– S. Geffray (Unistra, Strasbourg) at Frumam (St Charles) : A statistical solution to an inverse problem of illumination with applications to electron microscopy

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Date/heure
Date(s) - 22 novembre 2013

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A statistical solution to an inverse problem of illumination with applications to electron microscopy By Segolen Geffray, Unistra, Université de Strasbourg. Abstract: We are interested in a multi-dimensional signal denoted by R observed with an illumination artefact inherent in the recording technology. This may be the case with electron microscopy for example. The illumination artefact is modelled by a function L which is “smooth” enough, in a sense to be precised in the mathematical developments, and which acts in a multiplicative way on the original signal R. We also assume the presence of an additional additive noise b so that the observed signal denoted by Y is actually linked to the original signal R by the equation: Y(x)=R(x)L(x)+b(x). In this framework, our aim consists of reconstructing R from the observation of Y. That is, we try and solve an inverse problem in which the operator which maps R to (x-> R(x)L(x)) is unknown. To this aim, we set identifiability conditions and use a regression strategy. We project log (Y) on a suitable closed convex subspace of a Hilbert space so that we get an estimation of log (L) and deduce an estimation of R. The procedure quality is studied through the evaluation of the risk of the estimator of R. At last, an application to real images is presented.

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Date/heure
Date(s) - 22 novembre 2013

Catégories Pas de Catégories

A statistical solution to an inverse problem of illumination with applications to electron microscopy\n\nBy Segolen Geffray, Unistra, Université de Strasbourg.\n\nAbstract :\nWe are interested in a multi-dimensional signal denoted by R observed with an illumination artefact inherent in the recording technology. This may be the case with electron microscopy for example.\nThe illumination artefact is modelled by a function L which is “smooth” enough, in a sense to be precised in the mathematical developments, and which acts in a multiplicative way on the original signal R.\nWe also assume the presence of an additional additive noise b so that the observed signal denoted by Y is actually linked to the original signal R by the equation :\nY(x)=R(x)L(x)+b(x).\nIn this framework, our aim consists of reconstructing R from the observation of Y. That is, we try and solve an inverse problem in which the operator which maps R to (x-> R(x)L(x)) is unknown.\nTo this aim, we set identifiability conditions and use a regression strategy. We project log (Y) on a suitable closed convex subspace of a Hilbert space so that we get an estimation of log (L) and deduce an estimation of R.\nThe procedure quality is studied through the evaluation of the risk of the estimator of R.\nAt last, an application to real images is presented.[

Carte non disponible

Date/heure
Date(s) - 22 novembre 2013

Catégories Pas de Catégories

A statistical solution to an inverse problem of illumination with applications to electron microscopy\n\nBy Segolen Geffray, Unistra, Université de Strasbourg.\n\nAbstract :\nWe are interested in a multi-dimensional signal denoted by R observed with an illumination artefact inherent in the recording technology. This may be the case with electron microscopy for example.\nThe illumination artefact is modelled by a function L which is “smooth” enough, in a sense to be precised in the mathematical developments, and which acts in a multiplicative way on the original signal R.\nWe also assume the presence of an additional additive noise b so that the observed signal denoted by Y is actually linked to the original signal R by the equation :\nY(x)=R(x)L(x)+b(x).\nIn this framework, our aim consists of reconstructing R from the observation of Y. That is, we try and solve an inverse problem in which the operator which maps R to (x-> R(x)L(x)) is unknown.\nTo this aim, we set identifiability conditions and use a regression strategy. We project log (Y) on a suitable closed convex subspace of a Hilbert space so that we get an estimation of log (L) and deduce an estimation of R.\nThe procedure quality is studied through the evaluation of the risk of the estimator of R.\nAt last, an application to real images is presented.[

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