Chan, JYH;
Leistedt, B;
Kitching, TD;
McEwen, JD;
(2016)
Second-Generation Curvelets on the Sphere.
IEEE Transactions on Signal Processing
, 65
(1)
pp. 5-14.
10.1109/TSP.2016.2600506.
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Abstract
Curvelets are efficient to represent highly anisotropic signal content, such as a local linear and curvilinear structure. First-generation curvelets on the sphere, however, suffered from blocking artefacts. We present a new second-generation curvelet transform, where scale-discretized curvelets are constructed directly on the sphere. Scale-discretized curvelets exhibit a parabolic scaling relation, are well localized in both spatial and harmonic domains, support the exact analysis and synthesis of both scalar and spin signals, and are free of blocking artefacts. We present fast algorithms to compute the exact curvelet transform, reducing computational complexity from O(L5) to O(L3 log2 L) for signals band limited at L. The implementation of these algorithms is made publicly available. Finally, we present an illustrative application demonstrating the effectiveness of curvelets for representing directional curve-like features in natural spherical images.
| Type: | Article |
|---|---|
| Title: | Second-Generation Curvelets on the Sphere |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1109/TSP.2016.2600506 |
| Publisher version: | http://doi.org/10.1109/TSP.2016.2600506 |
| Language: | English |
| Additional information: | © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, 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 components of this work in other works. |
| Keywords: | Science & Technology, Technology, Engineering, Electrical & Electronic, Engineering, Curvelets, spheres, spherical wavelets, wavelet transform, harmonic analysis, rotation group, wigner transform, WAVELET ANALYSIS, NON-GAUSSIANITY, SAMPLING THEOREM, TIGHT FRAMES, DARK ENERGY, FULL-SKY, NEEDLETS, WMAP, RESOLUTION, DISCRETIZATION |
| 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/1524186 |
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