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

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 $\text{f}$ 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.