A1 Journal article (refereed)
Tensor tomography on Cartan-Hadamard manifolds (2018)

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

JYU authors or editors

Lehtonen, Jere
Railo, Jesse
Salo, Mikko

Publication details

All authors or editors: Lehtonen, Jere; Railo, Jesse; Salo, Mikko

Journal or series: Inverse Problems

ISSN: 0266-5611

eISSN: 1361-6420

Publication year: 2018

Volume: 34

Issue number: 4

Pages range: 044004

Publisher: Institute of Physics

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1088/1361-6420/aaaf85

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/57389

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.

Free keywords: tensor tomography; Cartan-Hadamard manifolds

Fields of science: