Elahi, U;
Khalid, Z;
Kennedy, RA;
McEwen, JD;
(2018)
An Optimal-Dimensionality Sampling for Spin-sFunctions on the Sphere.
IEEE Signal Processing Letters
, 25
(10)
pp. 1470-1474.
10.1109/LSP.2018.2865676.
Preview |
Text
1809.01321v1.pdf - Accepted Version Download (381kB) | Preview |
Abstract
For the representation of spin-$s$ band-limited functions on the sphere, we propose a sampling scheme with optimal number of samples equal to the number of degrees of freedom of the function in harmonic space. In comparison to the existing sampling designs, which require ${\sim}2L^2$ samples for the representation of spin-$s$ functions band-limited at $L$, the proposed scheme requires $N_o=L^2-s^2$ samples for the accurate computation of the spin-$s$ spherical harmonic transform~($s$-SHT). For the proposed sampling scheme, we also develop a method to compute the $s$-SHT. We place the samples in our design scheme such that the matrices involved in the computation of $s$-SHT are well-conditioned. We also present a multi-pass $s$-SHT to improve the accuracy of the transform. We also show the proposed sampling design exhibits superior geometrical properties compared to existing equiangular and Gauss-Legendre sampling schemes, and enables accurate computation of the $s$-SHT corroborated through numerical experiments.
| Type: | Article |
|---|---|
| Title: | An Optimal-Dimensionality Sampling for Spin-sFunctions on the Sphere |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/LSP.2018.2865676 |
| Publisher version: | http://dx.doi.org/10.1109/LSP.2018.2865676 |
| 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: | Harmonic analysis, Transforms, Computational modeling, Numerical models, Frequency modulation, Indexes, Pins, sampling, sphere, spherical harmonics, spin-$s$functions |
| 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/10059752 |
Loading...
Loading...Loading...| 1. |  United States | 2 |
| 2. |  China | 1 |
Archive Staff Only
 |
View Item |
