Frames of directional wavelets on n-dimensional spheres

Frames of directional wavelets on n-dimensional spheres

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 cons...

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Bibliographic Details
Published in:Applied and computational harmonic analysis Vol. 43; no. 1; pp. 148 - 161
Main Author: Iglewska-Nowak, I.
Format: Journal Article
Language:English
Published: Elsevier Inc 01-07-2017
Subjects:
Approximate identities
Frames
n-Spheres
Spherical wavelets
Spherical wavelets
Frames
Approximate identities
42C40
n-Spheres
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Summary: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.
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2016.01.004