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A Frame Decomposition of the Funk-Radon Transform

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arxiv 2303.05179 v1 pith:PU4EGV4E submitted 2023-03-09 math.NA cs.NAmath.FA

A Frame Decomposition of the Funk-Radon Transform

Michael Quellmalz , Lukas Weissinger , Simon Hubmer , Paul D.Erchinger This is my paper
classification math.NA cs.NAmath.FA
keywords decompositionfunk-radontransformframespherealongalternativeapplication
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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.

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