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Approche bayésienne pour la sélection de modèles : application à la restauration d’image

Abstract : Inversing main goal is about reconstructing objects from data. Here, we focus on the special case of image restauration in convolution problems. The data are acquired through a altering observation system and additionnaly distorted by errors. The problem becomes ill-posed due to the loss of information. One way to tackle it is to exploit Bayesian approach in order to regularize the problem. Introducing prior information about the unknown quantities osset the loss, and it relies on stochastic models. We have to test all the candidate models, in order to select the best one. But some questions remain : how do you choose the best model? Which features or quantities should we rely on ? In this work, we propose a method to automatically compare and choose the model, based on Bayesion decision theory : objectively compare the models based on their posterior probabilities. These probabilities directly depend on the marginal likelihood or “evidence” of the models. The evidence comes from the marginalization of the jointe law according to the unknow image and the unknow hyperparameters. This a difficult integral calculation because of the complex dependancies between the quantities and the high dimension of the image. That way, we have to work with computationnal methods and approximations. There are several methods on the test stand as Harmonic Mean, Laplace method, discrete integration, Chib from Gibbs approximation or the power posteriors. Comparing is those methods is significative step to determine which ones are the most competent in image restauration. As a first lead of research, we focus on the family of Gaussian models with circulant covariance matrices to lower some difficulties.
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https://tel.archives-ouvertes.fr/tel-03065948
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Submitted on : Tuesday, December 15, 2020 - 8:54:07 AM
Last modification on : Wednesday, December 16, 2020 - 3:35:59 AM

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HARROUE_BENJAMIN_2020.pdf
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  • HAL Id : tel-03065948, version 1

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Benjamin Harroue. Approche bayésienne pour la sélection de modèles : application à la restauration d’image. Traitement du signal et de l'image [eess.SP]. Université de Bordeaux, 2020. Français. ⟨NNT : 2020BORD0127⟩. ⟨tel-03065948⟩

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