# Recovery of non-smooth coefficients appearing in anisotropic wave equations

## TL;DR

This paper establishes the unique recovery of non-smooth coefficients in anisotropic wave equations on simple Riemannian manifolds using geometric optics and light ray transform inversion, advancing inverse problem theory.

## Contribution

It proves uniqueness of a non-smooth one-form and scalar function from boundary measurements, extending previous results to less regular coefficients and non-smooth settings.

## Key findings

- Unique recovery of non-smooth one-form and scalar function
- Extension of light ray transform inversion to non-smooth parameters
- Applicability to simple Riemannian manifolds

## Abstract

We study the problem of unique recovery of a non-smooth one-form $\mathcal A$ and a scalar function $q$ from the Dirichlet to Neumann map, $\Lambda_{\mathcal A,q}$, of a hyperbolic equation on a Riemannian manifold $(M,g)$. We prove uniqueness of the one-form $\mathcal A$ up to the natural gauge, under weak regularity conditions on $\mathcal A,q$ and under the assumption that $(M,g)$ is simple. Under an additional regularity assumption, we also derive uniqueness of the scalar function $q$. The proof is based on the geometric optic construction and inversion of the light ray transform extended as a Fourier Integral Operator to non-smooth parameters and functions.