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Documents  65T60 | enregistrements trouvés : 38

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Research talks;Analysis and its Applications;Partial Differential Equations

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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Research talks;Analysis and its Applications;Computer Science

The alternating direction method of multipliers (ADMM) is an optimization tool of choice for several imaging inverse problems, namely due its flexibility, modularity, and efficiency. In this talk, I will begin by reviewing our earlier work on using ADMM to deal with classical problems such as deconvolution, inpainting, compressive imaging, and how we have exploited its flexibility to deal with different noise models, including Gaussian, Poissonian, and multiplicative, and with several types of regularizers (TV, frame-based analysis, synthesis, or combinations thereof). I will then describe more recent work on using ADMM for other problems, namely blind deconvolution and image segmentation, as well as very recent work where ADMM is used with plug-in learned denoisers to achieve state-of-the-art results in class-specific image deconvolution. Finally, on the theoretical front, I will describe very recent work on tackling the infamous problem of how to adjust the penalty parameter of ADMM. The alternating direction method of multipliers (ADMM) is an optimization tool of choice for several imaging inverse problems, namely due its flexibility, modularity, and efficiency. In this talk, I will begin by reviewing our earlier work on using ADMM to deal with classical problems such as deconvolution, inpainting, compressive imaging, and how we have exploited its flexibility to deal with different noise models, including Gaussian, ...

65J22 ; 65K10 ; 65T60 ; 94A08

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- 274 p.
ISBN 978-3-7643-6648-3

I.S.N.M. , 0142

Localisation : Colloque 1er étage (WITT)

approximation dans un domaine complexe # approximation numérique # interpolation # approximation trigonométrique # fonction positive définie # théorie d'approximation des opérateurs # opérateur positif # interpolation # spline # algorithme pour une approximation fonctionnelle # intégration numérique # ondelette

30E10 ; 41A05 ; 42A10 ; 42A82 ; 47B65 ; 65D05 ; 65D07 ; 65D15 ; 65D20 ; 65D30 ; 65T60 ; 47A58 ; 33F05

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- vii; 148 p.
ISBN 978-1-4704-1923-3

Contemporary mathematics , 0660

Localisation : Collection 1er étage

équation aux dérivées partielles # traitement du signal # imagerie

35B10 ; 35B30 ; 35J05 ; 35J25 ; 35R30 ; 35R60 ; 65N15 ; 65T60 ; 86A15 ; 35-06 ; 35Bxx ; 35Jxx ; 35Rxx ; 00B25

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- 305 p.
ISBN 978-0-8218-2979-0

Contemporary mathematics , 0313

Localisation : Collection 1er étage

problème inverse # traitement d'image # imagerie médicale # problème malposé # analyse numérique # régularisation de variation bornée # fractale # ondelette # reconnaissance de courbe # enregistrement d'image # tomographie # projection arrière # solution approchée des EDP # espace abstrait # intégrale # programmation mathématique # méthode variationnelle

65-06 ; 65Jxx ; 65Rxx ; 65Kxx ; 65T60 ; 34G20 ; 35A15 ; 45Q05

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- xii; 314 p.
ISBN 978-3-642-24078-2

Lecture notes in mathematics , 2040

Localisation : Collection 1er étage

ondelettes # physique mathématique # dynamique des fluides # méthode des éléments finis # modélisation multi-échelles

65M50 ; 65N50 ; 65M55 ; 65T60 ; 65N30 ; 65M60 ; 76Mxx ; 65-06 ; 00B25

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- 414 p.
ISBN 978-0-8218-4676-8

Fields institute communications , 0052

Localisation : Collection 1er étage

EDP # opérateur pseudo-différentiel # analyse de Fourier # opérateur intégral # analyse globale # analyse de variétés # méthode numérique pour l'analyse de Fourier # ondes # théorie du signal

35-06 ; 35S05 ; 42-06 ; 47G10 ; 47G30 ; 58-06 ; 58J40 ; 65T60 ; 94A12

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- vi; 291 p.
ISBN 978-3-0346-0197-9

Operator theory: advances and applications , 0205

Localisation : Collection 1er étage

EDP # opérateur pseudo-différentiel # analyse complexe

30G30 ; 31A30 ; 32A25 ; 33C05 ; 42B10 ; 42B15 ; 42B35 ; 44A35 ; 46F12 ; 47 ; 35 ; 58J32 ; 58J40 ; 62M15 ; 65R10 ; 65T60 ; 92C55 ; 30E25 ; 31A10 ; 32A07 ; 32A26 ; 32A30 ; 32A40 ; 42C40 ; 45E05 ; 46F05 ; 65T50

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- 261 p.
ISBN 978-0-8218-2135-0

Contemporary mathematics , 0278

Localisation : Collection 1er étage

transformation intégrale # analyse numérique # tranformation de Radon # tomographie # application # imagerie médicale # traitement du signal # ondelette # problème inverse # analyse microlocale # twisteur # groupe de Lie # analyse harmonique # théorie de la distribution # problème de Pompeiu

