Optimal Isotropic Wavelets for Localized Tight Frame Representations

In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find the unique analytic solutions. In the one-...

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Bibliographic Details
Published in:IEEE signal processing letters 2015-11, Vol.22 (11), p.1918-1921
Main Authors: Ward, John Paul, Pad, Pedram, Unser, Michael
Format: Article
Language:English
Subjects:
Biomedical imaging
Calculus
Calculus of variations
Europe
Fourier transforms
localization
Simoncelli wavelets
Wavelet analysis
wavelet tight frames
Wavelet transforms
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Summary:In this letter, we aim to identify the optimal isotropic mother wavelet for a given spatial dimension based on a localization criterion. Within the framework of the calculus of variations, we specify an Euler-Lagrange equation for this problem, and we find the unique analytic solutions. In the one- and two-dimensional cases, the derived wavelets are well known.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2015.2448233