DOI QR코드

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APPROXIMATION AND BALANCING ORDERS FOR TOTALLY INTERPOLATING BIORTHOGONAL MULTIWAVELET SYSTEMS

  • 투고 : 2010.04.27
  • 발행 : 2011.11.30

초록

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.

참고문헌

  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. https://doi.org/10.1023/A:1019120621646
  2. Y. Choi and J. Jung, Totally interpolating biorthogonal multiwavelet systems with approximation order, Preprint.
  3. I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992.
  4. 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. https://doi.org/10.1137/S0036141093256526
  5. G. B. Folland, Fourier Analysis and Its Applications, Brooks/Cole Publishing Company, A Division of Wadsworth, Inc. 1992.
  6. D. P. Hardin and J. A. Marasovich, Biorthogonal Multiwavelets on [-1, 1], Appl. Comput. Harmon. Anal. 7 (1999), no. 1, 34-53. https://doi.org/10.1006/acha.1999.0261
  7. S. Hongli, C. Yuanli, and Q. Zulian, On Design of Multiwavelet Prefilters, Appl. Math. Comput. 172 (2006), no. 2, 1175-1187. https://doi.org/10.1016/j.amc.2005.03.014
  8. Q. Jiang, On the Regularity of Matrix Refinable Functions, SIAM J. Math. Anal. 29 (1998), no. 5, 1157-1176. https://doi.org/10.1137/S003614109630817X
  9. K. Koch, Interpolating scaling vectors, Int. J. Wavelets Multiresolut. Inf. Process. 3 (2005), no. 3, 389-416. https://doi.org/10.1142/S0219691305000919
  10. K. Koch, Multivariate orthogonal interpolating scaling vectors, Appl. Comput. Harmon. Anal. 22 (2007), no. 2, 198-216. https://doi.org/10.1016/j.acha.2006.06.002
  11. J. Lebrun and M. Vetterli, Balanced multiwavelets theory and design, IEEE Trans. Signal Process. 46 (1998), no. 4, 1119-1125. https://doi.org/10.1109/78.668561
  12. J. Lebrun and M. Vetterli, High order balanced multiwavelets: theory, factorization, and design, IEEE Trans. Signal Process. 49 (2001), no. 9, 1918-1930. https://doi.org/10.1109/78.942621
  13. 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. https://doi.org/10.1006/acha.1996.0018
  14. 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.
  15. I. W. Selesnick, Interpolating multiwavelet bases and the sampling theorem, IEEE Trans. Signal Process. 47 (1999), no. 6, 1615-1621. https://doi.org/10.1109/78.765131
  16. G. Strang and T. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA, 1995.
  17. W. Sweldens and R. Piessens, Wavelet sampling techniques, Proc. Statistical Computing Section, 20-29, 1993.
  18. 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. https://doi.org/10.1109/78.482009
  19. 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.
  20. S. Yang and H. Wang, High-order balanced multiwavelets with dilation factor a, Appl. Math. Comput. 181 (2006), no. 1, 362-369. https://doi.org/10.1016/j.amc.2006.01.041
  21. 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. https://doi.org/10.1006/acha.2001.0361

피인용 문헌

  1. INFINITUDE OF MINIMALLY SUPPORTED TOTALLY INTERPOLATING BIORTHOGONAL MULTIWAVELET SYSTEMS WITH LOW APPROXIMATION ORDERS vol.21, pp.3, 2013, https://doi.org/10.11568/kjm.2013.21.3.247