Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters

Abstract EN

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.