Signal and Image Multiresolution Analysis

Klappentext Multiresolution analysis using the wavelet transform has received considerable attention in recent years by researchers in various fields. It is a powerful tool for efficiently representing signals and images at multiple levels of detail with many inherent advantages, including compression, level-of-detail display, progressive transmission, level-of-detail editing, filtering, modeling, fractals and multifractals, etc.This book aims to provide a simple formalization and new clarity on multiresolution analysis, rendering accessible obscure techniques, and merging, unifying or completing the technique with encoding, feature extraction, compressive sensing, multifractal analysis and texture analysis. It is aimed at industrial engineers, medical researchers, university lab attendants, lecturer-researchers and researchers from various specializations. It is also intended to contribute to the studies of graduate students in engineering, particularly in the fields of medical imaging, intelligent instrumentation, telecommunications, and signal and image processing.Given the diversity of the problems posed and addressed, this book paves the way for the development of new research themes, such as brain-computer interface (BCI), compressive sensing, functional magnetic resonance imaging (fMRI), tissue characterization (bones, skin, etc.) and the analysis of complex phenomena in general. Throughout the chapters, informative illustrations assist the uninitiated reader in better conceptualizing certain concepts, taking the form of numerous figures and recent applications in biomedical engineering, communication, multimedia, finance, etc. Zusammenfassung Multiresolution analysis using the wavelet transform has received considerable attention in recent years by researchers in various fields. It is a powerful tool for efficiently representing signals and images at multiple levels of detail with many inherent advantages, including compression, level-of-detail display, progressive transmission, level-of-detail editing, filtering, modeling, fractals and multifractals, etc.This book aims to provide a simple formalization and new clarity on multiresolution analysis, rendering accessible obscure techniques, and merging, unifying or completing the technique with encoding, feature extraction, compressive sensing, multifractal analysis and texture analysis. It is aimed at industrial engineers, medical researchers, university lab attendants, lecturer-researchers and researchers from various specializations. It is also intended to contribute to the studies of graduate students in engineering, particularly in the fields of medical imaging, intelligent instrumentation, telecommunications, and signal and image processing.Given the diversity of the problems posed and addressed, this book paves the way for the development of new research themes, such as brain-computer interface (BCI), compressive sensing, functional magnetic resonance imaging (fMRI), tissue characterization (bones, skin, etc.) and the analysis of complex phenomena in general. Throughout the chapters, informative illustrations assist the uninitiated reader in better conceptualizing certain concepts, taking the form of numerous figures and recent applications in biomedical engineering, communication, multimedia, finance, etc. Inhaltsverzeichnis 22018317 ...

