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E-raamat: Primer on Wavelets and Their Scientific Applications

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(University of Wisconsin, Eau Claire, USA)
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Primer on Wavelets and Their Scientific ApplicationsSuurem pilt
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In the first edition of his seminal introduction to wavelets, James S. Walker informed us that the potential applications for wavelets were virtually unlimited. Since that time thousands of published papers have proven him true, while also necessitating the creation of a new edition of his bestselling primer. Updated and fully revised to include the latest developments, this second edition of A Primer on Wavelets and Their Scientific Applications guides readers through the main ideas of wavelet analysis in order to develop a thorough appreciation of wavelet applications.

Ingeniously relying on elementary algebra and just a smidgen of calculus, Professor Walker demonstrates how the underlying ideas behind wavelet analysis can be applied to solve significant problems in audio and image processing, as well in biology and medicine.

Nearly twice as long as the original, this new edition provides

· 104 worked examples and 222 exercises, constituting a veritable book of review material

· Two sections on biorthogonal wavelets

· A mini-course on image compression, including a tutorial on arithmetic compression

· Extensive material on image denoising, featuring a rarely covered technique for removing isolated, randomly positioned clutter

· Concise yet complete coverage of the fundamentals of time-frequency analysis, showcasing its application to audio denoising, and musical theory and synthesis

· An introduction to the multiresolution principle, a new mathematical concept in musical theory

· Expanded suggestions for research projects

· An enhanced list of references

· FAWAV: software designed by the author, which allows readers to duplicate described applications and experiment with other ideas.

To keep the book current, Professor Walker has created a supplementary website. This online repository includes ready-to-download software, and sound and image files, as well as access to many of the most important papers in the field.

Arvustused

"The books relative lack of formalism results in a low symbol-to-word ratio; here is a math text that can be read quickly yet with comprehension. This is in keeping with the goal of engaging the applications as quickly and painlessly as possible. With such accessibility and a first-rate supporting apparatus, this flexible book can teach various audiences the basics of wavelets, involve them in applications, and inspire them to learn more."

David A. Huckaby, Angelo State University, in MAA Online, July 2008

1 Overview 1
1.1 What is wavelet analysis?
1
1.2 Notes and references
4
2 Haar wavelets 5
2.1 The Haar transform
6
2.1.1 Haar transform, 1-level
7
2.2 Conservation and compaction of energy
9
2.2.1 Conservation of energy
10
2.2.2 Haar transform, multiple levels
11
2.2.3 Justification of conservation of energy
12
2.3 Haar wavelets
14
2.4 Multiresolution analysis
16
2.4.1 Multiresolution analysis, multiple levels
19
2.5 Signal compression
21
2.5.1 A note on quantization
26
2.6 Removing noise
26
2.6.1 RMS Error
29
2.7 Notes and references
30
2.8 Examples and exercises
31
3 Daubechies wavelets 41
3.1 The D aub4 wavelets
41
3.1.1 Remarks on small fluctuation values*
49
3.2 Conservation and compaction of energy
50
3.2.1 Justification of conservation of energy*
50
3.2.2 How wavelet and sealing numbers are found*
53
3.3 Other Daubechies wavelets
54
3.3.1 Coiflets
58
3.4 Compression of audio signals
61
3.4.1 Quantization and the significance map
62
3.5 Quantization, entropy, and compression.
65
3.6 Denoising audio signals
69
3.6.1 Choosing a threshold value
70
3.6.2 Removing pop noise and background static
73
3.7 Biorthogonal wavelets
75
3.7.1 Daub 5/3 system
76
3.7.2 Daub 5/3 inverse
78
3.7.3 MRA for the Daub 5/3 system
78
3.7.4 Daub 5/3 transform, multiple levels
80
3.7.5 Daub 5/3 integer-to-integer system
82
3.8 The Daub 9/7 system
83
3.9 Notes and references
85
3.10 Examples and exercises
87
4 Two-dimensional wavelets 97
4.1 Two-dimensional wavelet transforms
97
4.1.1 Discrete images
98
4.1.2 2D wavelet transforms
99
4.1.3 2D wavelets and scaling images
102
4.2 Compression of images fundamentals
104
4.2.1 Error measures in image processing
107
4.2.2 Comparing JPEG with wavelet-based compressors
108
4.3 Fingerprint compression
110
4.4 The WDR, algorithm
113
4.4.1 Bit-plane encoding
113
4.4.2 Difference reduction
116
4.4.3 Arithmetic compression
119
4.5 The ASWDR, algorithm
123
4.5.1 Arithmetic compression
125
4.5.2 Relation to vision
126
4.6 Important image compression features
127
4.6.1 Progressive transmission/reconstruction
197
4.6.2 Lossless compression
128
4.6.3 Region-of-interest
130
4.7 .IPEG 200(1 image compression
130
4.7.1 Compressing color images
132
4.8 Denoising images
133
4.8.1 The TAWS algorithm
133
4.8.2 Comparison with Wiener denoising
134
4.8.3 Estimation of noise standard deviation*
136
4.8.4 Removal of clutter noise
137
4.9 Sonic topics in image processing
139
4.9.1 Edge detection
139
4.9.2 Edge enhancement
140
4.9.3 Image recognition
141
4.10 Notes and references
144
4.11 Examples and exercises
147
5 Frequency analysis 167
5.1 Discrete Fourier analysis
168
5.1.1 Frequency content of wavelets
169
5.2 Definition of the DFT and its properties
170
5.2.1 Properties of the DFT
171
5.2.2 z-transforms*
173
5.3 Frequency description of wavelet analysis
174
5.3.1 Low-pass and high-pass filtering*
178
5.4 Correlation and feature detection
180
5.4.1 DFT method of computing correlations
181
5.4.2 Proof of DFT effect on correlation*
183
5.4.3 Normalized correlations and feature detection*
183
5.5 Object detection in 2D images
185
5.6 Creating scaling signals and wavelets*
188
5.7 Gabor transforms and spectrograms
192
5.8 Musical analysis
195
5.8.1 Analysis of Stravinsky's Firebird Suite
197
5.8.2 Analysis of a Chinese folk song
199
5.9 Inverting Gabor transforms
201
5.10 Gabor transforms and denoising
203
5.11 Notes and references
206
5.12 Examples and exercises
210
6 Beyond wavelets 223
6.1 Wavelet packet transforms
223
6.2 Wavelet packet transforms-applications
225
6.2.1 Fingerprint compression
228
6.3 Continuous wavelet transforms
228
6.4 Gabor wavelets and speech analysis
232
6.4.1 Musical analysis: formants in song lyrics
236
6.5 Percussion scalograms and musical rhythm
237
6.5.1 Analysis of a complex percussive rhythm
241
6.5.2 Multiresolution Principle for rhythm
241
6.6 Notes and references
241
6.6.1 Additional references
242
6.7 Examples and exercises
246
A Projects 255
A.1 Music
255
A.2 Noise removal from audio
256
A.3 Wavelet image processing
256
A.4 References
257
B Selected exercise solutions 259
B.1 Introduction
259
B.2
Chapter 2
259
B.3
Chapter 3
262
B.4
Chapter 4
268
B.5
Chapter 5
273
B.6
Chapter 6
279
C Wavelet software 283
C.1 Installing the book's software
284
C.2 Other software
284
C.3 References
285
Bibliography 287
Index 295


James S. Walker
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
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