A fast hybrid Jacket-Hadamard matrix based diagonal block-wise transform

In this paper, based on the block (element)-wise inverse Jacket matrix, a unified fast hybrid diagonal block-wise transform (FHDBT) algorithm is proposed. A new fast diagonal block matrix decomposition is made by the matrix product of successively lower order diagonal Jacket matrix and Hadamard matrix. Using a common lower order matrix in the form of 1 1, a fast recursive structure can be developed in the FHDBT, which is able to convert a newly developed discrete cosine transform (DCT)-II, discrete sine transform (DST)-II, discrete Fourier transform (DFT), and Haar-based wavelet transform (HWT). Since these DCT-II, DST-II, DFT, and HWT are widely used in different areas of applications, the proposed FHDBT can be applied to the heterogeneous system requiring several transforms simultaneously. Comparing with pre-existing DCT-II, DST-II, DFT, and HWT, it is shown that the proposed FHDBT exhibits less the complexity as its matrix size gets larger. The proposed algorithm is also well matched to circulant channel matrix. From the numerical experiments, it is shown that a better performance can be achieved by the use of DCT/DST-II compression scheme compared with the DCT-II only compression method. Signal Processing: Image Communication This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c © Mitsubishi Electric Research Laboratories, Inc., 2013 201 Broadway, Cambridge, Massachusetts 02139 Author's personal copy A fast hybrid Jacket–Hadamard matrix based diagonal block-wise transform Moon Ho Lee , Md. Hashem Ali Khan , Kyeong Jin Kim , Daechul Park c a Division Electronics and Information Engineering, Chonbuk National University, Jeonju 561-756, South Korea b Mitsubishi Electric Research Laboratories (MERL), 201 Broadway, Cambridge, MA 02139, USA c Department of Information and Communication Engineering, Hannam University, Daejeon 306-791, South Korea a r t i c l e i n f o Article history: Received 23 April 2013 Received in revised form 12 November 2013 Accepted 12 November 2013 Available online 4 December 2013