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

Jean-Pierre Antoine; Daniela Roşca

doi:10.1117/12.781312

25 April 2008 The wavelet transform on the two-sphere and related manifolds: a review

Jean-Pierre Antoine, Daniela Roşca

Proceedings Volume 7000, Optical and Digital Image Processing; 70000B (2008) https://doi.org/10.1117/12.781312
Event: SPIE Photonics Europe, 2008, Strasbourg, France

Abstract

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.

Citation Download Citation

Jean-Pierre Antoine and Daniela Roşca "The wavelet transform on the two-sphere and related manifolds: a review", Proc. SPIE 7000, Optical and Digital Image Processing, 70000B (25 April 2008); https://doi.org/10.1117/12.781312

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