Journal of Applied Mathematics
Volume 2011 (2011), Article ID 272801, 19 pages
Research Article

Shift Unitary Transform for Constructing Two-Dimensional Wavelet Filters

1School of Economics, Beijing Technology and Business University, Beijing 100048, China
2College of Math and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received 13 March 2011; Revised 27 May 2011; Accepted 8 June 2011

Academic Editor: F. Marcellán

Copyright © 2011 Fei Li and Jianwei Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.