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

By Sean Holman and Gunther Uhlmann

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.Peer reviewe

Topics: 111 Mathematics, INTEGRAL GEOMETRY, TENSOR TOMOGRAPHY, MANIFOLDS, SURFACES, WEIGHTS, FIELDS
Publisher: 'International Press of Boston'
Year: 2018
DOI identifier: 10.4310/jdg/1519959623
OAI identifier: oai:helda.helsinki.fi:10138/307447
Journal:

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