A Frame Decomposition of the Funk-Radon Transform
arXiv:2303.05179 · doi:10.1007/978-3-031-31975-4_4
Abstract
The Funk-Radon transform assigns to a function defined on the unit sphere its integrals along all great circles of the sphere. In this paper, we consider a frame decomposition of the Funk-Radon transform, which is a flexible alternative to the singular value decomposition. In particular, we construct a novel frame decomposition based on trigonometric polynomials and show its application for the inversion of the Funk-Radon transform. Our theoretical findings are verified by numerical experiments, which also incorporate a regularization scheme.
arXiv comment13 pages, 3 figures
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