The Light Ray transform on Lorentzian manifolds
Analysis of PDEs
2020-03-18 v1 Differential Geometry
Abstract
We study the weighted light ray transform of integrating functions on a Lorentzian manifold over lightlike geodesics. We analyze as a Fourier Integral Operator and show that if there are no conjugate points, one can recover the spacelike singularities of a function from its the weighted light ray transform by a suitable filtered back-projection.
Cite
@article{arxiv.1907.02210,
title = {The Light Ray transform on Lorentzian manifolds},
author = {Matti Lassas and Lauri Oksanen and Plamen Stefanov and Gunther Uhlmann},
journal= {arXiv preprint arXiv:1907.02210},
year = {2020}
}