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Framelets and Wavelets: Algorithms, Analysis, and Applications: Applied and Numerical Harmonic Analysis

Autor Bin Han
en Limba Engleză Paperback – 4 iun 2019
Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide.
As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, and supplementary exercises.

Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets.
Lastly, the book can also be used to teach on or study selected special topics in approximation theory, Fourier analysis, applied harmonic analysis, functional analysis, and wavelet-based signal/image processing.

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Specificații

ISBN-13: 9783319886176
ISBN-10: 3319886177
Pagini: 724
Ilustrații: XXXIII, 724 p. 73 illus.
Dimensiuni: 155 x 235 mm
Greutate: 1.15 kg
Ediția:Softcover reprint of the original 1st ed. 2017
Editura: Springer International Publishing
Colecția Birkhäuser
Seria Applied and Numerical Harmonic Analysis

Locul publicării:Cham, Switzerland

Cuprins

Preface.- Chapter 1. Discrete Framelet Transforms.- Chapter 2. Wavelet Filter Banks.- Chapter 3. Framelet Filter Banks.- Chapter 4. Analysis of Affine Systems and Dual Framelets.- Chapter 5. Analysis of Refinable Vector Functions.- Chapter 6. Framelets and Wavelets Derived from Refinable Functions.- Chapter 7. Applications of Framelets and Wavelets.- Appendix A. Basics on Fourier Analysis.- Notes and Acknowledgments.- Bibliography.- Index.

Notă biografică

Bin Han been working in the area of applied harmonic analysis and approximation theory, in particular, on wavelets and framelets with applications since 1992. He received his PhD in mathematics at the University of Alberta in 1998 and worked as a PDF at Princeton University in 1999. Bin Han is professor of mathematics at the University of Alberta. 

Textul de pe ultima copertă

Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide.
As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, and supplementary exercises.

Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets.
Lastly, the book can also be used to teach on or study selected special topics in approximation theory, Fourier analysis, applied harmonic analysis, functional analysis, and wavelet-based signal/image processing.

Caracteristici

Algorithmic approach to framelets and wavelets with self-contained proofs and illustrative examples Comprehensive treatments on refinable vector functions and theory of multiframelets/multiwavelets Recent advances on wavelet-based applications such as directional framelets for image processing