Overview
- Highlights promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics
- A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented
- Can be used as ?a textbook for graduate courses in applied harmonic analysis
Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)
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Table of contents (5 chapters)
Keywords
About this book
This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data.
After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as
- An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group
- An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces
- Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data
- Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities.
A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented.
Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook
for graduate courses in applied harmonic analysis.
Editors and Affiliations
About the editors
Stephan Dahlke is Professor in the Department of Mathematics and Computer Sciences at Philipps-University of Marburg, Germany.
Filippo De Mari is Associate Professor in the Department of Mathematics at the University of Genova, Italy.
Philipp Grohs is Assistant Professor in the Seminar for Applied Mathematics at the Swiss Federal Institute of Technology, Zurich, Switzerland.
Demetrio Labate is Associate Professor in the Department of Mathematics at the University of Houston, TX, USA
Bibliographic Information
Book Title: Harmonic and Applied Analysis
Book Subtitle: From Groups to Signals
Editors: Stephan Dahlke, Filippo De Mari, Philipp Grohs, Demetrio Labate
Series Title: Applied and Numerical Harmonic Analysis
DOI: https://doi.org/10.1007/978-3-319-18863-8
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-18862-1Published: 24 September 2015
Softcover ISBN: 978-3-319-35596-2Published: 22 October 2016
eBook ISBN: 978-3-319-18863-8Published: 12 September 2015
Series ISSN: 2296-5009
Series E-ISSN: 2296-5017
Edition Number: 1
Number of Pages: XV, 256
Number of Illustrations: 2 b/w illustrations, 11 illustrations in colour
Topics: Abstract Harmonic Analysis, Fourier Analysis, Group Theory and Generalizations, Topological Groups, Lie Groups, Signal, Image and Speech Processing