Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds (bibtex)
by Joonas Ilmavirta, Jere Lehtonen, Mikko Salo
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.
Reference:
Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds (Joonas Ilmavirta, Jere Lehtonen, Mikko Salo), 2017. [show abstract] [hide 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. [arXiv]
Bibtex Entry:
@unpublished{piecewise-constant-xrt,
	author = {Joonas Ilmavirta and Jere Lehtonen and Mikko Salo},
	title = {{Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds}},
	month = feb,
	year = {2017},
	arxiv = {1702.07622},
	url={http://users.jyu.fi/~jojapeil/pub/piecewise-constant-xrt.pdf},
	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.}
}
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