Microlocal inversion of a 3-dimensional restricted transverse ray transform of symmetric $m$-tensor fields

TL;DR

This paper demonstrates that a symmetric tensor field in three dimensions can be reconstructed from its restricted transverse ray transform along lines intersecting a specific curve, using microlocal analysis techniques.

Contribution

It introduces a microlocal inversion method for the restricted transverse ray transform of symmetric tensor fields in 3D, recovering the field up to known singular and smoothing terms.

Findings

Tensor fields can be reconstructed up to known singularities.

The method applies to lines intersecting a fixed smooth curve satisfying Kirillov-Tuy condition.

Microlocal analysis provides the theoretical foundation for the inversion.

Abstract

We study the problem of inverting a restricted transverse ray transform to recover a symmetric $m$-tensor field in $\mathbb{R}^3$ using microlocal analysis techniques. More precisely, we prove that a symmetric $m$-tensor field can be recovered up to a known singular term and a smoothing term if its transverse ray transform is known along all lines intersecting a fixed smooth curve satisfying the Kirillov-Tuy condition.