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The wavelet transform on the two-sphere and related manifolds: A review

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Antoine, Jean-Pierre [UCL] Rosca, Daniela [UCL]

In a first part, we discuss several properties that seem desirable for any type of wavelet, such as smoothness, orthogonality, local support, Riesz stability, or vanishing moments. Then we review the construction of the spherical continuous wavelet transform based on the stereographic projection. Next we turn to the discrete wavelet transform. We review the various existing constructions and compare them in the light of the requirements listed above. Finally, we briefly describe the continuous wavelet transform on a two-sheeted hyperboloid and give some hints concerning the case of a general conic section.

Document type Communication à un colloque (Conference Paper) – Conférence invitée / Keynote
Publication date 2008
Language Anglais
Conference "Optical and Digital Image Processing", Strasbourg, France (7 April 2008)
Peer reviewed yes
issn 0277-786X
Host document "Optical and Digital Image Processing"- Vol. 7000, p. 70000B-1-70000B-15
Collection Proceedings of SPIE
Publisher SPIE - the international society for optical engineering (Bellingham, Wa, USA)
Publication status Publié
Affiliation UCL - SC/PHYS - Département de physique
Links
Bibliographic reference Antoine, Jean-Pierre ; Rosca, Daniela. The wavelet transform on the two-sphere and related manifolds: A review.Optical and Digital Image Processing (Strasbourg, France, 7 April 2008). In: Optical and Digital Image Processing, SPIE - the international society for optical engineering : Bellingham, Wa, USA2008, p.Vol. 7000, p. 70000B-1-70000B-15
Permanent URL http://hdl.handle.net/2078.1/67762