Discrete Wavelet Transformations, 2nd Edition

Discrete Wavelet Transformations, 2nd Edition

by Patrick J. Van Fleet
Released April 2019
Publisher(s): Wiley
ISBN: 9781118979273

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Book description

Updated and Expanded Textbook Offers Accessible and Applications-First Introduction to Wavelet Theory for Students and Professionals

The new edition of Discrete Wavelet Transformations continues to guide readers through the abstract concepts of wavelet theory by using Dr. Van Fleet’s highly practical, application-based approach, which reflects how mathematicians construct solutions to challenges outside the classroom. By introducing the Haar, orthogonal, and biorthogonal filters without the use of Fourier series, Van Fleet allows his audience to connect concepts directly to real-world applications at an earlier point than other publications in the field.

Leveraging extensive graphical displays, this self-contained volume integrates concepts from calculus and linear algebra into the constructions of wavelet transformations and their applications, including data compression, edge detection in images and denoising of signals. Conceptual understanding is reinforced with over 500 detailed exercises and 24 computer labs. 

The second edition discusses new applications including image segmentation, pansharpening, and the FBI fingerprint compression specification. Other notable features include:

  • Two new chapters covering wavelet packets and the lifting method
  • A reorganization of the presentation so that basic filters can be constructed without the use of Fourier techniques
  • A new comprehensive chapter that explains filter derivation using Fourier techniques
  • Over 120 examples of which 91 are “live examples,” which allow the reader to quickly reproduce these examples in Mathematica or MATLAB and deepen conceptual mastery
  • An overview of digital image basics, equipping readers with the tools they need to understand the image processing applications presented
  • A complete rewrite of the DiscreteWavelets package called WaveletWare for use with Mathematica and MATLAB
  • A website, www.stthomas.edu/wavelets, featuring material containing the WaveletWare package, live examples, and computer labs in addition to companion material for teaching a course using the book 

Comprehensive and grounded, this book and its online components provide an excellent foundation for developing undergraduate courses as well as a valuable resource for mathematicians, signal process engineers, and other professionals seeking to understand the practical applications of discrete wavelet transformations in solving real-world challenges.

Table of contents

  1. COVER
  2. PREFACE TO THE FIRST EDITION
    1. Why This Book?
    2. To the Student
    3. To the Instructor
    4. What You Won't Find in This Book
  3. PREFACE
    1. What Has Changed?
    2. To the Instructor
    3. Problem Sets, Software Package, Labs, Live Examples
    4. Text Web Site
    5. Text Topics
    6. Course Outlines
  4. ACKNOWLEDGMENTS
  5. CHAPTER 1: INTRODUCTION: WHY WAVELETS?
    1. Image Compression
    2. Other Applications That Use Wavelet Transformations
    3. Wavelet Transformations Are Local Transformations
    4. Classical Wavelet Theory in a Nutshell
    5. The Approach in This Book
  6. CHAPTER 2: VECTORS AND MATRICES
    1. 2.1 Vectors, Inner Products, and Norms
    2. 2.2 Basic Matrix Theory
    3. 2.3 Block Matrix Arithmetic
    4. 2.4 Convolution and Filters
  7. CHAPTER 3: AN INTRODUCTION TO DIGITAL IMAGES
    1. 3.1 The Basics of Grayscale Digital Images
    2. 3.2 Color Images and Color Spaces
    3. 3.3 Huffman Coding
    4. 3.4 Qualitative and Quantitative Measures
  8. CHAPTER 4: THE HAAR WAVELET TRANSFORMATION
    1. 4.1 Constructing the Haar Wavelet Transformation
    2. 4.2 Iterating the Process
    3. 4.3 The Two‐Dimensional Haar Wavelet Transformation
    4. 4.4 Applications: Image Compression and Edge Detection
  9. CHAPTER 5: DAUBECHIES WAVELET TRANSFORMATIONS
    1. 5.1 Daubechies Filter of Length 4
    2. 5.2 Daubechies Filter of Length 6
    3. 5.3  Daubechies Filters of Even Length
  10. CHAPTER 6: WAVELET SHRINKAGE: AN APPLICATION TO DENOISING
    1. 6.1 An Overview of Wavelet Shrinkage
    2. 6.2 VisuShrink
    3. 6.3 SureShrink
  11. CHAPTER 7: BIORTHOGONAL WAVELET TRANSFORMATIONS
    1. 7.1 The (5, 3) Biorthogonal Spline Filter Pair
    2. 7.2 The (8, 4) Biorthogonal Spline Filter Pair
    3. 7.3 Symmetry and Boundary Effects
    4. 7.4 Image Compression and Image Pansharpening
  12. CHAPTER 8: COMPLEX NUMBERS AND FOURIER SERIES
    1. 8.1 The Complex Plane and Arithmetic
    2. 8.2 Fourier Series
    3. 8.3 Filters and Convolution in the Fourier Domain
  13. CHAPTER 9: FILTER CONSTRUCTION IN THE FOURIER DOMAIN
    1. 9.1 Filter Construction
    2. 9.2 Daubechies Filters
    3. 9.3 Coiflet Filters
    4. 9.4 Biorthogonal Spline Filter Pairs
    5. 9.5 The Cohen–Daubechies–Feauveau 9/7 Filter
  14. CHAPTER 10: WAVELET PACKETS
    1. 10.1 The Wavelet Packet Transform
    2. 10.2 Cost Functions and the Best Basis Algorithm
    3. 10.3 The FBI Fingerprint Compression Specification
  15. CHAPTER 11: LIFTING
    1. 11.1 The LeGall Wavelet Transform
    2. 11.2 Z–Transforms and Laurent Polynomials
    3. 11.3 A General Construction of the Lifting Method
    4. 11.4 The Lifting Method – Examples
  16. CHAPTER 12: THE JPEG2000 IMAGE COMPRESSION STANDARD
    1. 12.1 An Overview of JPEG
    2. 12.2 The Basic JPEG2000 Algorithm
    3. 12.3 Examples
  17. APPENDIX A: BASIC STATISTICS
    1. A.1 Descriptive Statistics
    2. A.2 Sample Spaces, Probability, and Random Variables
    3. A.3 Continuous Distributions
    4. A.4 Expectation
    5. A.5 Two Special Distributions
  18. REFERENCES
  19. INDEX
  20. END USER LICENSE AGREEMENT

Product information

  • Title: Discrete Wavelet Transformations, 2nd Edition
  • Author(s): Patrick J. Van Fleet
  • Release date: April 2019
  • Publisher(s): Wiley
  • ISBN: 9781118979273