Fourier Analysis of Periodic Radon Transforms
Abstract
We study reconstruction of an unknown function from its d-plane Radon transform on the flat torus {\mathbb {T}}^n = {\mathbb {R}}^n /{\mathbb {Z}}^n when 1 \le d \le n-1. We prove new reconstruction formulas and stability results with respect to weighted Bessel potential norms. We solve the associated Tikhonov minimization problem on H^s Sobolev spaces using the properties of the adjoint and normal operators. One of the inversion formulas implies that a compactly supported distribution on the plane with zero average is a weighted sum of its X-ray data.
Main Author
Format
Articles
Research article
Published
2020
Series
Subjects
Publication in research information system
Publisher
Springer; Birkhäuser
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202008035460Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
1069-5869
DOI
https://doi.org/10.1007/s00041-020-09775-1
Language
English
Published in
Journal of Fourier Analysis and Applications
Citation
- Railo, J. (2020). Fourier Analysis of Periodic Radon Transforms. Journal of Fourier Analysis and Applications, 26(4), Article 64. https://doi.org/10.1007/s00041-020-09775-1
License
Funder(s)
Research Council of Finland
Research Council of Finland
Funding program(s)
Centre of Excellence, AoF
Academy Project, AoF
Huippuyksikkörahoitus, SA
Akatemiahanke, SA
Additional information about funding
Open access funding provided by University of Jyväskylä (JYU). This work was supported by the Academy of Finland (Center of Excellence in Inverse Modelling and Imaging, Grant Numbers 284715 and 309963).
Copyright© The Author(s) 2020