Hostname: page-component-cb9f654ff-mx8w7 Total loading time: 0 Render date: 2025-08-30T02:28:36.907Z Has data issue: false hasContentIssue false
  • English
  • Français

Biorthogonal interpolatory multiscaling functions and corresponding multiwavelets

Published online by Cambridge University Press:  17 February 2009

Yang Shouzhi
Yang Shouzhi
Affiliation:
Dept of Maths Shantou UniversityShantou 515063 P.R. Chinaszyang@stu.edu.cn.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A method for constructing a pair of biorthogonal interpolatory multiscaling functions is given and an explicit formula for constructing the corresponding biorthogonal multiwavelets is obtained. A multiwavelet sampling theorem is also established. In addition, we improve the stability of the biorthogonal interpolatory multiwavelet frame by the linear combination of a pair of biorthogonal interpolatory multiwavelets. Finally, we give an example illustrating how to use our method to construct biorthogonal interpolatory multiscaling functions and corresponding multiwavelets.

Keywords

biorthogonalinterpolatorymultiscaling functionsmultiwaveletsframe

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 1 , July 2007 , pp. 85 - 97
Copyright
Copyright © Australian Mathematical Society 2007

References

references

[1]Chui, C. K.andLian, J., “A study on orthonormal multiwavelets", J Appl Numer Math. 20 (1996) 273–298.CrossRefGoogle Scholar
[2]Chui, C.K. and Wang, J. Z., “A cardinal spline approach to wavelets”, Proc Amen Math Soc. 113 (1991)785–793.CrossRefGoogle Scholar
[3]Daubechies, I. andLagarias, J. C., “Two-scale difference equations. II. Local regularity, infinite products of matrices and fractals”, S1AMJ Math Anal. 23 (1991) 1031–1079.CrossRefGoogle Scholar
[4]Donovan, G. C., Geronimo, J. S. and Hardin, D. P., “Construction of orthogonal wavelets using fractal interpolation functions”, SIAM J Math Anal. 27(1996) 1158–1192.CrossRefGoogle Scholar
[5]Geronimo, J. S., Hardin, D. P. and Massopust, P. R., “Fractal functions and wavelet expansions based on several scaling functions”, J Approx Theory 78 (1994) 371–401.CrossRefGoogle Scholar
[6]Goh, S. S., Jiang, Qingtang and Xia, Tao, “Construction of biorthogonal multiwavelets using the lifting scheme”, Appl Comput Harmon Anal. 9 (2000) 336–352.CrossRefGoogle Scholar
[7]Goodman, T. N. T., Lee, S. L. and Tang, W. S., “Wavelets in wandering subspaces”, Trans Amer Math Soc. 338 (1993) 639–654.CrossRefGoogle Scholar
[8]Lian, J., “Orthogonal criteria for multiscaling functions”, Appl Comp Harm Anal 5 (1998) 277–311.CrossRefGoogle Scholar
[9]Rota, G. C. and Strang, G., “A note on the joint spectral radius”, Indag Math 22 (1960) 379–381.CrossRefGoogle Scholar
[10]Yang, Shouzhi, “A fast algorithm for constructing orthogonal multiwavelets”, ANZIAM J 46 (2004) 185–202.Google Scholar
[11]Yang, Shouzhi, “An algorithm for constructing biorthogonal multiwavelets with higher approximation orders”, ANZ1AM J 47 (2006) 513–526.Google Scholar
[12]Yang, Shouzhi, Cheng, Zhengxing and Wang, Hongyong, “Construction of biorthogonal multiwavelets”, J Math Anal Appl 276 (2002) 1–12.CrossRefGoogle Scholar
[13]Strang, G. and Zhou, D. X., “Inhomogeneous refinement equations”, J Fourier Anal Appl 4 (1998) 733–747.CrossRefGoogle Scholar
[14]Xia, X. G. and Zhang, Z., “On sampling theorem, wavelets, and wavelet transforms”, IEEE Trans Signal Processing 41 (1993) 3524–3535.CrossRefGoogle Scholar
[15]Zhou, D. X., “Existence of multiple refinable distributions”, Michigan Math J 44 (1997) 317–329.CrossRefGoogle Scholar
[16]Zhou, D. X., “The p-norm joint spectral radius for even integers”, Methods Appl Anal 5 (1998) 39–54.CrossRefGoogle Scholar
[17]Zhou, D. X, “Multiple refinable Hermite interpolants”, J Approx Theory 102(2000) 46–71.CrossRefGoogle Scholar
[18]Zhou, D. X., “Interpolatory orthogonal multiwavelets and refinable functions”, IEEE Trans Signal Processing 50 (2002) 520–527.CrossRefGoogle Scholar