The attenuated ray transform on simple surfaces

TL;DR

This paper proves the injectivity of the attenuated geodesic ray transform on simple surfaces, provides a stability estimate, and develops a reconstruction method, advancing the mathematical understanding of inverse problems on such surfaces.

Contribution

It establishes injectivity, stability, and reconstruction techniques for the attenuated ray transform on simple surfaces, a significant step in inverse geometry.

Findings

Injectivity of the transform on simple surfaces

Stability estimate for the inverse problem

Reconstruction procedure developed

Abstract

We show that the attenuated geodesic ray transform on two dimensional simple surfaces is injective. Moreover we give a stability estimate and develop a reconstruction procedure.