Book description
The last 15 years have seen an explosion of interest in wavelets with applications in fields such as image compression, turbulence, human vision, radar and earthquake prediction.
Wavelets represent an area that combines signal in image processing, mathematics, physics and electrical engineering.
As such, this title is intended for the wide audience that is interested in mastering the basic techniques in this subject area, such as decomposition and compression.
Table of contents
 Coverpage
 Titlepage
 Copyright
 Table of Contents
 Notations
 Introduction

Chapter 1. A Guided Tour
 1.1. Introduction
 1.2. Wavelets
 1.3. An electrical consumption signal analyzed by wavelets
 1.4. Denoising by wavelets: before and afterwards
 1.5. A Doppler signal analyzed by wavelets
 1.6. A Doppler signal denoised by wavelets
 1.7. An electrical signal denoised by wavelets
 1.8. An image decomposed by wavelets
 1.9. An image compressed by wavelets
 1.10. A signal compressed by wavelets
 1.11. A fingerprint compressed using wavelet packets
 Chapter 2. Mathematical Framework

Chapter 3. From Wavelet Bases to the Fast Algorithm
 3.1. Introduction
 3.2. From orthonormal bases to the Mallat algorithm
 3.3. Four filters
 3.4. Efficient calculation of the coefficients
 3.5. Justification: projections and twin scales
 3.6. Implementation of the algorithm
 3.7. Complexity of the algorithm
 3.8. From 1D to 2D
 3.9. Translation invariant transform

Chapter 4. Wavelet Families
 4.1. Introduction
 4.2. What could we want from a wavelet?
 4.3. Synoptic table of the common families
 4.4. Some well known families
 4.5. Cascade algorithm
 Chapter 5. Finding and Designing a Wavelet

Chapter 6. A Short 1D Illustrated Handbook
 6.1. Introduction

6.2. Discrete 1D illustrated handbook
 6.2.1. The analyzed signals
 6.2.2. Processing carried out

6.2.3. Commented examples
 6.2.3.1. A sum of sines
 6.2.3.2. A frequency breakdown
 6.2.3.3. White noise
 6.2.3.4. Colored noise
 6.2.3.5. A breakdown
 6.2.3.6. Two breakdowns of the derivative
 6.2.3.7. A breakdown of the second derivative
 6.2.3.8. A superposition of signals
 6.2.3.9. A ramp with colored noise
 6.2.3.10. A first real signal
 6.2.3.11. A second real signal
 6.3. The contribution of analysis by wavelet packets
 6.4. “Continuous” 1D illustrated handbook

Chapter 7. Signal Denoising and Compression
 7.1. Introduction
 7.2. Principle of denoising by wavelets
 7.3. Wavelets and statistics
 7.4. Denoising methods
 7.5. Example of denoising with stationary noise
 7.6. Example of denoising with nonstationary noise
 7.7. Example of denoising of a real signal
 7.8. Contribution of the translation invariant transform
 7.9. Density and regression estimation
 7.10. Principle of compression by wavelets
 7.11. Compression methods
 7.12. Examples of compression
 7.13. Denoising and compression by wavelet packets
 7.14. Bibliographical comments
 Chapter 8. Image Processing with Wavelets

Chapter 9. An Overview of Applications
 9.1. Introduction
 9.2. Wind gusts
 9.3. Detection of seismic jolts
 9.4. Bathymetric study of the marine floor
 9.5. Turbulence analysis
 9.6. Electrocardiogram (ECG): coding and moment of the maximum
 9.7. Eating behavior
 9.8. Fractional wavelets and fMRI
 9.9. Wavelets and biomedical sciences
 9.10. Statistical process control
 9.11. Online compression of industrial information
 9.12. Transitories in underwater signals
 9.13. Some applications at random
 Appendix. The EZW Algorithm
 Bibliography
 Index
Product information
 Title: Wavelets and their Applications
 Author(s):
 Release date: May 2007
 Publisher(s): Wiley
 ISBN: 9781905209316
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