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

Orthogonal Hilbert Transform Filter Banks and Wavelets

R. van Spaendonck, T. Blu, R. Baraniuk, M. Vetterli

Proceedings of the Twenty-Eighth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'03), Hong Kong SAR, People's Republic of China, April 6-10, 2003, vol. VI, pp. 505-508.

Complex wavelet transforms offer the opportunity to perform directional and coherent processing based on the local magnitude and phase of signals and images. Although denoising, segmentation, and image enhancement are significantly improved using complex wavelets, the redundancy of most current transforms hinders their application in compression and related problems. In this paper we introduce a new orthonormal complex wavelet transform with no redundancy for both real— and complex-valued signals. The transform's filterbank features a real lowpass filter and two complex highpass filters arranged in a critically sampled, three-band structure. Placing symmetry and orthogonality constraints on these filters, we find that each high-pass filter can be factored into a real highpass filter followed by an approximate Hilbert transform filter. 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/spaendonck0301.html,
AUTHOR="van Spaendonck, R. and Blu, T. and Baraniuk, R. and Vetterli,
	M.",
TITLE="Orthogonal {H}ilbert Transform Filter Banks and Wavelets",
BOOKTITLE="Proceedings of the Twenty-Eighth {IEEE} International
	Conference on Acoustics, Speech, and Signal Processing
	({ICASSP'03})",
YEAR="2003",
editor="",
volume="{VI}",
series="",
pages="505--508",
address="Hong Kong SAR, People's Republic of China",
month="April 6-10,",
organization="",
publisher="",
note="")

© 2003 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.