Microlocal analysis of a restricted ray transform on symmetric $m$-tensor fields in $\mathbb{R}^n$

TL;DR

This paper investigates the microlocal inversion of a restricted ray transform on symmetric tensor fields in Euclidean space, showing how to recover the wavefront set of the solenoidal component from incomplete line data passing through a curve.

Contribution

It introduces a microlocal inversion method for the restricted ray transform on symmetric tensor fields, handling incomplete data from lines passing through a curve.

Findings

Wavefront set of the solenoidal component can be recovered.

Inversion is possible modulo a known singular error term.

The method applies to incomplete line data in Euclidean space.

Abstract

We study the microlocal inversion of the ray transform on symmetric $m$-tensor fields restricted to all lines passing through a curve in $\mathbb{R}^{n}$. From this incomplete data, we show that the wavefront set of the solenoidal component of a symmetric $m$-tensor field can be recovered modulo a known singular error term.