John Wiley & Sons Discrete Wavelet Transformations Cover Updated and Expanded Textbook Offers Accessible and Applications-First Introduction to Wavelet Theor.. Product #: 978-1-118-97927-3 Regular price: $107.48 $107.48 Auf Lager

Discrete Wavelet Transformations

An Elementary Approach with Applications

Van Fleet, Patrick

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2. Auflage Mai 2019
624 Seiten, Hardcover
Wiley & Sons Ltd

ISBN: 978-1-118-97927-3
John Wiley & Sons

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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.

1 Introduction: Why Wavelets? 1

2 Vectors and Matrices 15

2.1 Vectors, Inner Products, and Norms 16

Problems 21

2.2 Basic Matrix Theory 23

Problems 38

2.3 Block Matrix Arithmetic 40

Problems 48

2.4 Convolution and Filters 51

Problems 65

3 An Introduction to Digital Images 69

3.1 The Basics of Grayscale Digital Images 70

Problems 88

Computer Lab 91

3.2 Color Images and Color Spaces 91

Problems 103

Computer Lab 106

3.3 Huffman Coding 106

Problems 113

3.4 Qualitative and Quantitative Measures 114

Problems 120

Computer Labs 123

4 The Haar Wavelet Transformation 125

4.1 Constructing the Haar Wavelet Transformation 127

Problems 137

Computer Lab 140

4.2 Iterating the Process 140

Problems 146

Computer Lab 147

4.3 The Two-Dimensional Haar Wavelet Transformation 147

Problems 159

Computer Lab 161

4.4 Applications: Image Compression and Edge Detection 161

Problems 177

Computer Labs 181

5 Daubechies Wavelet Transformations 183

5.1 Daubechies Filter of Length 4 185

Problems 196

Computer Lab 203

5.2 Daubechies Filter of Length 6 203

Problems 212

Computer Lab 215

5.3 Daubechies Filters of Even Length 215

Problems 225

Computer Lab 228

6 Wavelet Shrinkage: An Application to Denoising 231

6.1 An Overview of Wavelet Shrinkage 232

Problems 237

Computer Lab 238

6.2 VisuShrink 238

Problems 245

Computer Lab 246

6.3 SureShrink 246

Problems 257

Computer Labs 260

7 Biorthogonal Wavelet Transformations 261

7.1 The (5; 3) Biorthogonal Spline Filter Pair 262

Problems 273

Computer Lab 278

7.2 The (8; 4) Biorthogonal Spline Filter Pair 278

Problems 283

Computer Lab 288

7.3 Symmetry and Boundary Effects 288

Problems 307

Computer Lab 311

7.4 Image Compression and Image Pansharpening 312

Computer Lab 320

8 Complex Numbers and Fourier Series 321

8.1 The Complex Plane and Arithmetic 322

Problems 332

8.2 Fourier Series 334

Problems 344

8.3 Filters and Convolution in the Fourier Domain 349

Problems 360

9 Filter Construction in the Fourier Domain 365

9.1 Filter Construction 366

Problems 377

9.2 Daubechies Filters 378

Problems 382

9.3 Coiflet Filters 382

Problems 395

9.4 Biorthogonal Spline Filter Pairs 400

Problems 410

Computer Lab 413

9.5 The Cohen-Daubechies-Feauveau 9/7 Filter 414

Problems 423

Computer Lab 426

10 Wavelet Packets 427

10.1 The Wavelet Packet Transform 428

Problems 435

10.2 Cost Functions and the Best Basis Algorithm 436

Problems 444

10.3 The FBI Fingerprint Compression Specification 446

Computer Lab 460

11 Lifting 461

11.1 The LeGall Wavelet Transform 462

Problems 471

Computer Lab 473

11.2 Z-Transforms and Laurent Polynomials 474

Problems 484

11.3 A General Construction of the Lifting Method 486

Problems 499

11.4 The Lifting Method - Examples 504

Problems 517

12 The JPEG2000 Image Compression Standard 525

12.1 An Overview of JPEG 526

Problems 532

12.2 The Basic JPEG2000 Algorithm 533

Problems 539

12.3 Examples 540

A Basic Statistics 547

A.1 Descriptive Statistics 547

Problems 549

A.2 Sample Spaces, Probability, and Random Variables 550

Problems 553

A.3 Continuous Distributions 553

Problems 559

A.4 Expectation 559

Problems 565

A.5 Two Special Distributions 566

Problems 568
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.

P. Van Fleet, University of St. Thomas