Four short courses on harmonic analysis: wavelets, frames, time-frequency methods, and applications to signal and image analysis
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2010
|
| Series: | Applied and numerical harmonic analysis
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 247 S. Ill., graph. Darst. |
| ISBN: | 9780817648909 |
Staff View
MARC
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| 245 | 1 | 0 | |a Four short courses on harmonic analysis |b wavelets, frames, time-frequency methods, and applications to signal and image analysis |c Brigitte Forster ... (eds.) With contributions by Ole Christensen ... |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2010 | |
| 300 | |a XVIII, 247 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Applied and numerical harmonic analysis | |
| 650 | 4 | |a Analyse harmonique | |
| 650 | 4 | |a Harmonic analysis | |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Frame |g Mathematik |0 (DE-588)4528312-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zeit-Frequenz-Analyse |0 (DE-588)4626990-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Wavelet |0 (DE-588)4215427-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
| 689 | 0 | 1 | |a Wavelet |0 (DE-588)4215427-3 |D s |
| 689 | 0 | 2 | |a Frame |g Mathematik |0 (DE-588)4528312-6 |D s |
| 689 | 0 | 3 | |a Zeit-Frequenz-Analyse |0 (DE-588)4626990-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Forster, Brigitte |e Sonstige |4 oth | |
| 700 | 1 | |a Christensen, Ole |d 1966- |e Sonstige |0 (DE-588)12445836X |4 oth | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-017989626 | ||
Record in the Search Index
| _version_ | 1804139919925313536 |
|---|---|
| adam_text | Contents
ANHA
Series
Preface
Preface
............................................................ ix
List of Contributors
................................................xvii
1
Introduction: Mathematical Aspects of Time-Frequency Analysis
... 1
Peter
Massopust
and
Brigitte
Forster
1.1
Aims of Time-Frequency Analysis
........................... 1
1.1.1
Signal and Model
................................. 2
1.1.2
Transforms
....................................... 3
1.1.3
Signal Manipulations
—
Filters
....................... 8
1.1.4
Why Discretizing? Techniques, Challenges, Pitfalls
..... 8
1.2
Basic Methods of Time-Frequency Analysis:
Orthonormal
Bases
and Generalized Fourier Series
.............................. 10
1.2.1 Schauder
Bases in Banach Spaces
.................... 10
1.2.2
Generalized Fourier Series
.......................... 14
1.3
The Fourier Integral Transform
.............................. 15
1.3.1
Definition and Properties
........................... 15
1.3.2
The Plancherel Transform
.......................... 26
1.3.3
The Theorem of Paley-Wiener
...................... 29
1.3.4
Discretization: The
Poisson
Summation Formula and
the Sampling Theorem
............................. 30
1.4
Windowed Fourier Transforms
.............................. 31
1.4.1
The Short-Time Fourier Transform (STFT)
............ 31
1.4.2
The
Gabor
Transform
.............................. 32
1.4.3
The
Heisenberg
Uncertainty Principle
................ 36
1.4.4
Discretization:
Gabor
Frames
....................... 38
1.4.5
Shortcomings of the Windowed Fourier Transform
...... 38
1.5
The Wavelet Transform
.................................... 39
1.5.1
Definition and Properties
........................... 39
1.5.2
Scale Discretization
—
The Dyadic Wavelet Transform
... 42
1.5.3
Multiresolution Analyses
........................... 43
1.6
Other Multiscale Transforms
................................ 45
1.6.1
Tensor Product Wavelets in 2D
...................... 45
1.6.2
Some Wavelet-Type Transforms
..................... 46
1.6.3
Moving to Other Manifolds
—
Wavelets on the Sphere
... 47
Exercises
...................................................... 49
B-Spline
Generated Frames
................................... 51
Ole Christensen
2.1
Introduction
.............................................. 51
2.2
Bessel Sequences in Hubert Spaces
.......................... 52
2.3
General Bases and
Orthonormal
Bases
........................ 54
2.4
Riesz Bases
.............................................. 56
2.5
Frames and Their Properties
................................ 59
2.6
Frames and Riesz Bases
.................................... 62
2.7
B-Splines
................................................ 64
2.8
Frames of Translates
....................................... 65
2.9
Basic
Gabor
Frame Theory
................................. 67
2.10
Tight
Gabor
Frames
....................................... 70
2.11
The Duals of
a
Gabor
Frame
................................ 72
2.12
Explicit Construction of Dual
Gabor
Frame Pairs
............... 73
2.13
Wavelets and the Unitary Extension Principle
.................. 77
Exercises
...................................................... 84
Continuous and Discrete Reproducing Systems That Arise from
Translations. Theory and Applications of Composite Wavelets
...... 87
Demetrio Labate
and
Guido
Weiss
3.1
Introduction
.............................................. 87
3.2
Unified Theory of Reproducing Systems
...................... 91
3.2.1
Unified Theorem for Reproducing Systems
............ 92
3.3
Continuous Wavelet Transform
.............................. 98
3.3.1
Admissible Groups
................................101
3.3.2
Wave Packet Systems
..............................102
3.4
Affine
Systems with Composite Dilations
.....................104
3.4.1
Affine
System with Composite Dilations
..............108
3.4.2
Other Examples
...................................110
3.5
Continuous Shearlet Transform
..............................116
3.5.1
Edge Analysis Using the Shearlet Transform
...........120
3.5.2
A Shearlet Approach to Edge Analysis and Detection
... 121
3.5.3
Discrete Shearlet System
...........................123
3.5.4
Optimal Representations Using Shearlets
..............126
Exercises
......................................................129
Wavelets on the Sphere
....................................... 131
Pierre Vandergheynst and Yves Wiaux
4.1
Introduction
..............................................131
4.2
Scale-Space Premises
......................................132
4.2.1
Directional Correlations
............................132
4.2.2
Harmonic Analysis
................................133
4.2.3
Affine
Transformations
