Wavelets and multiwavelets:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC Press
2004
|
| Schriftenreihe: | Studies in advanced mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XII, 275 S. graph. Darst. |
| ISBN: | 1584883049 |
Internformat
MARC
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| 245 | 1 | 0 | |a Wavelets and multiwavelets |c Fritz Keinert |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC Press |c 2004 | |
| 300 | |a XII, 275 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Studies in advanced mathematics | |
| 500 | |a Includes bibliographical references and index | ||
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Datensatz im Suchindex
| _version_ | 1804130253845561344 |
|---|---|
| adam_text | Contents
I Scalar Wavelets 1
1 Basic Theory 3
1.1 Refinable Functions 3
1.2 Orthogonal MRAs and Wavelets 10
1.3 Wavelet Decomposition 19
1.4 Biorthogonal MRAs and Wavelets 21
1.5 Moments 25
1.6 Approximation Order 28
1.7 Symmetry 32
1.8 Point Values and Normalization 35
2 Practical Computation 39
2.1 Discrete Wavelet Transform 40
2.2 Pre and Postprocessing 43
2.3 Handling Boundaries 45
2.3.1 Data Extension Approach 46
2.3.2 Matrix Completion Approach 48
2.3.3 Boundary Function Approach 49
2.3.4 Further Comments 51
2.4 Putting It All Together 52
2.5 Modulation Formulation 54
2.6 Polyphase Formulation 56
2.7 Lifting 58
2.8 Calculating Integrals 62
2.8.1 Integrals with Other Refinable Functions 62
2.8.2 Integrals with Polynomials 65
2.8.3 Integrals with General Functions 65
3 Creating Wavelets 69
3.1 Completion Problem 69
3.1.1 Finding Wavelet Functions 69
3.1.2 Finding Dual Scaling Functions 70
3.2 Projection Factors 71
3.3 Techniques for Modifying Wavelets 72
3.4 Techniques for Building Wavelets 73
ix
x Table of Contents
3.5 Bezout Equation 74
3.6 Daubechies Wavelets 75
3.6.1 Bezout Approach 75
3.6.2 Projection Factor Approach 78
3.7 Coiflets 79
3.7.1 Bezout Approach 79
3.7.2 Projection Factor Approach 81
3.7.3 Generalized Coiflets 82
3.8 Cohen Wavelets 85
3.9 Other Constructions 86
4 Applications 89
4.1 Signal Processing 89
4.1.1 Detection of Frequencies and Discontinuities 90
4.1.2 Signal Compression 90
4.1.3 Denoising 91
4.2 Numerical Analysis 93
4.2.1 Fast Matrix Vector Multiplication 93
4.2.2 Fast Operator Evaluation 95
4.2.3 Differential and Integral Equations 96
5 Existence and Regularity 97
5.1 Distribution Theory 98
5.2 Z^ Theory 100
5.3 Z2 Theory 102
5.3.1 Transition Operator 102
5.3.2 Sobolev Space Estimates 105
5.3.3 Cascade Algorithm 109
5.4 Pointwise Theory 110
5.5 Smoothness and Approximation Order 115
5.6 Stability 116
II Multiwavelets 121
6 Basic Theory 123
6.1 Refinable Function Vectors 124
6.2 MRAs and Multiwavelets 132
6.2.1 Orthogonal MRAs and Multiwavelets 132
6.2.2 Biorthogonal MRAs and Multiwavelets 137
6.3 Moments 140
6.4 Approximation Order 142
6.5 Point Values and Normalization 147
Table of Contents xi
7 Practical Computation 153
7.1 Discrete Multiwavelet Transform 154
7.2 Pre and Postprocessing 157
7.2.1 Interpolating Prefilters 158
7.2.2 Quadrature Based Prefilters 159
7.2.3 Hardin Roach Prefilters 159
7.2.4 Other Prefilters 161
7.3 Balanced Multiwavelets 1G1
7.4 Handling Boundaries 163
7.4.1 Data Extension Approach 163
7.4.2 Matrix Completion Approach 164
7.4.3 Boundary Function Approach 164
7.5 Putting It All Together 165
7.6 Modulation Formulation 167
7.7 Polyphase Formulation 169
7.8 Calculating Integrals 171
7.8.1 Integrals with Other Refinable Functions 172
7.8.2 Integrals with Polynomials 174
7.8.3 Integrals with General Functions 175
7.9 Applications 175
7.9.1 Signal Processing 175
7.9.2 Numerical Analysis 175
8 Two Scale Similarity Transforms 177
8.1 Regular TSTs 177
8.2 Singular TSTs 179
8.3 Multiwavelet TSTs 183
8.4 TSTs and Approximation Order 188
8.5 Symmetry 191
9 Factorizations of Polyphase Matrices 197
9.1 Projection Factors 197
9.1.1 Orthogonal Case 197
9.1.2 Biorthogonal Case 200
9.2 Lifting Steps 203
9.3 Raising Approximation Order by Lifting 206
10 Creating Multiwavelets 209
10.1 Orthogonal Completion 209
10.1.1 Using Projection Factors 209
10.1.2 Householder Type Approach 211
10.2 Biorthogonal Completion 212
10.3 Other Approaches 214
10.4 Techniques for Modifying Multiwavelets 215
10.5 Techniques for Building Multiwavelets 216
xii Table of Contents
11 Existence and Regularity 219
11.1 Distribution Theory 220
11.2 i^Theory 223
11.3 L2 Theory 225
11.3.1 Transition Operator 225
11.3.2 Sobolev Space Estimates 227
11.3.3 Cascade Algorithm 231
11.4 Pointwise Theory 231
11.5 Smoothness and Approximation Order 235
11.6 Stability 235
A Standard Wavelets 239
A.I Scalar Orthogonal Wavelets 239
A.2 Scalar Biorthogonal Wavelets 240
A.3 Orthogonal Multiwavelets 241
A.4 Biorthogonal Multiwavelets 244
B Mathematical Background 247
B.I Notational Conventions 247
B.2 Derivatives 247
B.3 Functions and Sequences 247
B.4 Fourier Transform 249
B.5 Laurent Polynomials 250
B.6 Trigonometric Polynomials 250
B.7 Linear Algebra 252
C Computer Resources 255
C.I Wavelet Internet Resources 255
C.2 Wavelet Software 255
C.3 Multiwavelet Software 257
References 259
Index 270
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:18:06Z |
| institution | BVB |
| isbn | 1584883049 |
| language | English |
| lccn | 2003055780 |
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| physical | XII, 275 S. graph. Darst. |
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| publisher | Chapman & Hall/CRC Press |
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| series2 | Studies in advanced mathematics |
| spelling | Keinert, Fritz Verfasser aut Wavelets and multiwavelets Fritz Keinert Boca Raton [u.a.] Chapman & Hall/CRC Press 2004 XII, 275 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Studies in advanced mathematics Includes bibliographical references and index Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd rswk-swf Wavelet (DE-588)4215427-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010510638&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Keinert, Fritz Wavelets and multiwavelets Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4215427-3 |
| title | Wavelets and multiwavelets |
| title_auth | Wavelets and multiwavelets |
| title_exact_search | Wavelets and multiwavelets |
| title_full | Wavelets and multiwavelets Fritz Keinert |
| title_fullStr | Wavelets and multiwavelets Fritz Keinert |
| title_full_unstemmed | Wavelets and multiwavelets Fritz Keinert |
| title_short | Wavelets and multiwavelets |
| title_sort | wavelets and multiwavelets |
| topic | Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Wavelets (Mathematics) Wavelet |
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