A Nash-game approach to joint data completion and location of small inclusions in Stokes flow

International audience We consider the coupled inverse problem of data completion and the determination of the best locations of an unknown number of small objects immersed in a stationary viscous fluid. We carefully introduce a novel method to solve this problem based on a game theory approach. A new algorithm is provided to recovering the missing data and the number of these objects and their approximate location simultaneously. The detection problem is formulated as a topological one. We present two test-cases that illustrate the efficiency of our original strategy to deal with the ill-posed problem. Nous étudions le problème de détection des petites inclusions immergées dans un fluide visqueux et incompressible, lorsque le mouvement de celui-ci est régi par les équations de Stokes. Des données du type Cauchy seront ainsi fournies seulement sur une partie frontière de l’écoulement.A cet égard, nous essayons de développer une méthode originale basée sur une approche de théorie des jeux, pour résoudre notre problème inverse. Un nouvel algorithme a été donc présenté traitant simultanément la question de la reconstruction des données manquantes avec celle de détection d’objets. La notion de gradient topologique a été utilisée afin de déterminer le nombre d’objets présents et leurs localisations approximatives. Dans cet objectif, une étude numérique présentée, a été effectuée pour prouver l’efficacité de la méthode.

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A Preconditioned Richardson Regularization for the Data Completion Problem and the Kozlov-Maz’ya-Fomin Method

Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées ◽

10.46298/arima.1934 ◽

2010 ◽

Vol Volume 13 - 2010 - Special... ◽

Author(s):

Duc Thang Du ◽

Faten Jelassi

Keyword(s):

Inverse Problems ◽

Stopping Rules ◽

Completion Problem ◽

Variational Framework ◽

Data Completion ◽

International Audience ◽

Ill Posed ◽

General Source ◽

Richardson Iterative Method ◽

Math Phys

International audience Using a preconditioned Richardson iterative method as a regularization to the data completion problem is the aim of the contribution. The problem is known to be exponentially ill posed that makes its numerical treatment a hard task. The approach we present relies on the Steklov-Poincaré variational framework introduced in [Inverse Problems, vol. 21, 2005]. The resulting algorithm turns out to be equivalent to the Kozlov-Maz’ya-Fomin method in [Comp. Math. Phys., vol. 31, 1991]. We conduct a comprehensive analysis on the suitable stopping rules that provides some optimal estimates under the General Source Condition on the exact solution. Some numerical examples are finally discussed to highlight the performances of the method. L’objectif est d’utiliser une méthode itérative de Richardson préconditionnée comme une technique de régularisation pour le problème de complétion de données. Le problème est connu pour être sévèrement mal posé qui rend son traitement numérique ardu. L’approche adoptée est basée sur le cadre variationnel de Steklov-Poincaré introduit dans [Inverse Problems, vol. 21, 2005].L’algorithme obtenu s’avère être équivalent à celui de Kozlov-Maz’ya-Fomin parû dans [Comp. Math. Phys., vol. 31, 1991]. Nous menons une analyse complète pour le choix du critère d’arrêt, et établissons des estimations optimales sous les Conditions Générale de Source sur la solution exacte. Nous discutons, enfin, quelques exemples numériques qui confortent les pertinence de la méthode.

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Reconstruction of missing boundary conditions from partially overspecified data : the Stokes system

Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées ◽

10.46298/arima.1494 ◽

2016 ◽

Vol Volume 23 - 2016 - Special... ◽

Author(s):

Amel Ben Abda ◽

Faten Khayat

Keyword(s):

Inverse Problem ◽

Stokes System ◽

Stokes Problem ◽

Domain Boundary ◽

The Other ◽

First Order ◽

Completion Problem ◽

Data Completion ◽

Ill Posed ◽

Problème Inverse

We are interested in this paper with the ill-posed Cauchy-Stokes problem. We consider a data completion problem in which we aim recovering lacking data on some part of a domain boundary , from the knowledge of partially overspecified data on the other part. The inverse problem is formulated as an optimization one using an energy-like misfit functional. We give the first order opti-mality condition in terms of an interfacial operator. Displayed numerical results highlight its accuracy. Nous nous intéressons à un problème de Cauchy mal posé, celui de la complétion de données frontières pour les équations de Stokes. Nous voulons reconstituer les données manquantes sur une partie non accessible de la frontière du domaine à partir de données peu surdéterminées sur la partie accessible. Nous formulons ce problème inverse sous forme de minimisation d'une fonctionnelle de type énergie. Les conditions d'optimalité du premier ordre sont écrites en termes d'équation d'interface utilisant les opérateurs de Stecklov-Poincaré. Nous donnons des résultats numériques attestant l'efficacité de la méthode.

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Information and estimation in image processing

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100125142 ◽

1987 ◽

Vol 45 ◽

pp. 14-17

Author(s):

B. Roy Frieden

Keyword(s):

Image Processing ◽

Optical System ◽

Large Amplitude ◽

Communication Theory ◽

Image Data ◽

Direct Approach ◽

Ill Posed

Despite the skill and determination of electro-optical system designers, the images acquired using their best designs often suffer from blur and noise. The aim of an “image enhancer” such as myself is to improve these poor images, usually by digital means, such that they better resemble the true, “optical object,” input to the system. This problem is notoriously “ill-posed,” i.e. any direct approach at inversion of the image data suffers strongly from the presence of even a small amount of noise in the data. In fact, the fluctuations engendered in neighboring output values tend to be strongly negative-correlated, so that the output spatially oscillates up and down, with large amplitude, about the true object. What can be done about this situation? As we shall see, various concepts taken from statistical communication theory have proven to be of real use in attacking this problem. We offer below a brief summary of these concepts.

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A novel method for the determination of linting propensity of paper

TAPPI Journal ◽

10.32964/tj11.10.9 ◽

2012 ◽

Vol 11 (10) ◽

pp. 9-17

Author(s):

ALESSANDRA GERLI ◽

LEENDERT C. EIGENBROOD

Keyword(s):

Ash Content ◽

The Novel ◽

Offset Printing ◽

Excellent Correlation ◽

End Conditions ◽

Bottom Side ◽

Novel Method ◽

Total Fraction

A novel method was developed for the determination of linting propensity of paper based on printing with an IGT printability tester and image analysis of the printed strips. On average, the total fraction of the surface removed as lint during printing is 0.01%-0.1%. This value is lower than those reported in most laboratory printing tests, and more representative of commercial offset printing applications. Newsprint paper produced on a roll/blade former machine was evaluated for linting propensity using the novel method and also printed on a commercial coldset offset press. Laboratory and commercial printing results matched well, showing that linting was higher for the bottom side of paper than for the top side, and that linting could be reduced on both sides by application of a dry-strength additive. In a second case study, varying wet-end conditions were used on a hybrid former machine to produce four paper reels, with the goal of matching the low linting propensity of the paper produced on a machine with gap former configuration. We found that the retention program, by improving fiber fines retention, substantially reduced the linting propensity of the paper produced on the hybrid former machine. The papers were also printed on a commercial coldset offset press. An excellent correlation was found between the total lint area removed from the bottom side of the paper samples during laboratory printing and lint collected on halftone areas of the first upper printing unit after 45000 copies. Finally, the method was applied to determine the linting propensity of highly filled supercalendered paper produced on a hybrid former machine. In this case, the linting propensity of the bottom side of paper correlated with its ash content.

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