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Documents  Critères de recherche : "Wavelets" | enregistrements trouvés : 60

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Ingrid Daubechies' construction of orthonormal wavelet bases with compact support published in 1988 started a general interest to employ these functions also for the numerical solution of partial differential equations (PDEs). Concentrating on linear elliptic and parabolic PDEs, I will start from theoretical topics such as the well-posedness of the problem in appropriate function spaces and regularity of solutions and will then address quality and optimality of approximations and related concepts from approximation the- ory. We will see that wavelet bases can serve as a basic ingredient, both for the theory as well as for algorithmic realizations. Particularly for situations where solutions exhibit singularities, wavelet concepts enable adaptive appproximations for which convergence and optimal algorithmic complexity can be established. I will describe corresponding implementations based on biorthogonal spline-wavelets.
Moreover, wavelet-related concepts have triggered new developments for efficiently solving complex systems of PDEs, as they arise from optimization problems with PDEs.
Ingrid Daubechies' construction of orthonormal wavelet bases with compact support published in 1988 started a general interest to employ these functions also for the numerical solution of partial differential equations (PDEs). Concentrating on linear elliptic and parabolic PDEs, I will start from theoretical topics such as the well-posedness of the problem in appropriate function spaces and regularity of solutions and will then address quality ...

65T60 ; 94A08 ; 65N12 ; 65N30 ; 49J20

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ISBN 978-0-19-853439-6

Oxford science publications

Localisation : Colloque 1er étage (LANC)

analyse numerique # interpolation # ondelette # spline

41A15 ; 65-06

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ISBN 978-2-225-82550-7

Research notes in applied mathematics , 0020

Localisation : Colloque 1er étage (MARS)

analyse de Fourier # analyse de Fourier non trigonométrique # développement de Fourier généralisé # ondelette # série de fonction orthogonale générale

42C15

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ISBN 978-0-86720-225-0

Localisation : Colloque 1er étage (LOWE)

analyse de signal # analyse numérique # mécanique quantique # ondelette

42-06 ; 60T10 ; 93E14 ; 94A05 ; 94A12

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ISBN 978-0-8218-5503-4

Proceedings of symposia in applied mathematics , 0047

Localisation : Collection 1er étage

analyse numérique # base d'ondelette orthonormale # base de paquets d'ondes le mieux adaptée # densité # méthode d'ondelette non linéaire # ondelette et algorithme numérique rapide # ondelette et analyse de forme d'onde adaptée # ondelette et opérateur différentiel # opérateur de projection en analyse multi-résolution # recouvrement de signal # spectre venant de données indirectes et bruillantes # traitement du signal # transformée ondelette

35A27 ; 42C15 ; 46E15 ; 62A99 ; 94A11

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- 354 p.
ISBN 978-0-8218-0384-4

Contemporary mathematics , 0190

Localisation : Collection 1er étage

Butzer # Egypte et Charlemagne # PDE # analyse mathématique # analyse multirésolution généralisée # antroïde # automaton attribué # base pseudo-bi-orthogonal # convergence d'approximation spline # convolution sinc # divergence presque partout # développement de Jacobi # espace de Hilbert à noyau reproduisant # estimation ou convergence modulaire # extrapolation de signal à bande limitée discret # fonction d'opérateur cosinus # fonction de type zeta # fraction continue hypergéométrique # interpolation sinc non-uniforme # lemme de Riemann-Lebesgue # norme SUP de polynôme pondéré # ondelette # opérateur de Askey- Wilson # opérateur intégral linéaire # phénomène de Gibbs # polynôme de Jacobi ou de Jack # problème aux limites à 2 points abstrait # processus de convolution # reconnaissance de numéral écrit à la main # représentation en série convergent rapidement # spline périodique # série de Fourier-Bessel # théorie de l'approximation # théorème ergodique pour semi-groupe # traitement du signal FSK/FA # transformée d'onde de carré simplifiée # transformée de Fourier rapide # transformée de Hankel ou Fourier # échantillonnage pour fonction multi-bande Butzer # Egypte et Charlemagne # PDE # analyse mathématique # analyse multirésolution généralisée # antroïde # automaton attribué # base pseudo-bi-orthogonal # convergence d'approximation spline # convolution sinc # divergence presque partout # développement de Jacobi # espace de Hilbert à noyau reproduisant # estimation ou convergence modulaire # extrapolation de signal à bande limitée discret # fonction d'opérateur cosinus # fonction de type ...

