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UID:5525@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20131122T140000
DTEND;TZID=Europe/Paris:20131122T150000
DTSTAMP:20241030T093209Z
URL:https://www.i2m.univ-amu.fr/evenements/s-geffray-unistra-strasbourg-at
 -frumam-st-charles-a-statistical-solution-to-an-inverse-problem-of-illumin
 ation-with-applications-to-electron-microscopy/
SUMMARY: (...): S. Geffray (Unistra\\\, Strasbourg) at Frumam (St Charles):
  A statistical solution to an inverse problem of illumination with applica
 tions to electron microscopy
DESCRIPTION:: 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 in
 herent in the recording technology. This may be the case with electron mic
 roscopy for example.\nThe illumination artefact is modelled by a function 
 L which is "smooth" enough\\\, in a sense to be precised in the mathematic
 al 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 origina
 l signal R by the equation:\nY(x)=R(x)L(x)+b(x).\nIn this framework\\\, ou
 r 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-&gt\; R(x)L(x)) is unknown.\nTo this aim\\\, we set identifiability con
 ditions and use a regression strategy. We project log (Y) on a suitable cl
 osed convex subspace of a Hilbert space so that we get an estimation of lo
 g (L) and deduce an estimation of R.\nThe procedure quality is studied thr
 ough the evaluation of the risk of the estimator of R.\nAt last\\\, an app
 lication to real images is presented.
CATEGORIES:Séminaire,Signal et Apprentissage
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