This self-contained, elementary introduction to wavelet theory and its applications provides a comprehensive treatment of the topic using two real-life applications: the FBI Wavelet Scalar Quantization Standard and image segmentation. Over 400 exercises plus extensive details and examples help readers gain a full understanding of the material. Supplemented with a software package called DiscreteWavelets, which helps both students and professionals to visualize the applications addressed throughout the book.

Author Biography

Patrick J. Van Fleet is Professor of Mathematics and Director of the Center for Applied Mathematics at the University of St. Thomas in St. Paul, Minnesota.

Preface	p. xi
Acknowledgments	p. xix
The Complex Plane and the Space L²(R)	p. 1
Complex Numbers and Basic Operations	p. 1
Problems	p. 5
The Space L²(R)	p. 7
Problems	p. 16
Inner Products	p. 18
Problems	p. 25
Bases and Projections	p. 26
Problems	p. 28
Fourier Series and Fourier Transformations	p. 31
Euler's Formula and the Complex Exponential Function	p. 32
Problems	p. 36
Fourier Series	p. 37
Problems	p. 49
The Fourier Transform	p. 53
Problems	p. 66
Convolution and B-Splines	p. 72
Problems	p. 82
Haar Spaces	p. 85
The Haar Space V₀	p. 86
Problems	p. 93
The General Haar Space V_j	p. 93
Problems	p. 107
The Haar Wavelet Space W₀	p. 108
Problems	p. 119
The General Haar Wavelet Space W_j	p. 120
Problems	p. 133
Decomposition and Reconstruction	p. 134
Problems	p. 140
Summary	p. 141
The Discrete Haar Wavelet Transform and Applications	p. 145
The One-Dimensional Transform	p. 146
Problems	p. 159
The Two-Dimensional Transform	p. 163
Problems	p. 171
Edge Detection and Naive Image Compression	p. 172
Multiresolution Analysis	p. 179
Multiresolution Analysis	p. 180
Problems	p. 196
The View from the Transform Domain	p. 200
Problems	p. 212
Examples of Multiresolution Analyses	p. 216
Problems	p. 224
Summary	p. 225
Daubechies Scaling Functions and Wavelets	p. 233
Constructing the Daubechies Scaling Functions	p. 234
Problems	p. 246
The Cascade Algorithm	p. 251
Problems	p. 265
Orthogonal Translates, Coding, and Projections	p. 268
Problems	p. 276
The Discrete Daubechies Transformation and Applications	p. 277
The Discrete Daubechies Wavelet Transform	p. 278
Problems	p. 290
Projections and Signal and Image Compression	p. 293
Problems	p. 310
Naive Image Segmentation	p. 314
Problems	p. 322
Biorthogonal Scaling Functions and Wavelets	p. 325
A Biorthogonal Example and Duality	p. 326
Problems	p. 333
Biorthogonality Conditions for Symbols and Wavelet Spaces	p. 334
Problems	p. 350
Biorthogonal Spline Filter Pairs and the CDF97 Filter Pair	p. 353
Problems	p. 368
Decomposition and Reconstruction	p. 370
Problems	p. 375
The Discrete Biorthogonal Wavelet Transform	p. 375
Problems	p. 388
Riesz Basis Theory	p. 390
Problems	p. 397
Wavelet Packets	p. 399
Constructing Wavelet Packet Functions	p. 400
Problems	p. 413
Wavelet Packet Spaces	p. 414
Problems	p. 424
The Discrete Packet Transform and Best Basis Algorithm	p. 424
Problems	p. 439
The FBI Fingerprint Compression Standard	p. 440
Huffman Coding	p. 455
Problems	p. 462
References	p. 465
Topic Index	p. 469
Author Index	p. 479
Table of Contents provided by Ingram. All Rights Reserved.

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