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Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds
Published online by Cambridge University Press: 12 September 2018
Abstract
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.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 1 , January 2020 , pp. 29 - 41
- Copyright
- Copyright © Cambridge Philosophical Society 2018
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