On the computation of directional scale-discretized wavelet transforms on the sphere

We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented struc- ture in data defined on the sphere. Furthermore, scale-discretized wavelets allow in practice the exact synthesis of a signal from its wavelet coefficients. We present exact and efficient algorithms to compute the scale-discretized wavelet transform of band-limited signals on the sphere. These algorithms are implemented in the publicly avail- able S2DW code. We release a new version of S2DW that is parallelized and contains additional code optimizations. Note that scale-discretized wavelets can be viewed as a directional generalization of needlets. Finally, we outline future improvements to the algorithms presented, which can be achieved by exploiting a new sampling theorem on the sphere developed recently by some of the authors.


Published in:
Proceedings of SPIE Volume 8858, 8858
Presented at:
Wavelets and Sparsity XV, San Diego, August 26-29, 2013
Year:
2013
Publisher:
SPIE
Keywords:
Laboratories:




 Record created 2013-07-06, last modified 2018-09-13

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