Gabor analysis and algorithms : theory and applications
著者
書誌事項
Gabor analysis and algorithms : theory and applications
（Applied and numerical harmonic analysis / series editor, John J. Benedetto）
Birkhäuser, 1998
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注記
Includes bibliographical references (p. [453]-488) and index
内容説明・目次
- 巻冊次
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ISBN 9780817639594
内容説明
In his paper Theory of Communication [Gab46], D. Gabor proposed the use of a family of functions obtained from one Gaussian by time-and frequency shifts. Each of these is well concentrated in time and frequency; together they are meant to constitute a complete collection of building blocks into which more complicated time-depending functions can be decomposed. The application to communication proposed by Gabor was to send the coeffi cients of the decomposition into this family of a signal, rather than the signal itself. This remained a proposal-as far as I know there were no seri ous attempts to implement it for communication purposes in practice, and in fact, at the critical time-frequency density proposed originally, there is a mathematical obstruction; as was understood later, the family of shifted and modulated Gaussians spans the space of square integrable functions [BBGK71, Per71] (it even has one function to spare [BGZ75] . . . ) but it does not constitute what we now call a frame, leading to numerical insta bilities. The Balian-Low theorem (about which the reader can find more in some of the contributions in this book) and its extensions showed that a similar mishap occurs if the Gaussian is replaced by any other function that is "reasonably" smooth and localized. One is thus led naturally to considering a higher time-frequency density.
目次
1 The duality condition for Weyl-Heisenberg frames.- 2 Gabor systems and the Balian-Low Theorem.- 3 A Banach space of test functions for Gabor analysis.- 4 Pseudodifferential operators, Gabor frames, and local trigonometric bases.- 5 Perturbation of frames and applications to Gabor frames.- 6 Aspects of Gabor analysis on locally compact abelian groups.- 7 Quantization of TF lattice-invariant operators on elementary LCA groups.- 8 Numerical algorithms for discrete Gabor expansions.- 9 Oversampled modulated filter banks.- 10 Adaptation of Weyl-Heisenberg frames to underspread environments.- 11 Gabor representation and signal detection.- 12 Multi-window Gabor schemes in signal and image representations.- 13 Gabor kernels for affine-invariant object recognition.- 14 Gabor's signal expansion in optics.
- 巻冊次
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ISBN 9783764339593
内容説明
This text provides an introduction to mathematicians and engineers who want to learn about the different approaches and aspects of Gabor analysis or want to apply Gabor-based techniques to tasks in signal and image processing. It should be of interest to those working in the fields of harmonic analysis, applied mathematics, numerical analysis, engineering, signal and image processing, optics and pattern recognition. Features include: self-contained introduction to basic Gabor analysis; survey of fundamental results in Gabor theory; efficient numerical algorithms; Gabor expansions in signal and image processing; and applications in pattern recognition, filter bank design and optics.
目次
- The duality condition for Weyl-Heisenberg frames, A.J.E.M. Janssen
- Gabor systems and the Balian-Low theorem, John J. Benedetto et al
- A Banach space of test functions for Gabor analysis, Hans G. Feichtinger, Georg Zimmermann
- Pseudodifferential operators, Gabor frames, and local trigonometric bases, Richard Rochberg, Kazuya Tachizawa
- Perturbation of frames and applications to gabor frames, Ole Christensen
- aspects of Gabor analysis on locally compact abelian groups, Karlheinz Grochenig
- Quantization of TF lattice-invariant operators on elementary LCA groups, Hans G. Feichtinger, Werner Kozek
- Numerical algorithms for discrete Gabor expansions, Thomas Strohmer
- Oversampled modulated filter banks, Helmut Bolcskei, Franz Hlawatsch
- Adaptation of Weyl-Heisenberg frames to underspread environments, werner Kozek
- gabor representation and signal detection, Ariela Zeira, Benjamin Friedlander
- Multi-window Gabor schemes in signal and image representations, Yoshua Y. Zeevi et al
- Gabor kernels for affine-invariant object recognition, Jezekiel Ben-Arie, Zhiqian Wang
- Gabor's signal expansion in optics, Martin J. Bastiaans.
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