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.

13 pages, 3 figures, Proceedings of Wavelets and Sparsity XV, SPIE Optics and Photonics 2013, Code is publicly available at http://www.s2dw.org/

References in corpus (5)

• Spherical Needlets for CMB Data Analysis
• Exact reconstruction with directional wavelets on the sphere
• S2LET: A code to perform fast wavelet analysis on the sphere
• Probing dark energy with steerable wavelets through correlation of WMAP and NVSS local morphological measures
• Complex data processing: fast wavelet analysis on the sphere

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