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Wavelets in Geodesy and Geodynamics - Wolfgang Keller

Wavelets in Geodesy and Geodynamics

Hardcover Published: 26th April 2004
ISBN: 9783110175462
Number Of Pages: 279
For Ages: 22+ years old

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For many years, digital signal processing has been governed by the theory of Fourier transform and its numerical implementation. The main disadvantage of Fourier theory is the underlying assumption that the signals have time-wise or space-wise invariant statistical properties. In many applications the deviation from a stationary behavior is precisely the information to be extracted from the signals. Wavelets were developed to serve the purpose of analysing such instationary signals.

The book gives an introduction to wavelet theory both in the continuous and the discrete case. After developing the theoretical fundament, typical examples of wavelet analysis in the Geosciences are presented.

The book has developed from a graduate course held at The University of Calgary and is directed to graduate students who are interested in digital signal processing. The reader is assumed to have a mathematical background on the graduate level.

Prefacep. v
Notationp. ix
Fourier analysis and filteringp. 1
Fourier analysisp. 1
Linear filtersp. 14
Waveletsp. 24
Motivationp. 24
Continuous wavelet transformationp. 30
Conceptp. 30
Time-frequency resolutionp. 36
Approximation propertiesp. 37
Discrete wavelet transformationp. 40
Framesp. 40
Multi-resolution analysisp. 43
Mallat algorithmp. 55
Wavelet packagesp. 63
Biorthogonal waveletsp. 68
Compactly supported orthogonal waveletsp. 82
Daubechies waveletsp. 83
Solution of scaling equationsp. 96
Wavelet bases on an intervalp. 98
Two-dimensional waveletsp. 102
Continuous two-dimensional waveletsp. 102
Discrete two-dimensional waveletsp. 104
Wavelets on a spherep. 110
Harmonic waveletsp. 110
Triangulation based waveletsp. 123
Applicationsp. 131
Pattern recognitionp. 131
Polar motionp. 131
Atmospheric turbulencep. 135
Fault scarps from seafloor bathymetryp. 139
Seismic reflection horizonsp. 141
GPS cycle-slip detectionp. 147
Edge detection in imagesp. 153
Data compression and denoisingp. 156
Wavelet filters and estimationp. 156
Deconvolution thresholdingp. 164
Image compressionp. 173
Sub-band coding, filtering and predictionp. 181
QMF filter design and waveletsp. 181
Prediction of stationary signals with superimposed non-stationary noisep. 187
Operator approximationp. 196
Wavelet compression of operator equationsp. 196
Multi-grid solvers for wavelet discretized operatorsp. 204
Gravity field modellingp. 212
Hilbert spacesp. 217
Definition of Hilbert spacesp. 217
Complete orthonormal systems in Hilbert spacesp. 222
Linear functionals--dual spacep. 225
Examples of Hilbert spacesp. 226
Linear operators--Galerkin methodp. 234
Hilbert space valued random variablesp. 236
Distributionsp. 238
Exercisesp. 245
Bibliographyp. 269
Indexp. 277
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9783110175462
ISBN-10: 3110175460
Audience: General
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 279
Published: 26th April 2004
Country of Publication: DE
Dimensions (cm): 24.59 x 17.53  x 2.06
Weight (kg): 0.63