Reconstruction of functions on the sphere from their integrals over hyperplane sections

DOI10.1007/s13324-019-00290-1zbMath1440.44001arXiv1810.09017OpenAlexW2896716807WikidataQ125875312 ScholiaQ125875312MaRDI QIDQ2284977

Boris Rubin

Publication date: 15 January 2020

Published in: Analysis and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09017

zbMATH Keywords

Radon transformcosine transforminversion formulasFunk transformSemyanistyi integrals

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Radon transform (44A12)

Related Items (10)

Support theorems for Funk-type isodistant Radon transforms on constant curvature spaces ⋮ On the spherical slice transform ⋮ Vector fields with zero flux through circles of fixed radius on $\mathbb{H}^2$ ⋮ ON ONE ZALCMAN PROBLEM FOR THE MEAN VALUE OPERATOR ⋮ Reconstruction of the Cauchy-Riemann operator by complex integration operators along circles ⋮ Non-central Funk-Radon transforms: single and multiple ⋮ Inversion of a Convolution Operator Associated with Spherical Means ⋮ Non-geodesic Spherical Funk Transforms with One and Two Centers ⋮ On two families of Funk-type transforms ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An inversion formula for the spherical transform in \(S^{2}\) for a special family of circles of integration
• Reconstructing a function on the sphere from its means along vertical slices
• Funk, cosine, and sine transforms on Stiefel and Grassmann manifolds
• Semyanistyi's integrals and Radon transforms on matrix spaces
• Radon transforms and Gegenbauer-Chebyshev integrals. II: Examples
• Radon, cosine and sine transforms on real hyperbolic space
• Inversion formulas for the spherical Radon transform and the generalized cosine transform.
• The Funk-Radon transform for hyperplane sections through a common point
• Recovering functions defined on the unit sphere by integration on a special family of sub-spheres
• Intersection bodies and generalized cosine transforms
• Funk-Minkowski transform and spherical convolution of Hilbert type in reconstructing functions on the sphere
• A generalization of the Funk–Radon transform
• Integral Geometry and Radon Transforms
• A Radon-type transform arising in photoacoustic tomography with circular detectors: spherical geometry
• Reconstruction from Integral Data
• Sur la transformation de Radon de la sphère $S\sp d$
• Exact reconstruction in photoacoustic tomography with circular integrating detectors II: Spherical geometry
• Analytic and group-theoretic aspects of the Cosine transform
• Semyanistyi fractional integrals and Radon transforms
• The Radon Transform and Medical Imaging

This page was built for publication: Reconstruction of functions on the sphere from their integrals over hyperplane sections