Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds
Ilmavirta, J., Lehtonen, J., & Salo, M. (2020). Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds. Mathematical Proceedings of the Cambridge Philosophical Society, 168 (1), 29-41. doi:10.1017/S0305004118000543
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We show that on a two-dimensional compact nontrapping manifold with strictly convex boundary, a piecewise constant function is determined by its integrals over geodesics. In higher dimensions, we obtain a similar result if the manifold satisfies a foliation condition. These theorems are based on iterating a local uniqueness result. Our proofs are elementary.