Shift unitary transform for constructing two-dimensional wavelet filters (Q642751)

Summary: Due to the difficulty for constructing two-dimensional wavelet filters, the commonly used wavelet filters are tensor-products 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 Filters (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 a one-dimensional wavelet system. As a result, more ways are provided to randomly generate two-dimensional perfect reconstruction filters.