On the computation of directional scale-discretized wavelet transforms on the sphere
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.
Keywords
Cite
@article{arxiv.1308.5706,
title = {On the computation of directional scale-discretized wavelet transforms on the sphere},
author = {J. D. McEwen and P. Vandergheynst and Y. Wiaux},
journal= {arXiv preprint arXiv:1308.5706},
year = {2013}
}
Comments
13 pages, 3 figures, Proceedings of Wavelets and Sparsity XV, SPIE Optics and Photonics 2013, Code is publicly available at http://www.s2dw.org/