Practical wavelet design on the sphere

F. Guilloux (1, 2, 3) , G. Faÿ (4) , J.-F. Cardoso (1, 2)

1 APC (UMR_7164) - AstroParticule et Cosmologie
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 APC-Gravitation - APC - Gravitation

We address the question of designing isotropic analysis functions on the sphere which are perfectly limited in the spectral domain and optimally localized in the spatial domain. This work is motivated by the need of localized analysis tools in domains where the data is lying on the sphere, \eg{} the science of the Cosmic Microwave Background. Our construction is derived from the localized frames introduced by Narcowich, Petrushev, Ward, 2006. The analysis frames are optimized for given applications and compared numerically using various criteria.

Keywords: Wavelets onthe sphere; wavelet design; CMB analysis; Slepian concentration problem; statistical criterion

Domains: Numerical Analysis [math.NA]; Classical Analysis and ODEs [math.CA]; Statistics [math.ST]; Statistics Theory [stat.TH]; Cosmology and Extra-Galactic Astrophysics [astro-ph.CO]; Cosmology and Extra-Galactic Astrophysics [astro-ph.CO]; Astrophysics [astro-ph]

F. Guilloux, G. Faÿ, J.-F. Cardoso. Practical wavelet design on the sphere. 2007. ⟨hal-00155489⟩