Inversion of the exponential X-ray transform of symmetric 2-tensors

TL;DR

This paper presents a method for uniquely inverting the exponential X-ray transform of certain symmetric 2-tensor fields in two dimensions, using a Cauchy problem for a Beltrami-like equation related to A-analytic maps.

Contribution

It introduces a novel inversion technique for the exponential X-ray transform of symmetric 2-tensors based on a Beltrami-like equation approach.

Findings

Successful unique inversion in 2D convex sets

Application of A-analytic maps in tensor tomography

New mathematical framework for tensor field inversion

Abstract

A unique inversion of the exponential X-ray transform of some class of symmetric 2-tensor field in a two dimensional strictly convex set is considered. The approach to inversion is based on the Cauchy problem for a Beltrami-like equation associated with $A$-analytic maps.