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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, $\Lambda_{\mathcalA,q}$, of a hyperbolic equation on a Riemannian manifold $(M,g)$. We proveuniqueness of the one-form $\mathcal A$ up to the natural gauge, under weakregularity conditions on $\mathcal A,q$ and under the assumption that $(M,g)$is simple. Under an additional regularity assumption, we also derive uniquenessof the scalar function $q$. The proof is based on the geometric opticconstruction and inversion of the light ray transform extended as a FourierIntegral Operator to non-smooth parameters and functions.

Recovery of non-smooth coefficients appearing in anisotropic wave equations