Authors:
- 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
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
About this book
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.
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.
Keywords
- framelets and wavelets
- discrete framalet/wavelet transform
- orthogonal and biorthogonal wavelets
- tight and dual framelets
- wavelet and framelet filter banks
- nonhomogeneous and homogeneous affine systems
- refinable structure
- refinable vector functions
- mulitframelets and multiwavelets
- refinable splines
- linear independence and stability
- cascade algorithms and subdivision schemes
- sum rules
- vanishing moments
- linear-phase moments
- approximation order
- quasi-approximation operators
- shift-invariant spaces
- multiresolution analysis
Authors and Affiliations
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Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada
Bin Han
About the author
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.Â
Bibliographic Information
Book Title: Framelets and Wavelets
Book Subtitle: Algorithms, Analysis, and Applications
Authors: Bin Han
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-3-319-68530-4
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2017
Hardcover ISBN: 978-3-319-68529-8Published: 17 January 2018
Softcover ISBN: 978-3-319-88617-6Published: 04 June 2019
eBook ISBN: 978-3-319-68530-4Published: 04 January 2018
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XXXIII, 724
Number of Illustrations: 73 b/w illustrations
Topics: Approximations and Expansions, Fourier Analysis, Applications of Mathematics, Image Processing and Computer Vision, Computer-Aided Engineering (CAD, CAE) and Design