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Proceedings Paper

Theory and implementation of the sine-Gabor wavelet frame
Author(s): Sergio Schuler
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Paper Abstract

We unify two widely used image processing kernels, a Gaussian's first derivative (Canny's step edge detector) and the modulated Gaussian, by introducing a nonorthogonal wavelet family: the sine-Gabor functions. This parametrized wavelet trades off frame rightness and time-frequency localization; generating a `snug' frame of Gaussian's first derivatives and a `loose' frame of modulated Gaussians with nearly optimum time-frequency localization (easily tightened using voices). We review the discretization of the wavelet transform and its efficient computation when using nonorthogonal wavelets. We show that there exists wavelets (including the sine-Gabor function) for which the discrete wavelet transform is not invertible, describe how to evade this problem by modifying the strategy for selecting discrete filters, and show for the sine-Gabor wavelet that desirable properties such as constant phase and time- frequency localization are preserved by the alternative filters.

Paper Details

Date Published: 26 October 1999
PDF: 13 pages
Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); doi: 10.1117/12.366821
Show Author Affiliations
Sergio Schuler, Motorola, Inc. (United States)


Published in SPIE Proceedings Vol. 3813:
Wavelet Applications in Signal and Image Processing VII
Michael A. Unser; Akram Aldroubi; Andrew F. Laine, Editor(s)

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