33Dxx ; 41A05 ; 42C15 ; 94Axx

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- 175 p.
ISBN 978-0-8218-0793-4

Contemporary mathematics , 0216

Localisation : Collection 1er étage

analyse de Fourier # analyse de Fourier non trigonométrique # analyse harmonique abstraite # application # approximation # approximation trigonométrique # expansion de série # fonction d'espace sur des groupes # interpolation # multi-ondelette # ondelette # trigonométrie

41A25 ; 42A10 ; 42A15 ; 42A38 ; 42C15

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- 306 p.
ISBN 978-0-8218-1957-9

Contemporary mathematics , 0247

Localisation : Collection 1er étage

analyse de Fourier # analyse fonctionnelle # analyse harmonique # base # ondelette # théorie des opérateurs

41-XX ; 42-XX ; 43-XX ; 46-XX ; 47-XX

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- 342 p.
ISBN 978-0-8218-3380-3

Contemporary mathematics , 0345

Localisation : Collection 1er étage

analyse harmonique # ondelette # théorie des opérateurs # repère

20C20 ; 41A17 ; 42C15 ; 42C40 ; 43A85 ; 46C05 ; 46C99 ; 46E25 ; 47C05 ; 65T60

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- xiii, 264 p.
ISBN 978-0-8218-4327-7

Contemporary mathematics , 0464

Localisation : Collection 1er étage

géométrie convexe discrète # analyse de Fourier # analyse numérique # analyse armonique # ondelette # espace homogène # transformée de Radon # ensemble réel convexe # géométrie intégrale

42C40 ; 44A12 ; 43A85 ; 51M25 ; 52A22 ; 65T99

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- x; 177 p.
ISBN 978-1-4704-1040-7

Contemporary mathematics , 0626

Localisation : Collection 1er étage

théorie des frames # ondelettes # pavage # analyse harmonique

00B25 ; 41-06 ; 42-06 ; 43-06 ; 46-06 ; 47-06 ; 94-06 ; 41AXX ; 42Axx ; 42Cxx ; 43AXX ; 46Cxx ; 47Axx ; 94Axx

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- ix; 331 p.
ISBN 978-3-540-53014-5

Localisation : Colloque 1er étage (MARS)

ondelette # physique mathématique # mesure du temps # espace des phases

00B25 ; 46-06 ; 47-06 ; 35-06

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- xii; 343 p.
ISBN 978-1-4704-3619-3

Contemporary mathematics , 0706

Localisation : Collection 1er étage

système de Gabor # ondelette # analyse harmonique # théorie des opérateurs # construction de bases # analyse de Fourier

15AXX ; 41AXX ; 42Axx ; 42Cxx ; 43AXX ; 46Cxx ; 47Axx ; 94Axx ; 42-06 ; 42C15 ; 42C40 ; 46C05 ; 47A05

