Roddy, PJ;
McEwen, JD;
(2021)
Sifting convolution on the sphere.
IEEE Signal Processing Letters
, 28
pp. 304-308.
10.1109/LSP.2021.3050961.
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Abstract
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-pp.ucl.ac.uk/id/eprint/10120737 |
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