Wavelet Theory An Elementary Approach with Applications
by Ruch, David K.; Van Fleet, Patrick J.Edition: 1st
Format: Hardcover
Pub. Date: 2009-10-26
Publisher(s): Wiley-Interscience
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Summary
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.
Table of Contents
| 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 Vj | p. 93 |
| Problems | p. 107 |
| The Haar Wavelet Space W0 | p. 108 |
| Problems | p. 119 |
| The General Haar Wavelet Space Wj | 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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