The X-ray transform for a generic family of curves

TL;DR

This paper investigates the weighted X-ray transform on compact manifolds, establishing generic injectivity and stability results for a broad class of curves when the conormal bundle condition is satisfied.

Contribution

It introduces new injectivity and stability results for the X-ray transform over a generic family of curves on manifolds, under conormal bundle coverage conditions.

Findings

Proves generic injectivity of the weighted X-ray transform.

Establishes a stability estimate under conormal bundle coverage.

Results apply to a broad class of curves on compact manifolds.

Abstract

We study the weighted integral transform on a compact manifold with boundary over a smooth family of curves $\Gamma$. We prove generic injectivity and a stability estimate under the condition that the conormal bundle of $\Gamma$ covers $T^*M$.