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Sifting convolution on the sphere

Roddy, PJ; McEwen, JD; (2021) Sifting convolution on the sphere. IEEE Signal Processing Letters , 28 pp. 304-308. 10.1109/LSP.2021.3050961. Green open access

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A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the adoption of an alternative translation operator on the sphere. This translation operator follows by analogy with the Euclidean translation when viewed in harmonic space. The sifting convolution satisfies a variety of desirable properties that are lacking in alternate definitions, namely: it supports directional kernels; it has an output which remains on the sphere; and is efficient to compute. An illustration of the sifting convolution on a topographic map of the Earth demonstrates that it supports directional kernels to perform anisotropic filtering, while its output remains on the sphere.

Type: Article
Title: Sifting convolution on the sphere
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/LSP.2021.3050961
Publisher version: https://doi.org/10.1109/LSP.2021.3050961
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: Convolution, 2-sphere, spherical harmonics
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/10120737
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