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

fYear

2008

fDate

March 31 2008-April 4 2008

Firstpage

3277

Lastpage

3280

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;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on

Conference_Location

Las Vegas, NV

ISSN

1520-6149

Print_ISBN

978-1-4244-1483-3

Electronic_ISBN

1520-6149

Type

conf

DOI

10.1109/ICASSP.2008.4518350

Filename

4518350