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arXiv · 1711.10392

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

Victor Palamodov
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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.

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Victor Palamodov. 2017-11-28. Exact inversion of Funk-Radon transforms with non-algebraic geometries. https://arxiv.org/abs/1711.10392

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