DISCRETE WAVELET TRANSFORMS: ALGORITHMS AND APPLICATIONS Edited by Hannu Olkkonen Discrete Wavelet Transforms: Algorithms and Applications Edited by Hannu Olkkonen Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2011 InTech All chapters are Open Access articles distributed under the Creative Commons Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Ivana Lorkovic Technical Editor Teodora Smiljanic Cover Designer Jan Hyrat Image Copyright Scott Bowlin, 2010. Used under license from Shutterstock.com First published August, 2011 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Discrete Wavelet Transforms: Algorithms and Applications, Edited by Hannu Olkkonen p. cm. ISBN 978-953-307-482-5 free online editions of InTech Books and Journals can be found at www.intechopen.com Contents Preface IX Part 1 Discrete Wavelet Transform Based Hardware Algorithms 1 Chapter 1 Discrete Wavelet Multitone Modulation for ADSL & Equalization Techniques 3 Sobia Baig, Fasih-ud-Din Farrukh and M. Junaid Mughal Chapter 2 A Scalable Architecture for Discrete Wavelet Transform on FPGA-Based System 25 Xun Zhang Chapter 3 VLSI Architectures of Lifting-Based Discrete Wavelet Transform 41 Sayed Ahmad Salehi and Rasoul Amirfattahi Chapter 4 Simulation of Models and BER Performances of DWT-OFDM versus FFT-OFDM 57 Khaizuran Abdullah and Zahir M. Hussain Chapter 5 Several Kinds of Modified SPIHT Codec 67 Wenchao Zhang Part 2 Image Processing Applications 79 Chapter 6 Multiresolution Approaches for Edge Detection and Classification Based on Discrete Wavelet Transform 81 Guillermo Palacios, J. Ramón Beltrán and Raquel Lacuesta Chapter 7 Low Bit Rate Video Compression Algorithm Using 3-D Discrete Wavelet Decomposition 101 Awad Kh. Al-Asmari Chapter 8 Low Complexity Implementation of Daubechies Wavelets for Medical Imaging Applications 121 Khan Wahid VI Contents Chapter 9 Discrete Wavelets on Edges 135 Alexandre Chapiro, Tassio Knop De Castro, Virginia Mota, Eder De Almeida Perez, Marcelo Bernardes Vieira and Wilhelm Passarella Freire Chapter 10 Discrete Wavelet Transform and Optimal Spectral Transform Applied to Multicomponent Image Coding 151 Isidore Paul Akam Bita, Michel Barret, Florio Dalla Vedova, Jean-Louis Gutzwiller and Dinh-Tuan Pham Part 3 Discrete Wavelet Transforms for Watermaking 177 Chapter 11 Watermarking-Based Image Authentication System in the Discrete Wavelet Transform Domain 179 Clara Cruz Ramos, Rogelio Reyes Reyes, Mariko Nakano Miyatake and Héctor Manuel Pérez Meana Chapter 12 Application of Discrete Wavelet Transform in Watermarking 197 Corina Nafornita and Alexandru Isar Part 4 Discrete Wavelet Transform Algorithms 219 Chapter 13 Shift Invariant Discrete Wavelet Transforms 221 Hannu Olkkonen and Juuso T. Olkkonen Chapter 14 Condition on Word Length of Signals and Coefficients for DC Lossless Property of DWT 231 Masahiro Iwahashi and Hitoshi Kiya Chapter 15 Wavelet-Based Analysis and Estimation of Colored Noise 255 Bart Goossens, Jan Aelterman, Hiêp Luong, Aleksandra Pižurica and Wilfried Philips Chapter 16 An Adaptive Energy Discretization of the Neutron Transport Equation Based on a Wavelet Galerkin Method 281 D. Fournier and R. Le Tellier Preface The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave- scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The DWT algorithms were initially based on the compactly supported conjugate quadrature filters (CQFs). However, a drawback in CQFs is due to the nonlinear phase effects such as spatial dislocations in multi-scale analysis. This is avoided in biorthogonal discrete wavelet transform (BDWT) algorithms, where the scaling and wavelet filters are symmetric and linear phase. The BDWT algorithms are usually constructed by a ladder-type network called lifting scheme. The procedure consists of sequential down and uplifting steps and the reconstruction of the signal is made by running the lifting network in reverse order. Efficient lifting BDWT structures have been developed for VLSI and microprocessor applications. Only register shifts and summations are needed for integer arithmetic implementation of the analysis and synthesis filters. In many systems BDWT-based data and image processing tools have outperformed the conventional discrete cosine transform (DCT) -based approaches. For example, in JPEG2000 Standard the DCT has been replaced by the lifting BDWT. A difficulty in multi-scale DWT analyses is the dependency of the total energy of the wavelet coefficients in different scales on the fractional shifts of the analysed signal. This has led to the development of the complex shift invariant DWT algorithms, the real and imaginary parts of the complex wavelet coefficients are approximately a Hilbert transform pair. The energy of the wavelet coefficients equals the envelope, which provides shift-invariance. In two parallel CQF banks, which are constructed so that the impulse responses of the scaling filters have half-sample delayed versions of each other, the corresponding wavelet bases are a Hilbert transform pair. However, the CQF wavelets do not have coefficient symmetry and the nonlinearity disturbs the spatial timing in different scales and prevents accurate statistical analyses. Therefore the current developments in theory and applications of shift invariant DWT algorithms are concentrated on the dual-tree BDWT structures. This book reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into X Preface four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications. The editor is greatly indebted to all co-authors for giving their valuable time and expertise in constructing this book. The technical editors are also acknowledged for their tedious support and help. Hannu Olkkonen, Professor University of Eastern Finland, Department of Applied Physics, Kuopio, Finland [...]... standardized for many digital communication systems, including ADSL, the 802.11a and 802.11g Wireless LAN standards, Digital audio broadcasting including EUREKA 147 4 Discrete Wavelet Transforms: Algorithms and Applications and Digital Radio Mondiale, Digital Video Broadcasting (DVB), some Ultra Wide Band (UWB) systems, WiMax, and Power Line Communication (PLC) (Sari, et al., 1995) (Frederiksen and. .. bit-streams The proposed DWMT transceiver is based on discrete wavelet packet transform (DWPT) The DWPT is implemented through a reverse order perfect reconstruction filter bank transmultiplexer Wavelet packets can be 12 Discrete Wavelet Transforms: Algorithms and Applications implemented as a set of FIR filters, which leads to the filter bank realization of wavelet transform, according to Mallat’s algorithm... there are different channel impairments that pose 14 Discrete Wavelet Transforms: Algorithms and Applications difficulties in achieving the objective of high-speed and reliable communication (Cook, et al.,1999) These channel impairments include different types of noise and interference The noise sources include crosstalk, impulse noise and narrow band noise (Thomas Starr, et al., 2002) Also, interference... systems, in Proc Int Conf on Electronics, Circuits and Systems, Pafos, Cyprus, pp 1467-1470 24 Discrete Wavelet Transforms: Algorithms and Applications Weinstein, S.; Ebert, P (Oct 1971) Data Transmission by Frequency-Division Multiplexing Using the Discrete Fourier Transform IEEE Transactions on Communications,Volume 19, Issue 5,Part 1, pp:628 - 634 Yap, K.S and J.V McCanny, (2002) A mixed cost-function... prefix samples are discarded and remaining samples are subject to Fast Fourier transform (FFT) The frequency domain equalizer divides the received sub-symbols by the FFT coefficients of the shortened channel impulse response The resulting signal is demodulated to recover the original data bits and converted into a serial bit stream 10 Discrete Wavelet Transforms: Algorithms and Applications Fig 7 Functional... sensitivity to inter-carrier interference (ICI) and narrowband interference (NBI) Therefore, a Discrete Wavelet Transform (DWT) based MCM system was developed as an alternative to DFT based MCM scheme (Lindsey, 1995) DWT based MCM techniques came to be known as Wavelet- OFDM in wireless communications and as Discrete Wavelet Multitone (DWMT) for harsh and noisy wireline communication channels such as... areas of research 2 Basics of wavelet filter banks & multirate signal processing systems Wavelets and filter banks play an important role in signal decomposition into various subbands, signal analysis, modeling and reconstruction Some areas of DSP, such as audio and video compression, signal denoising, digital audio processing and adaptive filtering are based on wavelets and multirate DSP systems Digital...  f  (0  f  ) (9) where f is in Hz and the remaining parameters are defined in Table 1 The PSD of the ADSL transceiver downstream NEXT is given by (ITU-T, 2003),   NPSLn  1.5 PSDADSL , ds  NEXT  PSDADSL , ds  Disturber  10 10  f NXT   f 1.5 ,(0  f   )     (10) 16 Discrete Wavelet Transforms: Algorithms and Applications where f is in Hz and the remaining parameters are also given... is a relatively new area for multirate DSP applications The wavelets are implemented by utilizing multirate filter banks (Fliege, 1994) The discovery of Quadrature Mirror Filter banks (QMF) led to the idea of Perfect Reconstruction (PR), and thus to subband decomposition Mallat came up with the idea of implementing wavelets by filter banks for subband coding and multiresolution decomposition (Mallat,... different frequency bands with different resolutions by decomposing the signal into approximation and detail coefficients The decomposition of the signal into different frequency bands is obtained simply by successive high pass and low pass filtering of the time domain signal 2.1 Analysis and synthesis filter banks Analysis filter banks decomposes input signal into frequency subbands A two channel analysis . DISCRETE WAVELET TRANSFORMS: ALGORITHMS AND APPLICATIONS Edited by Hannu Olkkonen Discrete Wavelet Transforms: Algorithms and Applications Edited by Hannu Olkkonen. orders@intechweb.org Discrete Wavelet Transforms: Algorithms and Applications, Edited by Hannu Olkkonen p. cm. ISBN 978-953-307-482-5 free online editions of InTech Books and Journals can. including ADSL, the 802.11a and 802.11g Wireless LAN standards, Digital audio broadcasting including EUREKA 147 Discrete Wavelet Transforms: Algorithms and Applications 4 and Digital Radio Mondiale,