A1 Journal article (refereed)
Fourier Analysis of Periodic Radon Transforms (2020)

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

JYU authors or editors

Publication details

All authors or editors: Railo, Jesse

Journal or series: Journal of Fourier Analysis and Applications

ISSN: 1069-5869

eISSN: 1531-5851

Publication year: 2020

Publication date: 24/07/2020

Volume: 26

Issue number: 4

Article number: 64

Publisher: Springer; Birkhäuser

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s00041-020-09775-1

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/71312

Publication is parallel published: https://arxiv.org/abs/1909.00495

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.

Free keywords: Radon transform; Fourier analysis; periodic distributions; regularization

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Related projects

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 2