An explicit reconstruction algorithm for the transverse ray transform of a second rank tensor field from three axis data

TL;DR

This paper presents an explicit reconstruction algorithm for the transverse ray transform of symmetric second rank tensor fields in 3D, utilizing data from three orthogonal axes, and discusses conditions for reconstruction with fewer axes.

Contribution

It introduces a new explicit plane-by-plane filtered back-projection algorithm for tensor field reconstruction from multi-axis data, including a potential case with only two axes.

Findings

Reconstruction is possible with three axes data.

Two axes data suffices for potential tensor fields.

The algorithm is explicit and plane-by-plane.

Abstract

We give an explicit plane-by-plane filtered back-projection reconstruction algorithm for the transverse ray transform of symmetric second rank tensor fields on Euclidean 3-space, using data from rotation about three orthogonal axes. We show that in the general case two axis data is insufficient but give an explicit reconstruction procedure for the potential case with two axis data