Khalid, Z;
Durrani, S;
Kennedy, RA;
Wiaux, Y;
McEwen, JD;
(2016)
Gauss-Legendre Sampling on the Rotation Group.
IEEE Signal Processing Letters
, 23
(2)
pp. 207-211.
10.1109/LSP.2015.2503295.
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Abstract
We propose a Gauss-Legendre quadrature based sampling on the rotation group for the representation of a band-limited signal such that the Fourier transform (FT) of a signal can be exactly computed from its samples. Our figure of merit is the sampling efficiency, which is defined as a ratio of the degrees of freedom required to represent a band-limited signal in harmonic domain to the number of samples required to accurately compute the FT. The proposed sampling scheme is asymptotically as efficient as the most efficient scheme developed very recently. For the computation of FT and inverse FT, we also develop fast algorithms of complexity similar to the complexity attained by the fast algorithms for the existing sampling schemes. The developed algorithms are stable, accurate and do not have any pre-computation requirements. We also analyse the computation time and numerical accuracy of the proposed algorithms and show, through numerical experiments, that the proposed Fourier transforms are accurate with errors on the order of numerical precision.
| Type: | Article |
|---|---|
| Title: | Gauss-Legendre Sampling on the Rotation Group |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/LSP.2015.2503295 |
| Publisher version: | http://dx.doi.org/10.1109/LSP.2015.2503295 |
| Language: | English |
| Additional information: | Copyright © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. |
| Keywords: | Signal processing algorithms, Complexity theory, Fourier transforms, Algorithm design and analysis, Accuracy, Harmonic analysis, Polynomials, sampling, Band-limited signals, SO(3), Fourier transform, rotation group |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices 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/1520600 |
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