Fourier Analysis of Periodic Radon Transforms
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
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Journal of Fourier Analysis and ApplicationsAuthors
Date
2020Discipline
MatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse ProblemsCopyright
© The Author(s) 2020
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.
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Springer; BirkhäuserISSN Search the Publication Forum
1069-5869Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/41671248
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Related funder(s)
Research Council of FinlandFunding program(s)
Centre of Excellence, AoF; Academy Project, AoFAdditional 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).License
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