Olkkonen J. (ed.) Discrete Wavelet Transforms - Theory and Applications
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DISCRETE WAVELET
TRANSFORMS ͳ THEORY
AND APPLICATIONS
Edited by Juuso Olkkonen
Discrete Wavelet Transforms - Theory and Applications
Edited by Juuso Olkkonen
Published by InTech
Janeza Trdine 9, 51000 Rijeka, Croatia
Copyright © 2011 InTech
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Publishing Process Manager Ivana Lorkovic
Technical Editor Teodora Smiljanic
Cover Designer Martina Sirotic
Image Copyright Arvind Balaraman, 2010. Used under license from Shutterstock.com
First published March, 2011
Printed in India
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 - Theory and Applications, Edited by Juuso Olkkonen
p. cm.
ISBN 978-953-307-185-5
free online editions of InTech
Books and Journals can be found at
www.intechopen.com
Part 1
Chapter 1
Chapter 2
Chapter 3
Part 2
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Preface IX
Non-stationary Signals 1
Discrete Wavelet Analyses for Time Series 3
José S. Murguía and Haret C. Rosu
Discrete Wavelet Transfom
for Nonstationary Signal Processing 21
Yansong Wang, Weiwei Wu,
Qiang Zhu and Gongqi Shen
Transient Analysis and Motor Fault Detection
using the Wavelet Transform 43
Jordi Cusidó i Roura and Jose Luis Romeral Martínez
Image Processing and Analysis 61
A MAP-MRF Approach
for Wavelet-Based Image Denoising 63
Alexandre L. M. Levada, Nelson D. A. Mascarenhas
and Alberto Tannús
Image Equalization Using Singular Value
Decomposition and Discrete Wavelet Transform 87
Cagri Ozcinar, Hasan Demirel and Gholamreza Anbarjafari
Probability Distribution Functions
Based Face Recognition System
Using Discrete Wavelet Subbands 95
Hasan Demirel and Gholamreza Anbarjafari
An Improved Low Complexity Algorithm
for 2-D Integer Lifting-Based Discrete Wavelet
Transform Using Symmetric Mask-Based Scheme 113
Chih-Hsien Hsia, Jing-Ming Guo and Jen-Shiun Chiang
Contents
Contents
VI
Biomedical Applications 141
ECG Signal Compression
Using Discrete Wavelet Transform 143
Mohammed Abo-Zahhad
Shift Invariant Biorthogonal Discrete Wavelet Transform
for EEG Signal Analysis 169
Juuso T. Olkkonen and Hannu Olkkonen
Shift-Invariant DWT for Medical Image Classification 179
April Khademi, Sridhar Krishnan and Anastasios Venetsanopoulos
Industrial Applications 213
Discrete Wavelet Transforms for Synchronization
of Power Converters Connected to Electrical Grids 215
Alberto Pigazo and Víctor M. Moreno
Discrete Wavelet Transform Based Wireless
Digital Communication Systems 231
Ali A. A.
Part 3
Chapter 8
Chapter 9
Chapter 10
Part 4
Chapter 11
Chapter 12
Pref ac e
Discrete wavelet transform (DWT) algorithms have become standards tools for pro-
cessing of signals and images in several areas in research and industry. The fi rst DWT
structures were based on the compactly supported conjugate quadrature fi lters (CQFs).
However, a drawback in CQFs is related to the nonlinear phase eff ects such as image
blurring and spatial dislocations in multi-scale analyses. On the contrary, in biorthogo-
nal discrete wavelet transform (BDWT) the scaling and wavelet fi lters are symmetric
and linear phase. The BDWT algorithms are commonly constructed by a ladder-type
network called li ing scheme. The procedure consists of sequential down and upli -
ing steps and the reconstruction of the signal is made by running the li ing network
in reverse order. Effi cient li ing BDWT structures have been developed for VLSI and
microprocessor applications. The analysis and synthesis fi lters can be implemented
by integer arithmetics using only register shi s and summations. Many 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 li ing BDWT.
As DWT provides both octave-scale frequency and spatial timing of the analyzed sig-
nal, it is constantly used to solve and treat more and more advanced problems. One of
the main diffi culties in multi-scale analysis is the dependency of the total energy of the
wavelet coeffi cients in diff erent scales on the fractional shi s of the analysed signal. If
we have a discrete signal x[n] and the corresponding time shi ed signal x[n-τ], where
τ ∈ [0,1], there may exist a signifi cant diff erence in the energy of the wavelet coeffi cients
as a function of the time shi . In shi invariant methods the real and imaginary parts
of the complex wavelet coeffi cients are approximately a Hilbert transform pair. The
energy of the wavelet coeffi cients equals the envelope, which provides smoothness and
approximate shi -invariance. Using two parallel DWT banks, which are constructed
so that the impulse responses of the scaling fi lters have half-sample delayed versions
of each other, the corresponding wavelets are a Hilbert transform pair. The dual-tree
CQF wavelet fi lters do not have coeffi cient symmetry and the nonlinearity interferes
with the spatial timing in diff erent scales and prevents accurate statistical correlations.
Therefore the current developments in theory and applications of wavelets are concen-
trated on the dual-tree BDWT structures.
This book reviews the recent progress in theory and applications of wavelet transform
algorithms. The book is intended to cover a wide range of methods (e.g. li ing DWT,
shi
invariance, 2D image enhancement) for constructing DWTs and to illustrate the
utilization of DWTs in several non-stationary problems and in biomedical as well as
industrial applications. It is organized into four major parts. Part I focuses on non-
X
Preface
stationary signals. Application examples include non-stationary fractal and chaotic
time series, non-stationary vibration and sound signals in the vehicle engineering and
motor fault detection. Part II addresses image processing and analysis applications such
as image denoising and contrast enhancement, and face recognition. Part III is devoted
to biomedical applications, including ECG signal compression, multi-scale analysis of
EEG signals and classifi cation of medical images in computer aided diagnosis. Finally,
Part IV describes how DWT can be utilized in wireless digital communication systems
and synchronization of power converters.
It should be pointed that the book comprises of both tutorial and advanced material.
Therefore, it is intended to be a reference text for graduate students and researchers
to obtain in-depth knowledge on specifi c applications. The editor is 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.
Juuso T. Olkkonen, Ph.D.
VTT Technical Research Centre of Finland
Espoo, Finland