Publication

Wavelets on the two-sphere and other conic sections

Pierre Vandergheynst
2007
Journal Articles

Abstract

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.

Official source

https://infoscience.epfl.ch/entities/publication/ca29647f-f6e2-496f-8dd4-42d988f10f59

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Pierre Vandergheynst
2007
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ca29647f-f6e2-496f-8dd4-42d988f10f59

About this result

Related concepts (32)

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A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly one tenth of a second.

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