Complex Data Processing: Fast Wavelet Analysis on the Sphere

2007/04/10 by Yves Wiaux, Y. Wiaux, J. D. McEwen +2 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Data Compression Techniques #Algorithm #Artificial intelligence #Computer science #Data processing #Formalism (music) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Pattern recognition (psychology) #Wavelet #Wavelet transform #astro-ph #math-ph #math.MP

paper · pdf · doi:10.1007/s00041-006-6917-9

published as J. Fourier Anal. and Applic. 13 (2007) 477 · 20 pages, 5 figures, JFAA style, paper invited to J. Fourier Anal. and Applic

openalex publication_date 2007/04/10 · arxiv created 2007/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the plane and on the sphere. Two fast algorithms are also presented for the analysis of signals on the sphere with steerable wavelets.

Citations

• The design and use of steerable filters
• A high-significance detection of non-Gaussianity in theWMAP5-yr data using directional spherical wavelets
• First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Preliminary Maps and Basic Results
• Correspondence Principle between Spherical and Euclidean Wavelets
• Cosmological Applications of a Wavelet Analysis on the Sphere
• Computing Fourier Transforms and Convolutions on the 2-Sphere
• Quantum Theory of Angular Momentum

Cited by

• Poisson Wavelets on n n -Dimensional Spheres
• On the computation of directional scale-discretized wavelet transforms on the sphere