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Slepian Scale-Discretised Wavelets on the Sphere

Roddy, Patrick J; McEwen, Jason D; (2023) Slepian Scale-Discretised Wavelets on the Sphere. IEEE Transactions on Signal Processing , 70 pp. 6142-6153. 10.1109/tsp.2022.3233309. Green open access

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Abstract

This work presents the construction of a novel spherical wavelet basis designed for incomplete spherical datasets, i.e. datasets which are missing in a particular region of the sphere. The eigenfunctions of the Slepian spatial-spectral concentration problem (the Slepian functions) are a set of orthogonal basis functions which are more concentrated within a defined region. Slepian functions allow one to compute a convolution on the incomplete sphere by leveraging the recently proposed sifting convolution and extending it to any set of basis functions. Through a tiling of the Slepian harmonic line, one may construct scale-discretised wavelets. An illustration is presented based on an example region on the sphere defined by the topographic map of the Earth. The Slepian wavelets and corresponding wavelet coefficients are constructed from this region and are used in a straightforward denoising example.

Type: Article
Title: Slepian Scale-Discretised Wavelets on the Sphere
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/tsp.2022.3233309
Publisher version: https://doi.org/10.1109/tsp.2022.3233309
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Wavelet transforms, Convolution, Harmonic analysis, Eigenvalues and eigenfunctions, Wavelet domain, Standards, Inverse problems
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Space and Climate Physics
URI: https://discovery.ucl.ac.uk/id/eprint/10164545
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