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Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters

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  • Fei Li
  • Jianwei Yang

Abstract

Due to the difficulty for constructing two-dimensional wavelet filters, the commonly used wavelet filters are tensor-product of one-dimensional wavelet filters. In some applications, more perfect reconstruction filters should be provided. In this paper, we introduce a transformation which is referred to as Shift Unitary Transform (SUT) of Conjugate Quadrature Filter (CQF). In terms of this transformation, we propose a parametrization method for constructing two-dimensional orthogonal wavelet filters. It is proved that tensor-product wavelet filters are only special cases of this parametrization method. To show this, we introduce the SUT of one-dimensional CQF and present a complete parametrization of one-dimensional wavelet system. As a result, more ways are provided to randomly generate two-dimensional perfect reconstruction filters.

Suggested Citation

  • Fei Li & Jianwei Yang, 2011. "Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-19, September.
    • Handle: RePEc:hin:jnljam:272801
    DOI: 10.1155/2011/272801
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