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arXiv · 1308.5706

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

J. D. McEwen·P. Vandergheynst·Y. Wiaux
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Abstract

We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented structure 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 available 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.

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J. D. McEwen, P. Vandergheynst, Y. Wiaux. 2013-08-26. On the computation of directional scale-discretized wavelet transforms on the sphere. https://doi.org/10.1117/12.2022889

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