Framelets and Wavelets

Algorithms, Analysis, and Applications

Bin Han (Autor)

Buch | Softcover

XXXIII, 724 Seiten

2019 | 1. Softcover reprint of the original 1st ed. 2017
Springer International Publishing (Verlag)
978-3-319-88617-6 (ISBN)

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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.

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.

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.

Erscheinungsdatum	31.01.2019
Reihe/Serie	Applied and Numerical Harmonic Analysis
Zusatzinfo	XXXIII, 724 p. 73 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1129 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	approximation order • cascade algorithms and subdivision schemes • discrete framalet/wavelet transform • framelets and wavelets • linear independence and stability • linear-phase moments • mulitframelets and multiwavelets • multiresolution analysis • nonhomogeneous and homogeneous affine systems • orthogonal and biorthogonal wavelets • quasi-approximation operators • refinable splines • refinable structure • refinable vector functions • shift-invariant spaces • sum rules • tight and dual framelets • vanishing moments • wavelet and framelet filter banks
ISBN-10	3-319-88617-7 / 3319886177
ISBN-13	978-3-319-88617-6 / 9783319886176
Zustand	Neuware