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

2015/02/23 by Holman, Sean, Uhlmann, Gunther · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.06545

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 ∘ 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 in dimension three or higher.

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