Exact inversion of Funk-Radon transforms with non-algebraic geometries

2017/11/28 by Victor Palamodov, Palamodov, Victor
Engineering · Mathematics · #3D Shape Modeling and Analysis #44A12 (Secondary) #53C65 (Primary) #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.1711.10392

openalex publication_date 2017/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Any even function defined on 2-sphere is reconstructed from its integrals over big circles by means of the classical Funk formula. For the non-geodesic Funk transform on the sphere of arbitrary dimension, there is the explicit inversion formula similar to that for the geodesic transform. A function defined on the sphere of radius one is integrated over traces of hyperplanes tangent to a sphere contained in the unit ball. This reconstruction is generalized in the paper for Riemannian hypersurfaces in an affine space.

Related

• Reconstruction of a function defined on a sphere using the Funk transform
• Reconstruction of functions on the sphere from their integrals over hyperplane sections
• On Two Families of Funk-Type Transforms
• The Fourier Transform Approach to Inversion of lambda-Cosine and Funk Transforms on the Unit Sphere
• Non-geodesic Spherical Funk Transforms with One and Two Centers