McEwen, JD;
Leistedt, B;
Büttner, M;
Peiris, HV;
Wiaux, Y;
(2015)
Directional spin wavelets on the sphere.
IEEE Transactions on Signal Processing
(In press).
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Abstract
We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the sphere that is able to probe the directional intensity of spin signals. Furthermore, directional spin scale-discretised wavelets support the exact synthesis of a signal on the sphere from its wavelet coefficients and satisfy excellent localisation and uncorrelation properties. Consequently, directional spin scale-discretised wavelets are likely to be of use in a wide range of applications and in particular for the analysis of the polarisation of the cosmic microwave background (CMB). We develop new algorithms to compute (scalar and spin) forward and inverse wavelet transforms exactly and efficiently for very large data-sets containing tens of millions of samples on the sphere. By leveraging a novel sampling theorem on the rotation group developed in a companion article, only half as many wavelet coefficients as alternative approaches need be computed, while still capturing the full information content of the signal under analysis. Our implementation of these algorithms is made publicly available.
Type: | Article |
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Title: | Directional spin wavelets on the sphere |
Open access status: | An open access version is available from UCL Discovery |
Publisher version: | http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp... |
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. |
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 Physics and Astronomy 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/1508538 |
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