Wavelet analysis with applications to image processing:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla.
CRC Press
1997
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 279 S. |
| ISBN: | 0849331692 |
Staff View
MARC
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| 245 | 1 | 0 | |a Wavelet analysis with applications to image processing |c L. Prasad & S. S. Iyengar |
| 264 | 1 | |a Boca Raton, Fla. |b CRC Press |c 1997 | |
| 300 | |a XIV, 279 S. | ||
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| 650 | 4 | |a Ondelettes | |
| 650 | 4 | |a Traitement d'images - Mathématiques | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Image processing |x Mathematics | |
| 650 | 4 | |a Wavelets (Mathematics) | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Introduction and Mathematical Preliminaries 1
1.1 Notation and Abbreviations 1
1.2 Basic Set Operations 3
1.3 Cardinality of Sets Finite, Countable, and Uncountable Sets 6
1.4 Rings and Algebras of Sets 9
2 Linear Spaces, Metric Spaces, and Hilbert Spaces 11
2.1 Linear Spaces 11
2.1.1 Subspaces 14
2.1.2 Factor spaces (quotient spaces) 15
2.1.3 Linear functionals 15
2.1.4 Null space (kernel) of a functional hyperplanes . . 16
2.1.5 Geometric interpretation of linear functions 16
2.1.6 Normed linear spaces 17
2.2 Metric Spaces 18
2.2.1 Continuous mappings 18
vii
viii CONTENTS
2.2.2 Convergence 19
2.2.3 Dense subsets 20
2.2.4 Closed sets 21
2.2.5 Open sets 21
2.2.6 Complex metric spaces 22
2.2.7 Completion of metric spaces 22
2.2.8 Norm induced metric and Banach spaces 23
2.3 Euclidean Spaces 23
2.3.1 Scalar products, orthogonality and bases 23
2.3.2 Existence of an orthogonal basis 25
2.3.3 Bessel s inequality and closed orthogonal systems . . 26
2.3.4 Complete Euclidean spaces and the Riesz Fischer the¬
orem 28
2.4 Hilbert Spaces 29
2.4.1 Subspaces, orthogonal complements, and direct sums 30
2.5 Characterization of Euclidean spaces 33
3 Integration 37
3.1 The Riemann Integral 37
3.1.1 Upper and lower Riemann integrals 38
3.1.2 Riemann integration vs Lebesgue integration .... 41
3.2 The Lebesgue Measure on R 42
3.3 Measurable Functions 49
CONTENTS ix
3.3.1 Simple functions 55
3.4 Convergence of Measurable Functions 56
3.5 Lebesgue Integration 58
3.5.1 Some properties of the Lebesgue integral 68
4 Fourier Analysis 69
4.1 The Spaces Lx(x) and L2(x) 70
4.1.1 The space L1(x) 71
4.1.2 The space L2(x) 72
4.2 Fourier Series 79
4.2.1 Fourier series of square integrable functions 80
4.2.2 Fourier series of absolutely integrable functions ... 86
4.2.3 The convolution product on L1^1) 89
4.3 Fourier Transforms 90
4.3.1 Fourier transforms of functions in I?(R) 96
4.3.2 Fourier transforms of functions in L1 (R) 96
4.3.3 Poisson summation formula 99
5 Wavelet Analysis 101
5.1 Time Frequency Analysis and the Windowed Fourier Trans¬
form 101
5.1.1 Heisenberg s Uncertainty Principle 103
5.2 The Integral Wavelet Transform 105
5.3 The Discrete Wavelet Transform 112
x CONTENTS
5.4 Multiresolution Analysis (MRA) of L2(R) 116
5.4.1 Constructing an MRA from a scaling function . . . 124
5.5 Wavelet Decomposition and Reconstruction of Functions . 131
5.5.1 Multiresolution decomposition and reconstruction of
functions in L2(R) 131
5.6 The Fast Wavelet Algorithm 136
6 Construction of Wavelets 141
6.1 The Battle Lemarie Family of Wavelets 141
6.1.1 Cardinal B splines 142
6.1.2 Cardinal B spline MRA of L2(R) 144
6.2 Subband Filtering Schemes 152
6.2.1 Bandlimited functions 152
6.2.2 Discrete filtering 154
6.2.3 Conjugate quadrature filters (CQF) 158
6.2.4 CQFs arising from MRAs 159
6.3 Compactly Supported Orthonormal Wavelet Bases 160
6.3.1 The structure of ro0 160
6.3.2 Necessary and sufficient conditions for orthonormality 166
6.3.3 The cascade algorithm 174
6.4 Biorthogonal Wavelets 178
6.4.1 Linear phase FIR niters 178
6.4.2 Compactly supported orthonormal wavelets are asym¬
metric 184
CONTENTS xi
6.4.3 Dual FIR filters with exact reconstruction 187
6.4.4 Dual scaling functions and wavelets 191
