Frames of directional wavelets on $n$-dimensional spheres

Abstract

The major goal of the paper is to prove that discrete frames of (directional) wavelets derived from an approximate identity exist. Additionally, a kind of energy conservation property is shown to hold in the case when a wavelet family is not its own reconstruction family. Although an additional constraint on the spectrum of the wavelet family must be satisfied, it is shown that all the wavelets so far defined in the literature possess this property.

15 pages

References in corpus (4)

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

Cited by in corpus (4)

• Tight framelets and fast framelet filter bank transforms on manifolds
• Spherical framelets from spherical designs
• Uncertainty product of spherical wavelets
• Angular multiselectivity with spherical wavelets