Complex data processing: fast wavelet analysis on the sphere

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.

20 pages, 5 figures, JFAA style, paper invited to J. Fourier Anal. and Applic

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• 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
• Statistical challenges in the analysis of Cosmic Microwave Background radiation
• Wavelets and wavelet-like transforms on the sphere and their application to geophysical data inversion
• On the computation of directional scale-discretized wavelet transforms on the sphere
• Introducing Mexican needlets for CMB analysis: Issues for practical applications and comparison with standard needlets
• Poisson wavelets on $n$-dimensional spheres
• Sifting Convolution on the Sphere
• Band-limited localized Parseval frames and Besov spaces on compact homogeneous manifolds
• Spherical framelets from spherical designs
• Tail Behaviour of Mexican Needlets