Tensor tomography on Cartan-Hadamard manifolds
Abstract
We study the geodesic x-ray transform on Cartan–Hadamard manifolds, generalizing the x-ray transforms on Euclidean and hyperbolic spaces that arise in medical and seismic imaging. We prove solenoidal injectivity of this transform acting on functions and tensor fields of any order. The functions are assumed to be exponentially decaying if the sectional curvature is bounded, and polynomially decaying if the sectional curvature decays at infinity. This work extends the results of Lehtonen (2016 arXiv:1612.04800) to dimensions $n \geqslant 3$ and to the case of tensor fields of any order.
Main Authors
Format
Articles
Research article
Published
2018
Series
Subjects
Publication in research information system
Publisher
Institute of Physics
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201803191758Use this for linking
Review status
Peer reviewed
ISSN
0266-5611
DOI
https://doi.org/10.1088/1361-6420/aaaf85
Language
English
Published in
Inverse Problems
Citation
- Lehtonen, J., Railo, J., & Salo, M. (2018). Tensor tomography on Cartan-Hadamard manifolds. Inverse Problems, 34(4), 044004. https://doi.org/10.1088/1361-6420/aaaf85
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Funder(s)
Academy of Finland
European Commission
Academy of Finland
Funding program(s)
Huippuyksikkörahoitus, SA
EU:n 7. puiteohjelma (FP7)
Akatemiahanke, SA
Centre of Excellence, AoF
FP7 (EU's 7th Framework Programme)
Academy Project, AoF
Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Education and Culture Executive Agency (EACEA). Neither the European Union nor EACEA can be held responsible for them.
Additional information about funding
All authors were supported by the Academy of Finland (Finnish Centre of Excellence in Inverse Problems Research, grant numbers 284715 and 309963), and JL and MS were also partly supported by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007–2013) / ERC Starting Grant agreement no 307023.
Copyright© 2018 IOP Publishing Ltd. This is a final draft version of an article whose final and definitive form has been published by IOP Publishing Ltd. Published in this repository with the kind permission of the publisher.