Inhaltsverzeichnis

Introduction xi

Chapter 1. Introduction to Multiresolution Analysis 1

1.1. Introduction 1

1.2. Wavelet transforms: an introductory review 3

1.2.1. Brief history 3

1.2.2. Continuous wavelet transforms 6

1.2.2.1. Wavelet transform modulus maxima 9

1.2.2.2. Reconstruction 13

1.2.3. Discrete wavelet transforms 14

1.3. Multiresolution 16

1.3.1. Multiresolution analysis and wavelet bases 17

1.3.1.1. Approximation spaces 17

1.3.1.2. Detail spaces 19

1.3.2. Multiresolution analysis: points to remember 21

1.3.3. Decomposition and reconstruction 22

1.3.3.1. Calculation of coefficients 22

1.3.3.2. Implementation of MRA: Mallatalgorithm 24

1.3.3.3. Extension to images 26

1.3.4. Wavelet packets 28

1.3.5. Multiresolution analysis summarized 30

1.4. Which wavelets to choose? 33

1.4.1. Number of vanishing moments, regularity,

support (compactness), symmetry, etc 33

1.4.2. Well-known wavelets, scale functions and associatedfilters 34

1.4.2.1. Haar wavelet 34

vi Signal and Image Multiresolution Analysis

1.4.2.2. Daubechies wavelets 36

1.4.2.3. Symlets 38

1.4.2.4. Coiflets 39

1.4.2.5. Meyer wavelets 41

1.4.2.6. Polynomial spline wavelets 43

1.5. Multiresolution analysis and biorthogonal waveletbases 48

1.5.1. Why biorthogonal bases? 48

1.5.2. Multiresolution context 48

1.5.3. Example of biorthogonal wavelets, scaling functions

and associated filters 49

1.5.4. The concept of wavelet lifting 51

1.5.4.1. The notion of lifting 51

1.5.4.2. Significance of structure lifting 52

1.6. Wavelet choice at a glance 54

1.6.1. Regularity 54

1.6.2. Vanishing moments 54

1.6.3. Other criteria 55

1.6.4. Conclusion 55

1.7. Worked examples 55

1.7.1. Examples of multiresolution analysis 55

1.7.2. Compression 58

1.7.3. Denoising (reduction of noise) 64

1.8. Some applications 74

1.8.1. Discovery and contributions of wavelets 74

1.8.2. Biomedical engineering 76

1.8.2.1. ECG, EEG and BCI 77

1.8.2.2. Medical imaging 97

1.8.3. Telecommunications 110

1.8.3.1. Adaptive compression for sensor networks 110

1.8.3.2. Masking image encoding and transmission errors 114

1.8.3.3. Suppression of correlated noise 118

1.8.4. "Compressive sensing", ICA, PCA andMRA 119

1.8.4.1. Principal component analysis 120

1.8.4.2. Independent component analysis 121

1.8.4.3. Compressive sensing 122

1.8.5. Conclusion 128

1.9. Bibliography 129

Chapter 2. Discrete Wavelet Transform-Based MultifractalAnalysis 135

2.1. Introduction 135

2.1.1. Fractals and wavelets: a happy marriage? 135

2.1.2. Background 136

2.1.3. Mono/multifractal processes 137

2.1.4. Chapter outline 138

2.2. Fractality, variability and complexity 139

2.2.1. System complexity 139

2.2.2. Complex phenomena properties 141

2.2.2.1. Tendency of autonomous agents to self-organize 141

2.2.2.2. Variability and adaptability 142

2.2.2.3. Bifurcation concept and chaotic model 143

2.2.2.4. Hierarchy and scale invariance 146

2.2.2.5. Self-organized critical phenomena 146

2.2.2.6. Highly optimized tolerance 147

2.2.3. Fractality 148

2.3. Multifractal analysis 150

2.3.1. Point-wise regularity 150

2.3.2. Hölder exponent 150

2.3.3. Signal classification according to the regularityproperties 152

2.3.3.1. Monofractal signal 152

2.3.3.2. Multifractal signal 152

2.3.4. Hausdorff dimension 154

2.3.4.1. Theoretic approach 155

2.3.4.2. Qualitative approach and multifractalspectrum 155

2.4. Multifractal formalism 156

2.4.1. Reminder on wavelet decomposition 156

2.4.2. Point-wise regularity characterization 157

2.4.3. Structure function and power law behavior 158

2.4.4. Link between scaling exponents and singularityspectrum 159

2.4.5. Use of wavelet leaders 160

2.4.5.1. Indexing a dyadic square and wavelet leaders 161

2.4.5.2. Polynomial expansion and log-cumulants 162

2.4.6. Wa

Über den Autor / die Autorin

Abdeldjalil OUAHABI is Professor and Director of Polytech Tours's Signal & Image Group. His is currently Deputy Director for International Relations at Polytech Tour's (Ecole Polytechnique de l'Université de Tours).

Zusammenfassung

Owing to its ability to represent efficiently signals and images at multiple levels of detail, multiresolution analysis using the wavelet transform has received considerable attention in recent years. This book provides engineers and researchers with a simple formalization and new clarity on multiresolution analysis.

Produktdetails

• Autoren: A Ouahabi, A. Ouahabi, Abdeldjalil Ouahabi
• Mitarbeit: Francis Castanie (Herausgeber), Abdeldjali Ouahabi (Herausgeber), Abdeldjalil Ouahabi (Herausgeber), Abdelialil Ouahabi (Herausgeber)
• Verlag: Wiley, John and Sons Ltd
• Sprache: Englisch
• Produktform: Fester Einband
• Erschienen: 06.12.2011
• EAN: 9781848212572
• ISBN: 978-1-84821-257-2
• Serien: ISTE; Digital Signal and Image Proce; ISTE; Digital Signal and Image Proce
• Themen: Naturwissenschaften, Medizin, Informatik, Technik > Technik > Elektronik, Elektrotechnik, Nachrichtentechnik; Signalverarbeitung, Signal Processing, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik