On the microlocal analysis of the geodesic x-ray transform with conjugate points

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http://hdl.handle.net/10138/307447

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Holman , S & Uhlmann , G 2018 , ' On the microlocal analysis of the geodesic x-ray transform with conjugate points ' , Journal of Differential Geometry , vol. 108 , no. 3 , pp. 459-494 . https://doi.org/10.4310/jdg/1519959623

Title: On the microlocal analysis of the geodesic x-ray transform with conjugate points
Author: Holman, Sean; Uhlmann, Gunther
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2018-03
Language: eng
Number of pages: 36
Belongs to series: Journal of Differential Geometry
ISSN: 0022-040X
URI: http://hdl.handle.net/10138/307447
Abstract: We study the microlocal properties of the geodesic X-ray transform X on a manifold with boundary allowing the presence of conjugate points. Assuming that there are no self-intersecting geodesics and all conjugate pairs are nonsingular we show that the normal operator N = X-t o X can be decomposed as the sum of a pseudodifferential operator of order -1 and a sum of Fourier integral operators. We also apply this decomposition to prove inversion of X is only mildly ill-posed when all conjugate points are of order 1, and a certain graph condition is satisfied, in dimension three or higher.
Subject: 111 Mathematics
INTEGRAL GEOMETRY
TENSOR TOMOGRAPHY
MANIFOLDS
SURFACES
WEIGHTS
FIELDS
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