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Construction and decomposition of biorthogonal vector-valued wavelets with compact support

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  • Chen, Qingjiang
  • Cao, Huaixin
  • Shi, Zhi

Abstract

In this article, we introduce vector-valued multiresolution analysis and the biorthogonal vector-valued wavelets with four-scale. The existence of a class of biorthogonal vector-valued wavelets with compact support associated with a pair of biorthogonal vector-valued scaling functions with compact support is discussed. A method for designing a class of biorthogonal compactly supported vector-valued wavelets with four-scale is proposed by virtue of multiresolution analysis and matrix theory. The biorthogonality properties concerning vector-valued wavelet packets are characterized with the aid of time–frequency analysis method and operator theory. Three biorthogonality formulas regarding them are presented.

Suggested Citation

  • Chen, Qingjiang & Cao, Huaixin & Shi, Zhi, 2009. "Construction and decomposition of biorthogonal vector-valued wavelets with compact support," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2765-2778.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:5:p:2765-2778
    DOI: 10.1016/j.chaos.2009.03.187
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    References listed on IDEAS

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    8. Chen, Qingjiang & Shi, Zhi, 2008. "Biorthogonal multiple vector-valued multivariate wavelet packets associated with a dilation matrix," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 323-332.
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    Cited by:

    1. Zhihua Zhang, 2023. "The Improvement of the Discrete Wavelet Transform," Mathematics, MDPI, vol. 11(8), pages 1-12, April.

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