m
• E

F Nous contacter

0

# Documents  49N45 | enregistrements trouvés : 13

O

P Q

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Bayesian inference and mathematical imaging - Part 3: probability and convex optimisation Pereyra, Marcelo | CIRM H

Post-edited

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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Proceedings of the institute of mathematics and mechanics :ural branch of the Russian academy of sciencesDynamical systemsmodeling, optimization, and control | MAIK Nauka/Interperiodica Publishing;Russian Academy of Sciences 2006

Congrès

- 262 p.

Proceedings of the Steklov institute of mathematics, supplement

Localisation : Collection 1er étage

mécanique # système dynamique # contrôle optimal # problème inverse # problème mal-posé # programmation mthématique # Yurii Sergeevich Osipov

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Proceedings of the institute of mathematics and mechanics :ural branch of the Russian academy of sciencescontrol, stability, and inverse problems of dynamics | MAIK Nauka/Interperiodica Publishing;Russian Academy of Sciences 2006

Congrès

- 224 p.

Proceedings of the Steklov institute of mathematics, supplement

Localisation : Collection 1er étage

controle # stabilité # problème inverse # dynamique

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Recent advances in matrix and operator theory#July 24-27 Ball, Joseph A. ; Eidelman, Yuli ; helton, J.William ; Olshevsky, Vadim | Birkhäuser 2007

Congrès

- 338 p.
ISBN 978-3-7643-8538-5

Operator theory: advances and applications , 0179

Localisation : Collection 1er étage

théorie des opérateurs # algèbre linéaire et multi-linéaire # théorie des matrices # groupes ordonnés # problèmes inverses # fonction spectrale # mesure spectrale # transformation non-linéaire # fonctions à variables complexes # théorie des perturbations

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Methods of spectral analysis in mathematical physics:conference on operator theory, analysis and mathematical physics (OTAMP) Janas, Jan ; Kurasov, Pavel ; Laptev, Ari ; Naboko, S. ; Stolz, Günter | Birkhäuser Verlag 2009

Congrès

- vi, 443 p.
ISBN 978-3-7643-8754-9

Operator theory: advances and applications , 0186

Localisation : Collection 1er étage

analyse spectrale # graphe # Hamiltonien # approximation Ablowitz-Ladik # opérateur Schrödinger # opérateur Aharonov-Bohm # valeur propre # matrice Jacobi # estimation

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Recent advances in operator theory and applications:proceedings of IWOTA#July31-Aug.3 Ando, T. ; Curto, Raul E. ; Jung, Il Bong ; Lee, Woo Young | Birkhäuser Verlag 2009

Congrès

- viii, 247 p.
ISBN 978-3-7643-8892-8

Operator theory: advances and applications , 0187

Localisation : Collection 1er étage

théorie des opérateurs # espace Hilbert # fonction complexe # théorie des systèms # équation intégrale singulière # matrice Toeplitz

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Recent advances in scientific computing and applications:eighth international conference on scientific computing and applicationsLas Vegas # april 1-4, 2012 Li, Jichun ; Yang, Hongtao ; Machorro, Eric | American Mathematical Society 2013

Congrès

- ix; 382 p.
ISBN 978-0-8218-8737-0

Contemporary mathematics , 0586

Localisation : Collection 1er étage

analyse numérique # mathématiques appliquées # homogénisation # diffraction

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Dirichlet-Neumann shape optimization problems Buttazzo, Giuseppe | CIRM H

Multi angle

Research talks;Control Theory and Optimization;Partial Differential Equations

We consider spectral optimization problems of the form

$\min\lbrace\lambda_1(\Omega;D):\Omega\subset D,|\Omega|=1\rbrace$

where $D$ is a given subset of the Euclidean space $\textbf{R}^d$. Here $\lambda_1(\Omega;D)$ is the first eigenvalue of the Laplace operator $-\Delta$ with Dirichlet conditions on $\partial\Omega\cap D$ and Neumann or Robin conditions on $\partial\Omega\cap\partial D$. The equivalent variational formulation

$\lambda_1(\Omega;D)=\min\lbrace\int_\Omega|\nabla u|^2dx+k\int_{\partial D}u^2d\mathcal{H}^{d-1}:$

$u\in H^1(D),u=0$ on $\partial\Omega\cap D,||u||_{L^2(\Omega)}=1\rbrace$

reminds the classical drop problems, where the first eigenvalue replaces the total variation functional. We prove an existence result for general shape cost functionals and we show some qualitative properties of the optimal domains. The case of Dirichlet condition on a $\textit{fixed}$ part and of Neumann condition on the $\textit{free}$ part of the boundary is also considered
We consider spectral optimization problems of the form

$\min\lbrace\lambda_1(\Omega;D):\Omega\subset D,|\Omega|=1\rbrace$

where $D$ is a given subset of the Euclidean space $\textbf{R}^d$. Here $\lambda_1(\Omega;D)$ is the first eigenvalue of the Laplace operator $-\Delta$ with Dirichlet conditions on $\partial\Omega\cap D$ and Neumann or Robin conditions on $\partial\Omega\cap\partial D$. The equivalent variational formulation

\$\lam...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Bayesian inference and mathematical imaging - Part 2: Markov chain Monte Carlo Pereyra, Marcelo | CIRM H

Multi angle

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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Bayesian inference and mathematical imaging - Part 1: Bayesian analysis and decision theory Pereyra, Marcelo | CIRM H

Multi angle

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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Bayesian inference and mathematical imaging - Part 4: mixture, random fields and hierarchical models Pereyra, Marcelo | CIRM H

Multi angle

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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## The inverse problem of the calculus of variations for ordinary differential equations Anderson, Ian ; Thompson, Gerard | American Mathematical Society 1992

Ouvrage

ISBN 978-0-8218-2533-4

Memoirs of the american mathematical society , 0473

Localisation : Collection 1er étage

analyse globale # analyse sur les varietes # bicomplexe variationnel # calcul des variations # contrïle optimal # equation differentielle ordinaire sur les varietes # geometrie symplectique # jet pulverise # optimisation # principe variationnel # principe variationnel pour les equations differentielles ord # probleme inverse # probleme variationnel dans les espaces de dimension infinie # systeme differentiel exterieur # systeme dynamique # systeme hamiltonien et lagrangien # theorie generale des varietes differentiables analyse globale # analyse sur les varietes # bicomplexe variationnel # calcul des variations # contrïle optimal # equation differentielle ordinaire sur les varietes # geometrie symplectique # jet pulverise # optimisation # principe variationnel # principe variationnel pour les equations differentielles ord # probleme inverse # probleme variationnel dans les espaces de dimension infinie # systeme differentiel exterieur # systeme dynamique # ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Stable approximative evaluation of unbounded operators Groetsch, C. W. | Springer 2007

Ouvrage

- 127 p.
ISBN 978-3-540-39942-1

Lecture notes in mathematics , 1894

Localisation : Collection 1er étage

théorie des opérateurs # opérateur non borné # théorie d'approximation d'opérateur # problème inverse # méthode de Tikhonov-Morogov

#### Filtrer

##### Codes MSC

Titres de périodiques et e-books électroniques (Depuis le CIRM)

Ressources Electroniques

Books & Print journals

Recherche avancée

0
Z