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

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.

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