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In several applications in signal processing it has proven useful to decompose a given signal in a multiscale dictionary, for instance to achieve compression by coefficient thresholding or to solve inverse problems. The most popular family of such dictionaries are undoubtedly wavelets which have had a tremendous impact in applied mathematics since Daubechies' construction of orthonormal wavelet bases with compact support in the 1980s. While wavelets are now a well-established tool in numerical signal processing (for instance the JPEG2000 coding standard is based on a wavelet transform) it has been recognized in the past decades that they also possess several shortcomings, in particular with respect to the treatment of multidimensional data where anisotropic structures such as edges in images are typically present. This deficiency of wavelets has given birth to the research area of geometric multiscale analysis where frame constructions which are optimally adapted to anisotropic structures are sought. A milestone in this area has been the construction of curvelet and shearlet frames which are indeed capable of optimally resolving curved singularities in multidimensional data.
In this course we will outline these developments, starting with a short introduction to wavelets and then moving on to more recent constructions of curvelets, shearlets and ridgelets. We will discuss their applicability to diverse problems in signal processing such as compression, denoising, morphological component analysis, or the solution of transport PDEs. Implementation aspects will also be covered. (Slides in attachment).
In several applications in signal processing it has proven useful to decompose a given signal in a multiscale dictionary, for instance to achieve compression by coefficient thresholding or to solve inverse problems. The most popular family of such dictionaries are undoubtedly wavelets which have had a tremendous impact in applied mathematics since Daubechies' construction of orthonormal wavelet bases with compact support in the 1980s. While ...

42C15 ; 42C40

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In several applications in signal processing it has proven useful to decompose a given signal in a multiscale dictionary, for instance to achieve compression by coefficient thresholding or to solve inverse problems. The most popular family of such dictionaries are undoubtedly wavelets which have had a tremendous impact in applied mathematics since Daubechies' construction of orthonormal wavelet bases with compact support in the 1980s. While wavelets are now a well-established tool in numerical signal processing (for instance the JPEG2000 coding standard is based on a wavelet transform) it has been recognized in the past decades that they also possess several shortcomings, in particular with respect to the treatment of multidimensional data where anisotropic structures such as edges in images are typically present. This deficiency of wavelets has given birth to the research area of geometric multiscale analysis where frame constructions which are optimally adapted to anisotropic structures are sought. A milestone in this area has been the construction of curvelet and shearlet frames which are indeed capable of optimally resolving curved singularities in multidimensional data.
In this course we will outline these developments, starting with a short introduction to wavelets and then moving on to more recent constructions of curvelets, shearlets and ridgelets. We will discuss their applicability to diverse problems in signal processing such as compression, denoising, morphological component analysis, or the solution of transport PDEs. Implementation aspects will also be covered. (Slides in attachment).
In several applications in signal processing it has proven useful to decompose a given signal in a multiscale dictionary, for instance to achieve compression by coefficient thresholding or to solve inverse problems. The most popular family of such dictionaries are undoubtedly wavelets which have had a tremendous impact in applied mathematics since Daubechies' construction of orthonormal wavelet bases with compact support in the 1980s. While ...

42C15 ; 42C40

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Special events;30 Years of Wavelets;Mathematics in Science and Technology

In this conference, I start by presenting the first applications and developments of wavelet methods made in Marseille in 1985 in the framework of sounds and music. A description of the earliest wavelet transform implementation using the SYTER processor is given followed by a discussion related to the first signal analysis investigations. Sound examples of the initial sound transformations obtained by altering the wavelet representation are further presented. Then methods aiming at estimating sound synthesis parameters such as amplitude and frequency modulation laws are described. Finally, new challenges brought by these early works are presented, focusing on the relationship between low-level synthesis parameters and sound perception and cognition. An example of the use of the wavelet transforms to estimate sound invariants related to the evocation of the "object" and the "action" is presented.

Keywords : sound and music - first wavelet applications - signal analysis - sound synthesis - fast wavelet algorithms - instantaneous frequency estimation - sound invariants
In this conference, I start by presenting the first applications and developments of wavelet methods made in Marseille in 1985 in the framework of sounds and music. A description of the earliest wavelet transform implementation using the SYTER processor is given followed by a discussion related to the first signal analysis investigations. Sound examples of the initial sound transformations obtained by altering the wavelet representation are ...

