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Wavelet Analysis: Basic Concepts and Applications [Kõva köide]

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  • Formaat: Hardback, 254 pages, kõrgus x laius: 254x178 mm, kaal: 612 g, 18 Line drawings, black and white; 1 Halftones, black and white; 19 Illustrations, black and white
  • Ilmumisaeg: 21-Apr-2021
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367562189
  • ISBN-13: 9780367562182
Teised raamatud teemal:
Wavelet Analysis: Basic Concepts and ApplicationsSuurem pilt
  • Formaat: Hardback, 254 pages, kõrgus x laius: 254x178 mm, kaal: 612 g, 18 Line drawings, black and white; 1 Halftones, black and white; 19 Illustrations, black and white
  • Ilmumisaeg: 21-Apr-2021
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367562189
  • ISBN-13: 9780367562182
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367562182.html
Märksõnad:
Wavelet Analysis: Basic Concepts and Applications provides a basic and self-contained introduction to the ideas underpinning wavelet theory and its diverse applications. This book is suitable for masters or PhD students, senior researchers, or scientists working in industrial settings, where wavelets are used to model real-world phenomena and data needs (such as finance, medicine, engineering, transport, images, signals, etc.).

Features:











Offers a self-contained discussion of wavelet theory





Suitable for a wide audience of post-graduate students, researchers, practitioners, and theorists





