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

• 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
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2008.2009836

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.