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High Balanced Biorthogonal Multiwavelets with Symmetry

Author

Listed:
  • Youfa Li
  • Shouzhi Yang
  • Yanfeng Shen
  • Gengrong Zhang

Abstract

Balanced multiwavelet transform can process the vector‐valued data sparsely while preserving a polynomial signal. Yang et al. (2006) constructed balanced multiwavelets from the existing nonbalanced ones. It will be proved, however, in this paper that if the nonbalanced multiwavelets have antisymmetric component, it is impossible for the balanced multiwavelets by the method mentioned above to have symmetry. In this paper, we give an algorithm for constructing a pair of biorthogonal symmetric refinable function vectors from any orthogonal refinable function vector, which has symmetric and antisymmetric components. Then, a general scheme is given for high balanced biorthogonal multiwavelets with symmetry from the constructed pair of biorthogonal refinable function vectors. Moreover, we discuss the approximation orders of the biorthogonal symmetric refinable function vectors. An example is given to illustrate our results.

Suggested Citation

  • Youfa Li & Shouzhi Yang & Yanfeng Shen & Gengrong Zhang, 2014. "High Balanced Biorthogonal Multiwavelets with Symmetry," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:154269
    DOI: 10.1155/2014/154269
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    References listed on IDEAS

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    1. Li, Rui & Wu, Guochang, 2009. "The orthogonal interpolating balanced multiwavelet with rational coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 892-899.
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