Provides researchers with detailed proofs





Provides guides for readers to help them understand and practice wavelet analysis in different areas
List of Figures
ix
Preface xi
Chapter 1 Introduction
1(4)
Chapter 2 Wavelets on Euclidean Spaces
5(30)
2.1 Introduction
5(1)
2.2 Wavelets ON R
6(5)
2.2.1 Continuous wavelet transform
7(3)
2.2.2 Discrete wavelet transform
10(1)
2.3 Multi-Resolution Analysis
11(2)
2.4 Wavelet Algorithms
13(3)
2.5 Wavelet Basis
16(5)
2.6 Multidimensional Real Wavelets
21(1)
2.7 Examples Of Wavelet Functions And MRA
22(9)
2.7.1 Haar wavelet
22(2)
2.7.2 Faber-Schauder wavelet
24(1)
2.7.3 Daubechies wavelets
25(2)
2.7.4 Symlet wavelets
27(1)
2.7.5 Spline wavelets
27(2)
2.7.6 Anisotropic wavelets
29(1)
2.7.7 Cauchy wavelets
30(1)
2.8 Exercises
31(4)
Chapter 3 Wavelets extended
35(16)
3.1 Affine Group Wavelets
35(2)
3.2 Multiresolution Analysis On The Interval
37(3)
3.2.1 Monasse-Perrier construction
37(1)
3.2.2 Bertoluzza-Falletta construction
37(2)
3.2.3 Daubechies wavelets versus Bertoluzza-Faletta
39(1)
3.3 Wavelets On The Sphere
40(7)
3.3.1 Introduction
40(1)
3.3.2 Existence of scaling functions
41(2)
3.3.3 Multiresolution analysis on the sphere
43(1)
3.3.4 Existence of the mother wavelet
44(3)
3.4 Exercises
47(4)
Chapter 4 Clifford wavelets
51(48)
4.1 Introduction
51(1)
4.2 Different Constructions Of Clifford Algebras
52(4)
4.2.1 Clifford original construction
53(1)
4.2.2 Quadratic form-based construction
53(1)
4.2.3 A standard construction
54(2)
4.3 Graduation In Clifford Algebras
56(1)
4.4 Some Useful Operations On Clifford Algebras
57(3)
4.4.1 Products in Clifford algebras
57(1)
4.4.2 Involutions on a Clifford algebra
58(2)
4.5 Clifford Functional Analysis
60(7)
4.6 Existence Of Monogenic Extensions
67(3)
4.7 Clifford-Fourier Transform
70(6)
4.8 Clifford Wavelet Analysis
76(16)
4.8.1 Spin-group based Clifford wavelets
76(6)
4.8.2 Monogenic polynomial-based Clifford wavelets
82(10)
4.9 Some Experimentations
92(4)
4.10 Exercises
96(3)
Chapter 5 Quantum wavelets
99(38)
5.1 Introduction
99(1)
5.2 Bessel Functions
99(6)
5.3 Bessel Wavelets
105(2)
5.4 Fractional Bessel Wavelets
107(12)
5.5 Quantum Theory Toolkit
119(4)
5.6 Some Quantum Special Functions
123(4)
5.7 Quantum Wavelets
127(7)
5.8 Exercises
134(3)
Chapter 6 Wavelets in statistics
137(26)
6.1 Introduction
137(1)
6.2 Wavelet Analysis Of Time Series
138(3)
6.2.1 Wavelet time series decomposition
138(2)
6.2.2 The wavelet decomposition sample
140(1)
6.3 Wavelet Variance And Covariance
141(3)
6.4 Wavelet Decimated And Stationary Transforms
144(1)
6.4.1 Decimated wavelet transform
144(1)
6.4.2 Wavelet stationary transform
145(1)
6.5 Wavelet Density Estimation
145(7)
6.5.1 Orthogonal series for density estimation
145(2)
6.5.2 δ-series estimators of density
147(1)
6.5.3 Linear estimators
148(2)
6.5.4 Donoho estimator
150(1)
6.5.5 Hall-Patil estimator
150(1)
6.5.6 Positive density estimators
151(1)
6.6 Wavelet Thresholding
152(5)
6.6.1 Linear case
152(2)
6.6.2 General case
154(1)
6.6.3 Local thresholding
155(1)
6.6.4 Global thresholding
155(1)
6.6.5 Block thresholding
156(1)
6.6.6 Sequences thresholding
156(1)
6.7 Application To Wavelet Density Estimations
157(3)
6.7.1 Gaussian law estimation
158(1)
6.7.2 Claw density wavelet estimators
159(1)
6.8 Exercises
160(3)
Chapter 7 Wavelets for partial differential equations
163(20)
7.1 Introduction
163(2)
7.2 Wavelet Collocation Method
165(1)
7.3 Wavelet Galerkin Approach
166(5)
7.4 Reduction Of The Connection Coefficients Number
171(3)
7.5 Two Main Applications In Solving PDEs
174(5)
7.5.1 The Dirichlet Problem
174(2)
7.5.2 The Neumann Problem
176(3)
7.6 Appendix
179(1)
7.7 Exercises
180(3)
Chapter 8 Wavelets for fractal and multifractal functions
183(26)
8.1 Introduction
183(1)
8.2 Hausdorff Measure And Dimension
184(2)
8.3 Wavelets For The Regularity Of Functions
186(3)
8.4 The Multifractal Formalism
189(3)
8.4.1 Frisch and Parisi multifractal formalism conjecture
189(1)
8.4.2 Arneodo et al wavelet-based multifractal formalism
190(2)
8.5 Self-Similar-Type Functions
192(9)
8.6 Application To Financial Index Modeling
201(4)
8.7 Appendix
205(1)
8.8 Exercises
205(4)
Bibliography 209(28)
Index 237
Sabrine Arfaoui is the assistant professor of mathematics at the Faculty of Sciences, University of Monastir. Her main interests include wavelet harmonic analysis, especially in the Clifford algebra/analysis framework and their applications in other fields such as fractals, PDEs, bio-signals/bio-images. Currently Dr. Arfaoui is associated with the University of Tabuk, Saudi Arabia in a technical cooperation project.

Anouar Ben Mabrouk is currently working as the professor of mathematics. He is also the associate professor of Mathematics at the University of Kairouan, Tunisia, the Faculty of Sciences, University of Monastir. His main research interests are are wavelets, fractals, probability/statistics, PDEs and related fields such as financial mathematics, time series, image/signal processing, numerical and theoretical aspects of PDEs. Dr. Ben Mabrouk is currently associated with the University of Tabuk, Saudi Arabia in a technical cooperation project.

Carlo Cattani is currently the professor of Mathematical Physics and Applied Mathematics at the Engineering School (DEIM) of University of Tuscia. His scientific interests include but are not limited to wavelets, dynamical systems, fractals, fractional calculus, numerical methods, number theory, stochastic integro-differential equations, competition models, time-series analysis, nonlinear analysis, complexity of living systems, pattern analysis, computational biology, biophysics, history of science. He has (co)authored more than 150 scientific articles on international journals as well as several books.