3 - Filtres de Kalman 2-D rapides à modèle d'état non causal pour la restauration d'image

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URI: http://hdl.handle.net/2042/1645
Title: 3 - Filtres de Kalman 2-D rapides à modèle d'état non causal pour la restauration d'image
Abstract: Il s'agit d'un problème de restauration d'une image dégradée par un système linéaire invariant par translation
Description: The ill posed image restoration problem is treated in a Bayesian framework to deal with both noise and prior information required to stabilize the solution . Direct discretization of the convolution equation provides a state-space model whose huge dimensions make a standard Kalman f lter untractable in spite of its recursive nature . That is why the model dimension is usually reduced by introducing dynamics into the state equation, which requires an artificial causality assumption . To avoid this difficulty, we propose state-space models where the state is taken constant and equal to the entire object to be restored, and where dynamics appear only in the observation equation which may be either a vector or a scalar . When the image is scanned row by row, the shift properties of the convolution summation allow us to derive a fast Kalman algorithm through factorization techniques. When the image is scanned pixel by pixel, the computational requirement can be further reduced at the expense of an extra assumption. Sub-optimal asymptotic filters with a reduced update are then derived front these two filters . Finally, simulated and experimental results are presented .
Subject: Traitement image; Restauration image; Traitement numérique; Filtre numérique; Filtre Kalman; Filtre rapide; Filtre bidimensionnel; Estimation Bayes; Image floue; Méthode espace état; Equation Chandrasekhar
Publisher: GRETSI, Saint Martin d'Hères, France
Date: 1987

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