Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters

Fei Li and Jianwei Yang

Journal of Applied Mathematics, 2011, vol. 2011, 1-19

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.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:272801

DOI: 10.1155/2011/272801

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