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More About This Title Discrete Wavelet Transformations: An Elementary Approach with Applications, Second Edition
English
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.
English
PATRICK J. VAN FLEET is Professor and Chair of the Department of Mathematics at the University of St. Thomas in St. Paul, Minnesota. He has authored several journal articles on (multi)wavelets and conducted sponsored workshops for developing and teaching an applications-first course on wavelets. He received his PhD in Mathematics from Southern Illinois University-Carbondale in 1991.
English
Preface to the First Edition
Preface
Acknowledgements
Chapter 1: Introduction: Why Wavelets?
Chapter 2: Vectors and Matrices
2.1 Vectors, Inner Products, and Norms
Problems
2.2 Basic Matrix Theory
Problems
2.3 Block Matrix Arithmetic
Problems
2.4 Convolution and Filters
Problems
Chapter 3: An Introduction to Digital Images
3.1 The Basics of Grayscale Digital Images
Problems
Computer Lab
3.2 Color Images and Color Spaces
Problems
Computer Lab
3.3 Huffman Coding
Problems
Computer Lab
3.4 Qualitative and Quantitative Measures
Problems
Computer Labs
Chapter 4: The Haar Wavelet Transformation
4.1 Constructing the Haar Wavelet Transformation
Problems
Computer Lab
4.2 Iterating the Process
Problems
Computer Lab
4.3 The Two–Dimensional Haar Wavelet Transformation
Problems
Computer Lab
4.4 Applications: Image Compression and Edge Detection
Problems
Computer Labs
Chapter 5: Daubechies Wavelet Transformations
5.1 Daubechies Filter of Length Four
Problems
Computer Lab
5.2 Daubechies Filter of Length Six
Problems
Computer Lab
5.3 Daubechies Filters of Even Length
Problems
Computer Lab
Chapter 6: Wavelet Shrinkage: An Application to Denoising
6.1 An Overview of Wavelet Shrinkage
Problems
Computer Lab
6.2 VisuShrink
Problems
Computer Lab
6.3 SureShrink
Problems
Computer Labs
Chapter 7: Biorthogonal Wavelet Transformations
7.1 The (5; 3) Biorthogonal Spline Filter Pair
Problems
Computer Lab
7.2 The (8; 4) Biorthogonal Spline Filter Pair
Problems
Computer Lab
7.3 Symmetry and Boundary Effects
Problems
Computer Lab
7.4 Image Compression and Image Pansharpening
Computer Lab
Chapter 8: Complex Numbers and Fourier Series
8.1 The Complex Plane and Arithmetic
Problems
8.2 Fourier Series
Problems
8.3 Filters and Convolution in the Fourier Domain
Problems
Chapter 9: Filter Construction in the Fourier Domain
9.1 Filter Construction in the Fourier Domain
Problems
9.2 Daubechies Filters
Problems
9.3 Coiflet Filters
Problems
Computer Lab
9.4 Biorthogonal Spline Filter Pairs
Problems
Computer Lab
9.5 The Cohen–Daubechies–Feauveau 9/7 Filter
Problems
Computer Lab
Chapter 10: Wavelet Packets
10.1 The Wavelet Packet Transform
Problems
10.2 Cost Functions and the Best Basis Algorithm
Problems
10.3 The FBI Fingerprint Compression Specification
Computer Lab
Chapter 11: Lifting
11.1 The LeGall Wavelet Transform
Problems
Computer Lab
11.2 Z–Transforms and Laurent Polynomials
Problems
11.3 A General Construction of the Lifting Method
Problems
11.4 The Lifting Method – Examples
Problems
Computer Lab
Chapter 12: The JPEG2000 Image Compression Standard
12.1 An Overview of JPEG
Problems
12.2 The Basic JPEG2000 Algorithm
Problems
12.3 Examples
Appendix A: Basic Statistics
A.1Descriptive Statistics
Problems
A.2 Sample Spaces, Probability, and Random Variables
Problems
A.3 Continuous Distributions
Problems
A.4 Expectation
Problems
A.5 Two Special Distributions
Problems
References
Index
