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Documents  65J22 | enregistrements trouvés : 9

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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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Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

49N45 ; 65C40 ; 65C60 ; 65J22 ; 68U10 ; 62C10 ; 62F15 ; 94A08

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Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

49N45 ; 65C40 ; 65C60 ; 65J22 ; 68U10 ; 62C10 ; 62F15 ; 94A08

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Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

49N45 ; 65C40 ; 65C60 ; 65J22 ; 68U10 ; 62C10 ; 62F15 ; 94A08

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Déposez votre fichier ici pour le déplacer vers cet enregistrement.

Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

49N45 ; 65C40 ; 65C60 ; 65J22 ; 68U10 ; 62C10 ; 62F15 ; 94A08

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- 291 p.
ISBN 978-1-4020-3121-2

Mathematics and its applications , 0557

Localisation : Ouvrage RdC (BAKU)

analyse numérique # équation non-linéaire # problème mal posé # problème inverse # régularisation # espace de Banach # espace de Hilbert # théorème de convergence # approximation linéaire # approximation paramétrique # équation d'opérateur non-linéaire # processus itératif stable

65J15 ; 65J20 ; 65J22 ; 47J06 ; 65-02

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- xiii; 321 p.
ISBN 978-0-88385-141-8

The Carus mathematical monographs , 0032

Localisation : Ouvrage RdC (GOCK)

problème inverse # espace de Hilbert # espace de Sobolev # opérateur compact # équation intégrale du premier type # méthode de régularisation # principe de divergence # critère de la courbe en L # décomposition de valeur singulière # expansion de valeur singulière # pseudo-inverse de Moore-Penrose # régularisation de Tikhonov # saturation # résultat inverse # tomographie par transmission radiographique # pouvoir fractionnaire d'opérateur # méthode de régularisation asymptotique # équation d'opérateur linéaire # méthode des moindres carrés problème inverse # espace de Hilbert # espace de Sobolev # opérateur compact # équation intégrale du premier type # méthode de régularisation # principe de divergence # critère de la courbe en L # décomposition de valeur singulière # expansion de valeur singulière # pseudo-inverse de Moore-Penrose # régularisation de Tikhonov # saturation # résultat inverse # tomographie par transmission radiographique # pouvoir fractionnaire d'opérateur # ...

65J22 ; 65-01 ; 44A12 ; 47A52 ; 65F22 ; 65J20 ; 65L08 ; 65L09 ; 65R30 ; 65R32 ; 65J10 ; 65R10 ; 45B05 ; 45A05 ; 92C55

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- 709 p.
ISBN 978-0-8247-1987-6

Monographs and textbooks in pure and applied mathematics , 0231

Localisation : Ouvrage RdC (PRIL)

problème inverse # équation différentielle elliptique # équation différentielle parabolique # équation différentielle hyperbolique # équation de Navier-Stokes # équation de Bolzman # transfert de masse # transfert de chaleur # hydrodynamique # équation de transport # structure de Hilbert # élasticité # principe de Birkhoff-Tarsky # méthode des opérateurs # contrôle # tomographie # dynamique des fluides

35R30 ; 00A05 ; 47N20 ; 65M32 ; 65N21 ; 45Q05 ; 65J22

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- 198 p.
ISBN 978-3-540-71226-8

Lecture notes in mathematics , 1906

Localisation : Collection 1er étage

analyse numérique # problème inverse # L2-espace # espace de Hilbert # espace de distribution # imagerie médicale # test non-destructif # technique de régulation # tomographie # doppler # sonar # rayon X

65-02 ; 15A29 ; 35R30 ; 45Q05 ; 65J22 ; 65N21

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