Wavelets on the two-sphere and other conic sections

We review the construction of the continuous wavelet transform (CWT) on the two-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, obtaining various types of discrete frames, first half-continuous ones (only the scale is discretized), then ful ly discrete ones. Next we describe the construction of a CWT on the upper sheet of two-sheeted hyperboloid. Final ly we give some indications on the CWT on a paraboloid and we introduce a unified approach to the CWT on conic sections.


Published in:
Journal of Fourier Analysis and Applications, 13, 4, 369-386
Year:
2007
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 Record created 2006-10-31, last modified 2018-12-03

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