Tensor tomography for a set of generalized V-line transforms in $\mathbb{R}^2$

TL;DR

This paper investigates the mathematical problem of reconstructing symmetric tensor fields in two-dimensional space from generalized V-line transform data, employing two different techniques for different data sets.

Contribution

It introduces a study of generalized V-line transforms for tensor fields and develops methods for their reconstruction in the plane.

Findings

Reconstruction of tensor fields from V-line transforms demonstrated.

Two different techniques successfully applied for different data sets.

Theoretical framework established for tensor tomography in 2D.

Abstract

We study a set of generalized V-line transforms, namely longitudinal, mixed, and transverse V-line transforms, of a symmetric $m$-tensor field in $\mathbb{R}^2$. The goal of this article is to recover a symmetric $m$-tensor field $\textbf{f}$ supported in a disk $\mathbb{D}_R$, with radius $R$ and centered at the origin, by a combination of the aforementioned generalized V-line transforms, using two different techniques for different sets of data.