Theory and implementation of the sine-Gabor wavelet frame

Sergio Schuler

doi:10.1117/12.366821

26 October 1999 Theory and implementation of the sine-Gabor wavelet frame

Sergio Schuler

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366821
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

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.

Citation Download Citation

Sergio Schuler "Theory and implementation of the sine-Gabor wavelet frame", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366821

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available