BIOMEDICAL IMAGING GROUP (BIG)
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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. 

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AUTHOR="Chaudhury, K.N. and Unser, M.",
TITLE="Construction of {H}ilbert Transform Pairs of Wavelet Bases and
	Optimal Time-Frequency Localization",
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	Conference on Acoustics, Speech, and Signal Processing
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pages="3277--3280",
address="Las Vegas NV, USA",
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