains in inversion

Provides stable inversion under natural geometric conditions

Simplifies the inversion process using semiclassical analysis

Abstract

In this short paper we introduce a variant of the approach to inverting the X-ray transform that originated in the author's work with Uhlmann. The new method is based on semiclassical analysis and eliminates the need for using sufficiently small domains and layer stripping for obtaining the injectivity and stability results, assuming natural geometric conditions are satisfied.