Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 163758, 12 pages
doi:10.1155/2010/163758
Research Article

A General Approach for Orthogonal 4-Tap Integer Multiwavelet Transforms

Mingli Jing,1,2 Hua Huang,1 Wuling Liu,3 and Chun Qi1

1School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, China
2School of Statistics, Xi'an University of Finance and Economics, Xi'an 710061, China
3School of Information Science and Engineering, Southeast University, Nanjing 211189, China

Received 12 December 2009; Accepted 11 May 2010

Academic Editor: Angelo Luongo

Copyright © 2010 Mingli Jing et al. 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.

Abstract

An algorithm for orthogonal 4-tap integer multiwavelet transforms is proposed. We compute the singular value decomposition (SVD) of block recursive matrices of transform matrix, and then transform matrix can be rewritten in a product of two block diagonal matrices and a permutation matrix. Furthermore, we factorize the block matrix of block diagonal matrices into triangular elementary reversible matrices (TERMs), which map integers to integers by rounding arithmetic. The cost of factorizing block matrix into TERMs does not increase with the increase of the dimension of transform matrix, and the proposed algorithm is in-place calculation and without allocating auxiliary memory. Examples of integer multiwavelet transform using DGHM and CL are given, which verify that the proposed algorithm is an executable algorithm and outperforms the existing algorithm for orthogonal 4-tap integer multiwavelet transform.