Advertisement

Journal of Applied Mathematics and Computing

, Volume 22, Issue 3, pp 41–53 | Cite as

The properties of orthogonal matrix-valued wavelet packets in higher dimensions

  • Qing-jiang Chen
  • Jin-shun Feng
  • Zheng-xing Cheng
Article

Abstract

In the paper matrix-valued multiresolution analysis and matrix-valued wavelet packets of spaceL 2(R n ,C s x s) are introduced. A procedure for constructing a class of matrix-valued wavelet packets in higher dimensions is proposed. The properties for the matrix-valued multivariate wavelet packets are investigated by using integral transform, algebra theory and operator theory. Finally, a new orthonormal basis ofL 2(R n ,C s x s) is derived from the orthogonal multivariate matrix-valued wavelet packets.

AMS Mathematics Subject Classification

42C40 65T60 

Key words and phrases

Refinement equation matrix-valued multiresolution analysis matrix-valued scaling functions multivariate matrix-valued wavelet packets 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chui C. K.,An introduction to wavelets[M], Academic Press: New York, 1992.Google Scholar
  2. 2.
    Toliyat H. A., Abbaszadeh K., Rahimian M. M. and Olson L. E.,Rail defect diagnosis using wavelet packet decomposition, J. IEEE Trans. Indus. Appli.39 (2003), 1454–1461.CrossRefGoogle Scholar
  3. 3.
    F. Huang and F. Liu,The fundamental solution of the space-time fractional advectiondispersion equation, J. Appl. Math. & Computing18 (2005), 339–350.MATHMathSciNetGoogle Scholar
  4. 4.
    W. Kim and Hee-sing Hwang,On nonlinearity and Global Avalanche Characteristics of Vector Boolean Functions, J. Appl.Math. & Computing16 (2004), 407–417.Google Scholar
  5. 5.
    S. Markovski, D. Gligoroski and J. Markovski,Classification of quasigroups by random walk on torus, J. Appl. Math. & Computing16 (2005), 57–75.MathSciNetCrossRefGoogle Scholar
  6. 6.
    C. Belly,Variational and Quasi Variational Inequalities, J. Appl. Math. & Computing6 (1999), 234–266.Google Scholar
  7. 7.
    D. Pang,The generalized quasi variational inequality problems J. Appl. Math. & Computing8 (2002), 123–245.Google Scholar
  8. 8.
    Martin M.B., Bell A.E.,New Image compression technique using multiwavelet packets, J. IEEE Trans. Image Processing10 (2001), 500–511.MATHCrossRefGoogle Scholar
  9. 9.
    Deng Hai and Ling Hao,Fast Solution of Electromagnetic Integral Equations Using Adaptive Wavelet Packet Transform, J. IEEE Trans. on Antennas and Propagation47 (1999), 674–682.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Chui C. K., and Li Chun.,Nonorthonormal wavelet packets[J]. SIAM Math. Anal.24 (1993), 712–738.MATHCrossRefGoogle Scholar
  11. 11.
    Cohen A. and Daubeches I.,On the instability of arbitrary biorthogonal wavelet packets, J. SIAM Math. Anal.24 (1993), 1340–1354.MATHCrossRefGoogle Scholar
  12. 12.
    S. Yang and Z. Cheng.a-scale multiple orthogonal wavelet packets, J. Applied Math. China13 (2000), 61–65.MATHMathSciNetGoogle Scholar
  13. 13.
    Xia X. G. and Suter B. W.,Vector-valued wavelets and vector fiter banks, J. IEEE Trans. Signal Processing44 (1996), 508–518.CrossRefGoogle Scholar
  14. 14.
    Xia X. G., Geronimo J. S., Hardin D. P. and Suter B. W.,Design of prefilters for discrete multiwavelet transforms, J. IEEE Trans. Signal Processing44 (1996), 25–35.CrossRefGoogle Scholar
  15. 15.
    Shen Z.,Nontensor product wavelet packets in L 2(Rs), J. SIAM Math. Anal.26 (1995), 1061–1074.MATHCrossRefGoogle Scholar

Copyright information

© Korean Society for Computational & Applied Mathematics and Korean SIGCAM 2006

Authors and Affiliations

  • Qing-jiang Chen
    • 1
    • 2
  • Jin-shun Feng
    • 3
  • Zheng-xing Cheng
    • 2
  1. 1.College of ScienceXi’an University of Architecture and TechnologyXi’anChina
  2. 2.School of ScienceXi’an Jongtong UniversityXi’anP. R. China
  3. 3.School of EducationNanyang College of TechnologyNanyangP. R. China

Personalised recommendations