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Wavelets (Mathematics)

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Signal processing --- Wavelets (Mathematics) --- Time-series analysis --- Frequency spectra

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Boundary value problems --- Differential equations, Elliptic --- Wavelets (Mathematics). --- Numerical solutions. --- Numerical solutions.

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Wavelet methods have become a widely spread tool in signal and image process­ ing tasks. This book deals with statistical applications, especially wavelet based smoothing. The methods described in this text are examples of non-linear and non­ parametric curve fitting. The book aims to contribute to the field both among statis­ ticians and in the application oriented world (including but not limited to signals and images). Although it also contains extensive analyses of some existing methods, it has no intention whatsoever to be a complete overview of the field: the text would show too much bias towards my own algorithms. I rather present new material and own insights in the questions involved with wavelet based noise reduction. On the other hand, the presented material does cover a whole range of methodologies, and in that sense, the book may serve as an introduction into the domain of wavelet smoothing. Throughout the text, three main properties show up ever again: sparsity, locality and multiresolution. Nearly all wavelet based methods exploit at least one of these properties in some or the other way. These notes present research results of the Belgian Programme on Interuniver­ sity Poles of Attraction, initiated by the Belgian State, Prime Minister's Office for Science, Technology and Culture. The scientific responsibility rests with me. My research was financed by a grant (1995 - 1999) from the Flemish Institute for the Promotion of Scientific and Technological Research in the Industry (IWT).

Stochastic processes --- Numerical approximation theory --- Electronics --- Signal processing --- Electronic noise --- Wavelets (Mathematics) --- Active noise and vibration control. --- Traitement du signal --- Bruit électronique --- Ondelettes --- Contrôle actif du bruit et des vibrations --- Digital techniques --- Statistical methods. --- Automatic control. --- Techniques numériques --- Méthodes statistiques --- Commande automatique --- Statistical methods --- Automatic control --- 681.3*I43 --- -Signal processing --- -Wavelets (Mathematics) --- Wavelet analysis --- Harmonic analysis --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Noise, Electronic --- Electric noise --- Enhancement: filering; geometric correction; grayscale manipulation; registration; sharpening and deblurring; smoothing (Image processing) --- -Statistical methods --- Basic Sciences. Statistics --- Statistics (General) --- Active noise and vibration control --- Electrical & Computer Engineering --- Engineering & Applied Sciences --- Telecommunications --- Wavelets (Mathematics). --- Statistics (General). --- 681.3*I43 Enhancement: filering; geometric correction; grayscale manipulation; registration; sharpening and deblurring; smoothing (Image processing) --- Bruit électronique --- Contrôle actif du bruit et des vibrations --- Techniques numériques --- Méthodes statistiques --- Active noise and vibration cancellation --- Active noise control --- Active vibration control --- ANVC (Active noise and vibration control) --- Electro-acoustics --- Acoustic impedance --- Digital techniques&delete& --- Applied mathematics. --- Engineering mathematics. --- Vibration. --- Dynamical systems. --- Dynamics. --- Statistics . --- Mathematical and Computational Engineering. --- Vibration, Dynamical Systems, Control. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Statistical analysis --- Statistical data --- Statistical science --- Mathematics --- Econometrics --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Cycles --- Sound --- Engineering --- Engineering analysis --- Mathematical analysis --- Information, Théorie de l' --- Signal processing - Digital techniques - Statistical methods --- Electronic noise - Automatic control --- Theorie du signal