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| Material Type: | Internet resource |
|---|---|
| Document Type: | Book, Internet Resource |
| All Authors / Contributors: |
Yves Meyer |
| ISBN: | 0821829203 9780821829202 |
| OCLC Number: | 47136690 |
| Description: | x, 122 p. ; 26 cm. |
| Contents: | Still images compression -- A first glance at compression and denoising. The supernova SN1987A -- Atomic decompositions and modeling -- Wavelets and still image compression: some success stories -- Sampling, quantization, thresholding and compression -- A first visit to u + v models for still images -- Best-basis algorithms in signal processing -- The old JPEG -- Karhunen-Loeve expansions -- An example where the Karhunen-Loeve approach is ineffective: the ramp function -- A second visit to u + v image models -- The space BV of functions with bounded variation in the plane -- The Osher-Rudin model -- The mathematical properties of the Osher-Rudin model -- Modeling textures -- Wavelet shrinkage -- Littlewood-Paley analysis -- A survey of wavelet analysis -- Littlewood-Paley analysis and wavelet analysis -- Quantization issues: Fourier series vs. wavelet series -- Fourier series vs. wavelet series: expansions of BV functions -- The role of oscillations in some nonlinear PDE's -- Improved Gagliardo-Nirenberg inequalities -- Improved Poincare estimates -- Wavelet coefficients of integrable functions -- A first model case: the nonlinear heat equation -- The Navier-Stokes equations -- Modeling coherent structures -- The nonlinear Schrodinger equation -- Frequency modulated signals, chirps and the Virgo program -- Holder classes with negative exponents -- Infinitely oscillating functions -- A first definition of n-dimensional chirps -- A second definition of chirps -- Jaffard's criticism -- Chirps and two-microlocal spaces. |
| Series Title: | University lecture series (Providence, R.I.), 22. |
| Responsibility: | Yves Meyer. |
Abstract:
"Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of "oscillating patterns", which are present in many natural images, help to explain nonlinear equations. and are pivotal in studying chirps and frequency-modulated signals." "In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics involves new properties of various Besov-type function spaces and leads to many deep results, including new generalizations of famous Gagliardo-Nirenberg and Poincare inequalities.".
"This book can be used either as a textbook in studying applications of wavelets to image processing or as a supplementary resource for studying nonlinear evolution equations or frequency-modulated signals. Most of the material in the book did not appear previously in monograph literature."--BOOK JACKET.
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Similar Items
Related Subjects:(11)
- Evolution equations, Nonlinear.
- Image compression.
- Signal processing -- Mathematics.
- Oscillations.
- Équations d'évolution non linéaires.
- Compression d'images.
- Traitement du signal -- Mathématiques.
- Bildverarbeitung.
- Nichtlineare Evolutionsgleichung.
- Schwingung.
- Signalverarbeitung.
