On the Space of Orthonormal Wavelets: Additional Constraints to Ensure Two Vanishing Moments

This letter extends the formulation developed by Sherlock and Monro for parameterization of orthonormal wavelet filter banks. Additional constraints are proposed to ensure that the resulting wavelets have at least two vanishing moments. The remaining degrees of freedom are re-parameterized in a conv...

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Bibliographic Details
Published in:	IEEE signal processing letters Vol. 16; no. 2; pp. 101 - 104
Main Authors:	Paiva, H.M., Martins, M.N., Galvao, R.K.H., Paiva, J.P.L.M.
Format:	Journal Article
Language:	English
Published:	New York IEEE 01-02-2009 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Biomedical engineering Biomedical signal processing Constraint optimization Degrees of freedom Filter bank Filter banks Longitudinal waves Mathematical analysis Optimization Parameterization Parametrization Pattern recognition Performance analysis Signal processing algorithms Signal representations vanishing moments Wavelet Wavelet domain wavelets
Online Access:	Get full text
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Summary:	This letter extends the formulation developed by Sherlock and Monro for parameterization of orthonormal wavelet filter banks. Additional constraints are proposed to ensure that the resulting wavelets have at least two vanishing moments. The remaining degrees of freedom are re-parameterized in a convenient form, which results in a convex set of feasible parameter values. An example involving wavelet adaptation in the context of signal compression is presented for illustration. In this case, the additional constraints improve the outcome of the optimization algorithm employed to adjust the filter bank.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	1070-9908 1558-2361
DOI:	10.1109/LSP.2008.2009836