Shift Unitary Transform for Constructing Two‐Dimensional Wavelet Filters

Fei Li and Jianwei Yang

Journal of Applied Mathematics, 2011, vol. 2011, issue 1

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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https://doi.org/10.1155/2011/272801

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2011:y:2011:i:1:n:272801

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