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A note on the extension of a family of biorthogonal Coifman wavelet systems

Published online by Cambridge University Press:  17 February 2009

Zhuhan Jiang  and
Xiling Guo
Zhuhan Jiang
Affiliation:
School of Computing and Information Technology, University of Western Sydney, Penrith South DC NSW 1797, Australia; e-mail: z.jiang@uws.edu.au.
Xiling Guo
Affiliation:
Management Information Systems, Australian Catholic University, Strathfield NSW 2135, Australia; e-mail: x.guo@mary.acu.edu.au.
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Abstract

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Wavelet systems with a maximum number of balanced vanishing moments are known to be extremely useful in a variety of applications such as image and video compression. Tian and Wells recently created a family of such wavelet systems, called the biorthogonal Coifman wavelets, which have proved valuable in both mathematics and applications. The purpose of this work is to establish along with direct proofs a very neat extension of Tian and Wells' family of biorthogonal Coifman wavelets by recovering other “missing” members of the biorthogonal Coifman wavelet systems.

Type
Research Article
Information
The ANZIAM Journal , Volume 46 , Issue 1 , July 2004 , pp. 111 - 120
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Akansu, A. N. and Haddad, R. A., Multiresolution signal decomposition: transform, subbands and wavelets (Academic Press, Boston, 1992).Google Scholar
[2]Burrus, C. S., Gopinath, R. A. and Guo, H., Introduction to wavelets and waveler transforms: a primer (Prentice Hall, NJ, 1998).Google Scholar
[3]Daubechies, I., Ten lectures on wavelets (SIAM, Philadelphia, 1992).CrossRefGoogle Scholar
[4]Jiang, Z., “The intrinsicality of Lie symmetries of ”, J. Math. Anal. Appl. 227 (1998) 396–419.CrossRefGoogle Scholar
[5]Jiang, Z., “Lie symmetries and their local determinacy for a class of differential-difference equations”, Phys. Lett. A 240 (1998) 137–143.CrossRefGoogle Scholar
[6]Jiang, Z. and Guo, X., “Wavelets of vanishing moments and minimal filter norms and the application to image compression”, Technical Report 00–179, University of New England, 2000.Google Scholar
[7]Jiang, Z., De Vel, O. and Litow, B., “Unification and extension of weighted finite automata applicable to image compression”, Theor Comp. Sci. 302 (2003) 275–294.Google Scholar
[8]Kautsky, J. and Turcajova, R., “Discrete biorthogonal wavelet transforms as block circulant matrices”, Linear Algebra Appl. 223/224 (1995) 393–413.Google Scholar
[9]Kautsky, J. and Turcajova, R., “Pollen product factorization and construction of higher multiplicity wavelets”, Linear Algebra Appl. 222 (1995) 241–260.Google Scholar
[10]Mandal, M. K., Panchanathan, S. and Aboulnasr, T., “Choice of wavelets for image compression”, in Information theory and applications, II (Lac Delage, PQ, 1995), Lecture Notes in Comput. Sci. 1133, (Springer, Berlin, 1996) 239–249.Google Scholar
[11]Prasad, L. and Iyengar, S. S., Wavelet analysis with applications to image processing (CRC Press, Boca Raton, 1997).Google Scholar
[12]Tian, J. and Wells, R. O. Jr, “Vanishing moments and biorthogonal wavelet systems”, in Mathematics in Signal Processing IV (ed. McWhirter, J. G.), (Oxford University Press, Oxford, 1997).Google Scholar