00A65 ; 42C40 ; 65T60 ; 94A12 ; 97M10 ; 97M80

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Special events;30 Years of Wavelets

The introduction of wavelets in the mid 80's has significantly reshaped some areas of the scientific landscape by establishing bridges between previously disconnected domains, and eventually leading to a new paradigm. This generally accepted-yet loose-claim can be given a more precise form by exploiting bibliometric databases such as the ISI Web of Science. Preliminary results in this direction will be reported here, based on multiple entries where authors, references, keywords and disciplines are used as nodes of a network in which the links correspond to their co-appearance in the same paper. While the evolution in time of such an " heterogeneous net " gives a quantified perspective on the birth and growth of wavelets as a well-identified scientific field of its own, it also raises many interpretation issues (related, e.g., to automation vs. expertise) whose implications go beyond this peculiar case study.

Keywords : wavelets - history - bibliometry - network, paradigm
The introduction of wavelets in the mid 80's has significantly reshaped some areas of the scientific landscape by establishing bridges between previously disconnected domains, and eventually leading to a new paradigm. This generally accepted-yet loose-claim can be given a more precise form by exploiting bibliometric databases such as the ISI Web of Science. Preliminary results in this direction will be reported here, based on multiple entries ...

01-XX ; 42-XX ; 68-XX ; 94-XX

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Special events;30 Years of Wavelets

42C40 ; 65T60

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Special events;30 Years of Wavelets

We start with a brief historical account of wavelets and of the way they shattered some of the preconceptions of the 20th century theory of statistical signal processing that is founded on the Gaussian hypothesis. The advent of wavelets led to the emergence of the concept of sparsity and resulted in important advances in image processing, compression, and the resolution of ill-posed inverse problems, including compressed sensing. In support of this change in paradigm, we introduce an extended class of stochastic processes specified by a generic (non-Gaussian) innovation model or, equivalently, as solutions of linear stochastic differential equations driven by white Lévy noise. Starting from first principles, we prove that the solutions of such equations are either Gaussian or sparse, at the exclusion of any other behavior. Moreover, we show that these processes admit a representation in a matched wavelet basis that is "sparse" and (approximately) decoupled. The proposed model lends itself well to an analytic treatment. It also has a strong predictive power in that it justifies the type of sparsity-promoting reconstruction methods that are currently being deployed in the field.

Keywords: wavelets - fractals - stochastic processes - sparsity - independent component analysis - differential operators - iterative thresholding - infinitely divisible laws - Lévy processes
We start with a brief historical account of wavelets and of the way they shattered some of the preconceptions of the 20th century theory of statistical signal processing that is founded on the Gaussian hypothesis. The advent of wavelets led to the emergence of the concept of sparsity and resulted in important advances in image processing, compression, and the resolution of ill-posed inverse problems, including compressed sensing. In support of ...

42C40 ; 60G20 ; 60G22 ; 60G18 ; 60H40

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Special events;30 Years of Wavelets;Mathematics in Science and Technology

This presentation reminds of some early sonic representations and of their utility for musical sound synthesis and processing, prior to the introduction of wavelets by Morlet and Grossmann. It reminds the circumstances of the work performed at the Laboratoire de Mécanique et d'Acoustique, Marseille, by Richard Kronland-Martinet with Alex Grossmann on wavelet transforms of sounds and by Daniel Arfib and Frédéric Boyer on the Gabor representation. It is illustrated by short sound and video examples.

Keywords: wavelets - Gabor - analysis-synthesis - computer music
This presentation reminds of some early sonic representations and of their utility for musical sound synthesis and processing, prior to the introduction of wavelets by Morlet and Grossmann. It reminds the circumstances of the work performed at the Laboratoire de Mécanique et d'Acoustique, Marseille, by Richard Kronland-Martinet with Alex Grossmann on wavelet transforms of sounds and by Daniel Arfib and Frédéric Boyer on the Gabor representation. ...

42-03

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