Browse > Article
http://dx.doi.org/10.4134/BKMS.2011.48.6.1157

APPROXIMATION AND BALANCING ORDERS FOR TOTALLY INTERPOLATING BIORTHOGONAL MULTIWAVELET SYSTEMS  

Choi, Young-Woo (Department of Mathematics Ajou University)
Jung, Jae-Won (Department of Mathematics Ajou University)
Publication Information
Bulletin of the Korean Mathematical Society / v.48, no.6, 2011 , pp. 1157-1167 More about this Journal
Abstract
We consider totally interpolating biorthogonal multiwavelet systems with finite impulse response two-band multifilter banks, a study balancing order conditions of such systems. Based on FIR and interpolating properties, we show that approximation order condition is completely equivalent to balancing order condition. Consequently, a prefiltering can be avoided if a totally interpolating biorthogonal multiwavelet system satisfies suitable approximation order conditions. An example with approximation order 4 is provided to illustrate the result.
Keywords
multiwavelets; interpolating; balancing order;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
  • Reference
1 S. Bacchelli, M. Cotronei, and D. Lazzaro, An algebraic construction of k-balanced multiwavelets via the lifting scheme, Numer. Algorithms 23 (2000), no. 4, 329-356.   DOI
2 G. Plonka and V. Strela, From wavelets to multiwavelets, Mathematical Methods for Curves and Surface II(M. Dahlen, T. Lyche, and L. L. Schumaker, Eds. Vanderbilt Univ. Press, Nashville), (1998), 375-399.
3 I. W. Selesnick, Interpolating multiwavelet bases and the sampling theorem, IEEE Trans. Signal Process. 47 (1999), no. 6, 1615-1621.   DOI   ScienceOn
4 G. Strang and T. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA, 1995.
5 W. Sweldens and R. Piessens, Wavelet sampling techniques, Proc. Statistical Computing Section, 20-29, 1993.
6 X. G. Xia, J. S. Geronimo, D. P. Hardin, and B. W. Suter, Design of prefilters for discrete multiwavelet transforms, IEEE Trans. Signal Process. 44 (1996), 25-35.   DOI   ScienceOn
7 X. G. Xia, J. S. Geronimo, D. P. Hardin, and B. W. Suter, Why and how prefiltering for discrete multiwavelet transforms, Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Proces. Vol. 1, 1578-1581, 1996.
8 S. Yang and H. Wang, High-order balanced multiwavelets with dilation factor a, Appl. Math. Comput. 181 (2006), no. 1, 362-369.   DOI   ScienceOn
9 J. K. Zhang, T. N. Davidson, Z. Q. Luo, and K. M. Wong, Design of interpolating biorthogonal multiwavelet systems with compact support, Appl. Comput. Harmon. Anal. 11 (2001), no. 3, 420-438.   DOI   ScienceOn
10 Y. Choi and J. Jung, Totally interpolating biorthogonal multiwavelet systems with approximation order, Preprint.
11 I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
12 S. Hongli, C. Yuanli, and Q. Zulian, On Design of Multiwavelet Prefilters, Appl. Math. Comput. 172 (2006), no. 2, 1175-1187.   DOI   ScienceOn
13 G. Donovan, J. S. Geronimo, D. P. Hardin, and P. R. Massopust, Construction of orthogonal wavelets using fractal interpolation functions, SIAM J. Math. Anal. 27 (1996), no. 4, 1158-1192.   DOI   ScienceOn
14 G. B. Folland, Fourier Analysis and Its Applications, Brooks/Cole Publishing Company, A Division of Wadsworth, Inc. 1992.
15 D. P. Hardin and J. A. Marasovich, Biorthogonal Multiwavelets on [-1, 1], Appl. Comput. Harmon. Anal. 7 (1999), no. 1, 34-53.   DOI   ScienceOn
16 Q. Jiang, On the Regularity of Matrix Refinable Functions, SIAM J. Math. Anal. 29 (1998), no. 5, 1157-1176.   DOI   ScienceOn
17 K. Koch, Interpolating scaling vectors, Int. J. Wavelets Multiresolut. Inf. Process. 3 (2005), no. 3, 389-416.   DOI   ScienceOn
18 K. Koch, Multivariate orthogonal interpolating scaling vectors, Appl. Comput. Harmon. Anal. 22 (2007), no. 2, 198-216.   DOI   ScienceOn
19 J. Lebrun and M. Vetterli, Balanced multiwavelets theory and design, IEEE Trans. Signal Process. 46 (1998), no. 4, 1119-1125.   DOI   ScienceOn
20 J. Lebrun and M. Vetterli, High order balanced multiwavelets: theory, factorization, and design, IEEE Trans. Signal Process. 49 (2001), no. 9, 1918-1930.   DOI   ScienceOn
21 P. R. Massopust, D. K. Rush, and P. J. Fleet, On the support properties of scaling vectors, Appl. Comput. Harmon. Anal. 3 (1996), no. 3, 229-238.   DOI   ScienceOn