2013/08/26 by J. D. McEwen, Jason D. McEwen, Pierre Vandergheynst +3
Computer Science · Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Code (set theory) #Computation #Computer science #Discrete wavelet transform #Discretization #Generalization #Image and Signal Denoising Methods #Mathematical analysis #Mathematical optimization #Mathematics #Physics #Scale (ratio) #Seismic Imaging and Inversion Techniques #Sparse and Compressive Sensing Techniques #Theoretical computer science #Wavelet #Wavelet transform #astro-ph.IM #cs.IT #math.IT
paper · pdf · doi:10.1117/12.2022889
published as Proc. SPIE 8858, Wavelets and Sparsity XV, 88580I (2013) · 13 pages, 3 figures, Proceedings of Wavelets and Sparsity XV, SPIE Optics and Photonics 2013, Code is publicly available at http://www.s2dw.org/
arxiv created 2013/08/26 · openalex publication_date 2013/09/26 · arxiv updated 2013/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.