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
Julkaistu sarjassa
Journal of Fourier Analysis and ApplicationsTekijät
Päivämäärä
2020Oppiaine
MatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse ProblemsTekijänoikeudet
© 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.
Julkaisija
Springer; BirkhäuserISSN Hae Julkaisufoorumista
1069-5869Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/41671248
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Rahoittaja(t)
Suomen AkatemiaRahoitusohjelmat(t)
Huippuyksikkörahoitus, SA; Akatemiahanke, SALisätietoja rahoituksesta
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).Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
On Radon transforms on compact Lie groups
Ilmavirta, Joonas (American Mathematical Society, 2016)We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to S 1 nor to S 3 . This is true for both smooth functions and ... -
On Radon Transforms on Tori
Ilmavirta, Joonas (Springer US, 2015) -
Spectral multipliers and wave equation for sub-Laplacians : lower regularity bounds of Euclidean type
Martini, Alessio; Müller, Detlef; Nicolussi Golo, Sebastiano (European Mathematical Society - EMS - Publishing House GmbH, 2023)Let L be a smooth second-order real differential operator in divergence form on a manifold of dimension n. Under a bracket-generating condition, we show that the ranges of validity of spectral multiplier estimates of ... -
A fast Fourier transform based direct solver for the Helmholtz problem
Toivanen, Jari; Wolfmayr, Monika (John Wiley & Sons, 2020)This article is devoted to the efficient numerical solution of the Helmholtz equation in a two‐ or three‐dimensional (2D or 3D) rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is ... -
Abel transforms with low regularity with applications to x-ray tomography on spherically symmetric manifolds
Hoop, Maarten V de; Ilmavirta, Joonas (Institute of Physics, 2017)We study ray transforms on spherically symmetric manifolds with a piecewise C 1,1 metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of L 2 functions on such manifolds. We also prove ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.