6.4.5 Biorthogonai Riesz bases of wavelets and associated
MRAs 192
6.4.6 Conditions for biorthogonality 193
6.4.7 Symmetry for mo and mo 210
6.4.8 Biorthogonai spline wavelets with compact support . 211
7 Wavelets in Image Processing 215
7.1 The Burt Adelson Pyramidal Decomposition Scheme .... 217
7.1.1 The smoothing function H,*, 222
7.2 Mallat s Wavelet Based Pyramidal Decomposition Scheme . 224
7.2.1 The one dimensional fast wavelet algorithm 225
7.2.2 An MRA of L2(R2) 228
7.2.3 The two dimensional wavelet algorithm 230
7.3 Multiscale Edge Representation of Images 235
7.3.1 The one dimensional dyadic wavelet transform . . . 239
7.3.2 Signal reconstruction from its one dimensional dyadic
wavelet transform 242
7.3.3 Method of alternate projections 245
7.3.4 The dyadic wavelet transform of images 247
7.3.5 Image reconstruction from its two dimensional dyadic
wavelet transform 251
7.3.6 Method of alternate projections in two dimensional. 254
xii CONTENTS
7.3.7 The discrete finite dyadic wavelet transform 256
7.4 Double Layered Image encoding 258
7.4.1 Multiscale edge based image encoding 259
7.4.2 Texture based image encoding 260
7.5 Additional Wavelet Applications 261
A Bezout s Theorem 269
|
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| author | Prasad, Laksham Iyengar, S. S. 1947- |
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| dewey-ones | 621 - Applied physics |
| dewey-raw | 621.36/7 |
| dewey-search | 621.36/7 |
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| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik Elektrotechnik / Elektronik / Nachrichtentechnik |
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| id | DE-604.BV011523551 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:11:11Z |
| institution | BVB |
| isbn | 0849331692 |
| language | English |
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| physical | XIV, 279 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Prasad, Laksham Verfasser aut Wavelet analysis with applications to image processing L. Prasad & S. S. Iyengar Boca Raton, Fla. CRC Press 1997 XIV, 279 S. txt rdacontent n rdamedia nc rdacarrier Ondelettes Traitement d'images - Mathématiques Mathematik Image processing Mathematics Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 gnd rswk-swf Bildverarbeitung (DE-588)4006684-8 s Wavelet (DE-588)4215427-3 s DE-604 Iyengar, S. S. 1947- Verfasser (DE-588)121802485 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007755050&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prasad, Laksham Iyengar, S. S. 1947- Wavelet analysis with applications to image processing Ondelettes Traitement d'images - Mathématiques Mathematik Image processing Mathematics Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd Bildverarbeitung (DE-588)4006684-8 gnd |
| subject_GND | (DE-588)4215427-3 (DE-588)4006684-8 |
| title | Wavelet analysis with applications to image processing |
| title_auth | Wavelet analysis with applications to image processing |
| title_exact_search | Wavelet analysis with applications to image processing |
| title_full | Wavelet analysis with applications to image processing L. Prasad & S. S. Iyengar |
| title_fullStr | Wavelet analysis with applications to image processing L. Prasad & S. S. Iyengar |
| title_full_unstemmed | Wavelet analysis with applications to image processing L. Prasad & S. S. Iyengar |
| title_short | Wavelet analysis with applications to image processing |
| title_sort | wavelet analysis with applications to image processing |
| topic | Ondelettes Traitement d'images - Mathématiques Mathematik Image processing Mathematics Wavelets (Mathematics) Wavelet (DE-588)4215427-3 gnd Bildverarbeitung (DE-588)4006684-8 gnd |
| topic_facet | Ondelettes Traitement d'images - Mathématiques Mathematik Image processing Mathematics Wavelets (Mathematics) Wavelet Bildverarbeitung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007755050&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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