BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Construction of Hilbert Transform Pairs of Wavelet Bases and Optimal Time-Frequency Localization

K.N. Chaudhury, M. Unser

Proceedings of the Thirty-Third IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'08), Las Vegas NV, USA, March 30-April 4, 2008, pp. 3277-3280.

We propose a novel method of constructing exact Hilbert transform (HT) pairs of wavelet bases using fractional B-splines and state necessary and sufficient conditions for generating such wavelet pairs. In particular, we demonstrate how HT pairs of biorthogonal wavelet bases of L2(ℝ) can be constructed using well-localized scaling functions with identical Riesz bounds. Finally, we illustrate this concept by constructing a family of analytic Gabor-like wavelets that exhibit near optimal time-frequency localization. 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/chaudhury0801.html,
AUTHOR="Chaudhury, K.N. and Unser, M.",
TITLE="Construction of {H}ilbert Transform Pairs of Wavelet Bases and
	Optimal Time-Frequency Localization",
BOOKTITLE="Proceedings of the Thirty-Third {IEEE} International
	Conference on Acoustics, Speech, and Signal Processing
	({ICASSP'08})",
YEAR="2008",
editor="",
volume="",
series="",
pages="3277--3280",
address="Las Vegas NV, USA",
month="March 30-April 4,",
organization="",
publisher="",
note="")

© 2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.