.............................136
4.3
Continuous Formalism
.....................................141
4.3.1
Generic Wavelets
..................................141
4.3.2 Stereographic
Wavelets
.............................145
4.3.3 Kernel
Wavelets
................................... 149
4.3.4
Discretization of Variables
.......................... 152
4.4
Analysis Algorithms
....................................... 153
4.4.1
Pixelization
...................................... 153
4.4.2
Fast Algorithms
................................... 155
4.5
Discrete Formalism
....................................... 159
4.5.1
Discrete Wavelets
................................. 159
4.5.2
Other Constructions
............................... 165
4.6
Reconstruction Algorithm
.................................. 167
4.6.1
Multiresolution
................................... 167
4.6.2
Fast Algorithm
.................................... 168
4.7
Applications
............................................. 169
4.7.1
Cosmic Microwave Background Analysis
............. 169
4.7.2
Human Cortex Image Denoising
..................... 170
4.8
Conclusion
............................................... 173
Exercises
...................................................... 174
5
Wiener s Lemma: Theme and Variations. An Introduction to
Spectral
Invariance
and Its Applications
........................ 175
Karlheinz Gröchenig
5.1
Introduction
..............................................175
5.2
Wiener s Lemma
—
Classical
................................177
5.2.1
Definitions from Banach Algebras
...................178
5.2.2
Absolutely Convergent Fourier Series
.................178
5.2.3
Wiener s Lemma
..................................179
5.2.4
Proof of Wiener s Lemma
..........................180
5.2.5
Abstract Concepts
—
Inverse-Closedness
..............182
5.2.6
Convolution Operators
.............................188
Exercises for Section
5.2.........................................193
5.3
Variations
................................................195
5.3.1
Weighted Versions of Wiener s Lemma
...............195
5.3.2
Matrix Algebras
...................................200
5.3.3
Absolutely Convergent Series of Time-Frequency Shifts
. 208
5.3.4
Convolution Operators on Groups
....................216
5.3.5
Pseudodifferential Operators
........................220
5.3.6
Time-Varying Systems and Wireless Communications
... 227
Exercises for Section
5.3.........................................234
References
.........................................................235
Index
.............................................................245
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| id | DE-604.BV035712725 |
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| indexdate | 2024-07-09T21:51:44Z |
| institution | BVB |
| isbn | 9780817648909 |
| language | English |
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| physical | XVIII, 247 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
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| publisher | Birkhäuser |
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| series2 | Applied and numerical harmonic analysis |
| spelling | Four short courses on harmonic analysis wavelets, frames, time-frequency methods, and applications to signal and image analysis Brigitte Forster ... (eds.) With contributions by Ole Christensen ... Boston [u.a.] Birkhäuser 2010 XVIII, 247 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied and numerical harmonic analysis Analyse harmonique Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Frame Mathematik (DE-588)4528312-6 gnd rswk-swf Zeit-Frequenz-Analyse (DE-588)4626990-3 gnd rswk-swf Wavelet (DE-588)4215427-3 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 s Wavelet (DE-588)4215427-3 s Frame Mathematik (DE-588)4528312-6 s Zeit-Frequenz-Analyse (DE-588)4626990-3 s DE-604 Forster, Brigitte Sonstige oth Christensen, Ole 1966- Sonstige (DE-588)12445836X oth Erscheint auch als Online-Ausgabe 978-0-8176-4891-6 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017989626&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Four short courses on harmonic analysis wavelets, frames, time-frequency methods, and applications to signal and image analysis Analyse harmonique Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd Frame Mathematik (DE-588)4528312-6 gnd Zeit-Frequenz-Analyse (DE-588)4626990-3 gnd Wavelet (DE-588)4215427-3 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4528312-6 (DE-588)4626990-3 (DE-588)4215427-3 |
| title | Four short courses on harmonic analysis wavelets, frames, time-frequency methods, and applications to signal and image analysis |
| title_auth | Four short courses on harmonic analysis wavelets, frames, time-frequency methods, and applications to signal and image analysis |
| title_exact_search | Four short courses on harmonic analysis wavelets, frames, time-frequency methods, and applications to signal and image analysis |
| title_full | Four short courses on harmonic analysis wavelets, frames, time-frequency methods, and applications to signal and image analysis Brigitte Forster ... (eds.) With contributions by Ole Christensen ... |
| title_fullStr | Four short courses on harmonic analysis wavelets, frames, time-frequency methods, and applications to signal and image analysis Brigitte Forster ... (eds.) With contributions by Ole Christensen ... |
| title_full_unstemmed | Four short courses on harmonic analysis wavelets, frames, time-frequency methods, and applications to signal and image analysis Brigitte Forster ... (eds.) With contributions by Ole Christensen ... |
| title_short | Four short courses on harmonic analysis |
| title_sort | four short courses on harmonic analysis wavelets frames time frequency methods and applications to signal and image analysis |
| title_sub | wavelets, frames, time-frequency methods, and applications to signal and image analysis |
| topic | Analyse harmonique Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd Frame Mathematik (DE-588)4528312-6 gnd Zeit-Frequenz-Analyse (DE-588)4626990-3 gnd Wavelet (DE-588)4215427-3 gnd |
| topic_facet | Analyse harmonique Harmonic analysis Harmonische Analyse Frame Mathematik Zeit-Frequenz-Analyse Wavelet |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017989626&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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