Orthogonal Hilbert transform filter banks and wavelets

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 tran...

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Bibliographic Details
Main Authors: van Spaendonck, R., Blu, T., Baraniuk, R., Vetterli, M.
Format: Conference Proceeding
Language:English
Subjects:
Channel bank filters
Filter bank
Frequency
IIR filters
Image coding
Image enhancement
Polynomials
Signal processing
Wavelet coefficients
Wavelet transforms
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Summary: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 filter bank features a real low pass filter and two complex high pass 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 high pass filter followed by an approximate Hilbert transform filter.
ISSN:1520-6149
2379-190X
DOI:10.1109/ICASSP.2003.1201729