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Approches bayésiennes pour le débruitage des images dans le domaine des transformées multi-échelles parcimonieuses orientées et non orientées

Larbi Boubchir 1
1 Equipe Image - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
Abstract : Image data observed at the output of an image acquisition device are generally degraded by the sensor noise. The task which aims at recovering a good quality image from its noisy observations is widely known as denoising. Denoising has been at the heart of a flurry of research activity in the image processing literature. In this work, after defining the denoising problem when data are corrupted by an additive gaussian noise, we provide an extensive and methodical review of the literature. Most of image denoising methods try to narrow down the class of candidate solutions by imposing some prior regularity constraints on the recovered solution. We have chosen to formulate our prior in a bayesian framework, through multi-scale transform coefficients of the image. Towards this end, and by appropriately exploiting the sparsity of these multi-scale representations, we designed prior models to capture the marginal and joint statistics of such coefficients in oriented (e.g. curvelets) and non-oriented (e.g. wavelets) multiscale pyramids. These priors were then utilized in newly proposed bayesian denoisers. The implementation of these bayesian estimators relies on two key steps for which we suggested efficient solutions: (i) estimate the hyperparameters of the prior model in presence of noise, and (ii) find an analytical form for the corresponding bayesian estimator. In the first part of this thesis, we designed term-by-term univariate bayesian estimators by taking advantage of the marginal statistics of coefficients of images in sparse multiscale representations, e.g. wavelets. These marginal statistics were modelled analytically using alpha-stable and Bessel K Form distributions. In the second part, we improved upon the performance of univariate estimators by introducing the geometrical information contained in the neighborhood of each representation coefficients. More precisely, we proposed a multivariate statistical bayesian framework which takes into account the intra- and inter-scale dependencies of coefficients and models the joint statistics of groups of coefficients in the curvelet and the undecimated wavelet domains. The associated multivariate bayesian estimator was also provided based on a multivariate extension of the Bessel K Form distribution. A comprehensive comparative study has been carried out to compare our denoising algorithms to state-of-the-art competitors.
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Submitted on : Wednesday, July 11, 2007 - 10:13:29 AM
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Larbi Boubchir. Approches bayésiennes pour le débruitage des images dans le domaine des transformées multi-échelles parcimonieuses orientées et non orientées. Traitement des images [eess.IV]. Université de Caen, 2007. Français. ⟨tel-00161573⟩



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