Uncertainty of Poisson wavelets

Abstract

Poisson wavelets are a powerful tool in analysis of spherical signals. In order to have a deeper characterization of them, we compute their uncertainty product, a quantity introduced for the first time by Narcowich and Ward in~\cite{NW96} and used to measure the trade-off between the space and frequency localization of a function. Surprisingly, the uncertainty product of Poisson wavelets tends to the minimal value in some limiting cases. This shows that in the case of spherical functions, not only Gauss kernel has this property.

15 pages

References in corpus (4)

• Continuous wavelet transforms on $n$-dimensional spheres
• Poisson wavelets on $n$-dimensional spheres
• Semi-continuous and discrete wavelet frames on $n$-dimensional spheres
• Multiresolution on n-dimensional spheres

Cited by in corpus (1)

• Uncertainty product of spherical wavelets