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

The Fractional Hilbert Transform and Dual-Tree Gabor-Like Wavelet Analysis

K.N. Chaudhury, M. Unser

Proceedings of the Thirty-Fourth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'09), Taipei, Taiwan (People's Republic of China), April 19-24, 2009, pp. 3205-3208.

We provide an amplitude-phase representation of the dual-tree complex wavelet transform by extending the fixed quadrature relationship of the dual-tree wavelets to arbitrary phase-shifts using the fractional Hilbert transform (fHT). The fHT is a generalization of the Hilbert transform that extends the quadrature phase-shift action of the latter to arbitrary phase-shifts—a real shift parameter controls this phase-shift action.

Next, based on the proposed representation and the observation that the fHT operator maps well-localized B-spline wavelets (that resemble Gaussian-windowed sinusoids) into B-spline wavelets of the same order but different shift, we relate the corresponding dual-tree scheme to the paradigm of multiresolution windowed Fourier analysis. 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/chaudhury0901.html,
AUTHOR="Chaudhury, K.N. and Unser, M.",
TITLE="The Fractional {H}ilbert Transform and Dual-Tree {G}abor-Like
	Wavelet Analysis",
BOOKTITLE="Proceedings of the Thirty-Fourth {IEEE} International
	Conference on Acoustics, Speech, and Signal Processing
	({ICASSP'09})",
YEAR="2009",
editor="",
volume="",
series="",
pages="3205--3208",
address="Taipei, Taiwan (People's Republic of China)",
month="April 19-24,",
organization="",
publisher="",
note="")

© 2009 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.