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E-grāmata: Two-Dimensional Wavelets and their Relatives

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(Concordia University, Montréal), (Université Catholique de Louvain, Belgium), (Swiss Federal Institute of Technology, Zürich), (Clark Atlanta University, Georgia)
  • Formāts: PDF+DRM
  • Izdošanas datums: 12-Jun-2008
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9780511227080
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Two-Dimensional Wavelets and their RelativesPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 12-Jun-2008
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9780511227080
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Two-dimensional wavelets offer a number of advantages over discrete wavelet transforms when processing rapidly varying functions and signals. In particular, they offer benefits for real-time applications such as medical imaging, fluid dynamics, shape recognition, image enhancement and target tracking. This book introduces the reader to 2-D wavelets via 1-D continuous wavelet transforms, and includes a long list of useful applications. The authors then describe in detail the underlying mathematics before moving on to more advanced topics such as matrix geometry of wavelet analysis, three-dimensional wavelets and wavelets on a sphere. Throughout the book, practical applications and illustrative examples are used extensively, ensuring the book's value to engineers, physicists and mathematicians alike.

Recenzijas

Review of the hardback: 'This book is of great interest to anyone working in 2-d CWT and their applications.' Zentralblatt MATH

Papildus informācija

Comprehensive treatment of 2-D wavelets for engineers, physicists and mathematicians.
Prologue ix
Warm-up: the 1-D continuous wavelet transform
1(31)
What is wavelet analysis?
1(4)
The continuous wavelet transform
5(5)
Discretization of the CWT, frames
10(4)
Ridges and skeleton
14(5)
The discrete WT: orthonormal bases of wavelets
19(5)
Generalizations
24(5)
Applications of the 1-D CWT
29(3)
The 2-D continuous wavelet transform
32(65)
Derivation
32(4)
Basic properties of the 2-D CWT
36(5)
Implementation and interpretation of the 2-D CWT
41(13)
Discretization, frames
54(14)
Comparison with the 2-D discrete wavelet transform
68(10)
Bridging the gap: continuous wavelet packets and fast algorithms
78(15)
Steerable filters
93(3)
Redundancy: Plus and minus
96(1)
Some 2-D wavelets and their performance
97(28)
Which wavelets?
97(2)
Isotropic wavelets
99(4)
Directional wavelets
103(15)
Wavelet calibration: evaluating the performances of the CWT
118(7)
Applications of the 2-D CWT.I: image processing
125(50)
Contour detection, character recognition
125(9)
Object detection and recognition in noisy images
134(11)
Image retrieval
145(5)
Medical imaging
150(1)
Detection of symmetries in patterns
150(12)
Image denoising
162(1)
Nonlinear extensions of the CWT
163(12)
Applications of the 2-D CWT.II: physical applications
175(39)
Astronomy and astrophysics
175(17)
Geophysics
192(5)
Applications in fluid dynamics
197(8)
Fractals and the thermodynamical formalism
205(5)
Texture analysis
210(2)
Applications of the DWT
212(2)
Matrix geometry of wavelet analysis.I
214(33)
Group theory and matrix geometry of wavelets
214(16)
Phase space analysis
230(8)
The case of Gabor wavelets
238(9)
Matrix geometry of wavelet analysis. II
247(34)
A group-adapted wavelet analysis
247(12)
The 2-D continuous wavelet transform
259(9)
2-D wavelets on phase space
268(8)
The affine Poincare group
276(5)
Minimal uncertainty and Wigner transforms
281(19)
Phase space distributions and minimal uncertainty gaborettes
281(3)
Minimal uncertainty wavelets
284(3)
Wigner functions
287(4)
Wigner functions for the wavelet groups
291(9)
Higher-dimensional wavelets
300(43)
Three-dimensional wavelets
300(8)
Wavelets on the 2-sphere and other manifolds
308(24)
Wavelet approximations on the sphere
332(11)
Spatio-temporal wavelets and motion estimation
343(30)
Introduction
343(1)
Spatio-temporal signals and their transformations
344(4)
The transformation group and its representations
348(4)
The spatio-temporal wavelet transform
352(4)
A motion estimation (ME) algorithm
356(17)
Beyond wavelets
373(40)
New transforms: ridgelets, curvelets, etc
374(9)
Rate-distortion analysis of anisotropic approximations
383(6)
Sparse approximations in redundant dictionaries
389(9)
Algebriac wavelets
398(15)
Epilogue 413(2)
Appendix Some elements of group theory 415(16)
References 431(24)
Index 455
Jean-Pierre Antoine is the Professor of Mathematical Physics at the Institut de Physique Théorique, Université catholique de Louvain. Romain Murenzi is currently Minister of Education, Science, Technology, and Scientific Research of the Republic of Rwanda, on leave of absence from the Department of Physics, Clark Atlanta University, Atlanta, Georgia. Pierre Vandergheynst is a Professor at the Signal Processing Institute, Swiss Federal Insitute of Technology, Lausanne. Syed Twareque Ali is a Professor at the Department of Mathematics and Statistics, Concordia University, Montréal.
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