Title :
Construction of Hilbert transform pairs of wavelet bases and optimal time-frequency localization
Author :
Chaudhury, Kunal N. ; Unser, Michael
Author_Institution :
Biomed. Imaging Group, Ecole Polytech. Fed. de Lausanne, Lausanne
fDate :
March 31 2008-April 4 2008
Abstract :
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 (K) 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.
Keywords :
Hilbert transforms; splines (mathematics); time-frequency analysis; wavelet transforms; Hilbert transform pair construction; Riesz bound; analytic Gabor-like wavelets; fractional B-splines; optimal time-frequency localization; wavelet bases; well-localized scaling function; Biomedical imaging; Deconvolution; Finite difference methods; Noise reduction; Performance analysis; Spline; Sufficient conditions; Time frequency analysis; Wavelet analysis; Wavelet transforms; B-spline; Biorthogonal wavelet basis; Gabor function; Hilbert transform; Time-frequency localization;
Conference_Titel :
Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on
Conference_Location :
Las Vegas, NV
Print_ISBN :
978-1-4244-1483-3
Electronic_ISBN :
1520-6149
DOI :
10.1109/ICASSP.2008.4518350
