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Wavelets and wavelet frames on the 2-sphere

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Antoine, Jean-Pierre [UCL]

We review the construction of the continuous wavelet transform (CWT) on the 2-sphere by two methods, the group-theoretical approach and the geometrical method based on conformal invariance. Then we discuss the discretization of the spherical CWT and build associated discrete wavelet frames, first half-continuous ones (only the scale is discretized), then fully discrete ones. To that effect, we generalize the notion of frame, introducing weighted and controlled frames.

Document type Contribution à ouvrage collectif (Book Chapter) – Chapitre
Access type Accès libre
Publication date 2006
Language Anglais
Host document J.Govaerts, M.N.Hounkonnou, and A.Z.Msezane (eds.) ; "Proc. Fourth Int. Workshop on Contemporary Problems in Mathematical Physics (Cotonou, Bénin, Nov. 2005)"- p. 344-362 (ISBN : 9812568530)
Publisher World Scientific (Singapore)
Publication status Publié
Affiliation UCL - SST/IRMP - Institut de recherche en mathématique et physique
Links
Bibliographic reference Antoine, Jean-Pierre. Wavelets and wavelet frames on the 2-sphere. In: J.Govaerts, M.N.Hounkonnou, and A.Z.Msezane (eds.), Proc. Fourth Int. Workshop on Contemporary Problems in Mathematical Physics (Cotonou, Bénin, Nov. 2005), World Scientific  : Singapore 2006, p. 344-362
Permanent URL http://hdl.handle.net/2078.1/75178