Shift unitary transform for constructing two-dimensional wavelet filters

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. copyright © 2011 fei li and jianwei yang.