44A12 ; 92C55 ; 92F05 ; 35R30 ; 65T60

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- 326 p.
ISBN 978-0-8218-2991-2

Studies in advanced mathematics (AMS/IP) , 0025

Localisation : Collection 1er étage

ondelette # analyse de Fourier # raffinement de fonction # raffinement d'équation # ondelette spline # multi-ondelette # paquet d'ondelette # schéma d'approximation # algorithme de subdivision

42C40 ; 42-06 ; 65T60

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- viii; 382 p.
ISBN 978-1-138-44266-5

Lecture notes in pure and applied mathematics , 0212

Localisation : Colloque 1er étage (URBA)

analyse par ondelettes # méthode multirésolution

00B25 ; 42-06 ; 65-06 ; 42C40 ; 65T60

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- ix; 178 p.
ISBN 978-981-4322-86-7

Series in contemporary applied mathematics , 0014

Localisation : Ouvrage RdC (WAVE)

ondelettes # analyse numérique # physique # traitement d'image # reconnaissance de formes # approximation non-linéaire # analyse multifractale

65-06 ; 65T60 ; 00B25

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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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Special events;30 Years of Wavelets;Analysis and its Applications;Mathematical Physics;Mathematics in Science and Technology

We start by recalling the essential features of frames, both discrete and continuous, with some emphasis on the notion of frame duality. Then we turn to generalizations, namely upper and lower semi-frames, and their duality. Next we consider arbitrary measurable maps and examine the standard operators, analysis, synthesis and frame operators, and study their properties. Finally we analyze the recent notion of reproducing pairs. In view of their duality structure, we introduce two natural partial inner product spaces and formulate a number of open questions.

Keywords: continuous frames - semi-frames - frame duality - reproducing pairs - partial inner product spaces
We start by recalling the essential features of frames, both discrete and continuous, with some emphasis on the notion of frame duality. Then we turn to generalizations, namely upper and lower semi-frames, and their duality. Next we consider arbitrary measurable maps and examine the standard operators, analysis, synthesis and frame operators, and study their properties. Finally we analyze the recent notion of reproducing pairs. In view of their ...

42C15 ; 42C40 ; 46C50 ; 65T60

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

94A12 ; 65T60 ; 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;Analysis and its Applications

42C40 ; 65T60

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Research talks;Analysis and its Applications

The unitary extension principle (UEP) by Ron & Shen yields a convenient way of constructing tight wavelet frames in L2(R). Since its publication in 1997 several generalizations and reformulations have been obtained, and it has been proved that the UEP has important applications within image processing. In the talk we will present a recent extension of the UEP to the setting of generalized shift-invariant systems on R (or more generally, on any locally compact abelian group). For example, this generalization immediately leads to a discrete version of the UEP.
(The results are joint work with Say Song Goh).
The unitary extension principle (UEP) by Ron & Shen yields a convenient way of constructing tight wavelet frames in L2(R). Since its publication in 1997 several generalizations and reformulations have been obtained, and it has been proved that the UEP has important applications within image processing. In the talk we will present a recent extension of the UEP to the setting of generalized shift-invariant systems on R (or more generally, on any ...

42C15 ; 42C40 ; 65T60

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Special events;30 Years of Wavelets;Analysis and its Applications;Mathematical Physics

sparsity - morphological diversity - inpainting - cosmology - weak lensing - cosmic microwave background

65T60 ; 94A12 ; 85A35

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

In this talk, we will briefly look at the history of wavelets, from signal processing algorithms originating in speech and image processing, and harmonic analysis constructions of orthonormal bases. We review the promises, the achievements, and some of the limitations of wavelet applications, with JPEG and JPEG2000 as examples. We then take two key insights from the wavelet and signal processing experience, namely the time-frequency-scale view of the world, and the sparsity property of wavelet expansions, and present two recent results. First, we show new bounds for the time-frequency spread of sequences, and construct maximally compact sequences. Interestingly they differ from sampled Gaussians. Next, we review work on sampling of finite rate of innovation signals, which are sparse continuous-time signals for which sampling theorems are possible. We conclude by arguing that the interface of signal processing and applied harmonic analysis has been both fruitful and fun, and try to identify lessons learned from this experience.

Keywords: wavelets - filter banks - subband coding - uncertainty principle - sampling theory - sparse sampling
In this talk, we will briefly look at the history of wavelets, from signal processing algorithms originating in speech and image processing, and harmonic analysis constructions of orthonormal bases. We review the promises, the achievements, and some of the limitations of wavelet applications, with JPEG and JPEG2000 as examples. We then take two key insights from the wavelet and signal processing experience, namely the time-frequency-scale view ...

94A08 ; 94A12 ; 65T60 ; 42C40

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