Dissertation/ Thesis
Fast variational Bayesian algorithms and their application to large dimensional inverse problems ; Algorithmes bayésiens variationnels accélérés et applications aux problèmes inverses de grande taille
| العنوان: | Fast variational Bayesian algorithms and their application to large dimensional inverse problems ; Algorithmes bayésiens variationnels accélérés et applications aux problèmes inverses de grande taille |
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| المؤلفون: | Zheng, Yuling |
| المساهمون: | Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Université Paris Sud - Paris XI, Thomas Rodet, Aurélia Fraysse |
| المصدر: | https://theses.hal.science/tel-01135180 ; Traitement des images [eess.IV]. Université Paris Sud - Paris XI, 2014. Français. ⟨NNT : 2014PA112354⟩. |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2014 |
| مصطلحات موضوعية: | Variational Bayesian approximation, Subspace optimization, Large dimensional problem, Unsupervised approach, Sparsity, Piecewise smooth, Total variation, GSM, Approximation bayésienne variationnelle, Optimisation par sous-espace, Problème de grande dimension, Approche non-supervisée, Parcimonie, Régularité par morceau, Variation totale, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] |
| الوصف: | In this thesis, our main objective is to develop efficient unsupervised approaches for large dimensional problems. To do this, we consider Bayesian approaches, which allow us to jointly estimate regularization parameters and the object of interest. In this context, the main difficulty is that the posterior distribution is generally complex. To tackle this problem, we consider variational Bayesian (VB) approximation, which provides a separable approximation of the posterior distribution. Nevertheless, classical VB methods suffer from slow convergence speed. The first contribution of this thesis is to transpose the subspace optimization methods to the functional space involved in VB framework, which allows us to propose a new VB approximation method. We have shown the efficiency of the proposed method by comparisons with the state of the art approaches.Then we consider the application of our new methodology to large dimensional problems in image processing. Moreover, we are interested in piecewise smooth images. As a result, we have considered a Total Variation (TV) prior and a Gaussian location mixture-like hidden variable model. With these two priors, using our VB approximation method, we have developed two fast unsupervised approaches well adapted to piecewise smooth images.In fact, the priors introduced above are correlated which makes the estimation of regularization parameters very complicated: we often have a non-explicit partition function. To sidestep this problem, we have considered working in the wavelet domain. As the wavelet coefficients of natural images are generally sparse, we considered prior distributions of the Gaussian scale mixture family to enforce sparsity. Another contribution is therefore the development of an unsupervised approach for a prior distribution of the GSM family whose density is explicitly known, using the proposed VB approximation method. ; Dans le cadre de cette thèse, notre préoccupation principale est de développer des approches non supervisées permettant de résoudre des ... |
| نوع الوثيقة: | doctoral or postdoctoral thesis |
| اللغة: | French |
| Relation: | NNT: 2014PA112354; tel-01135180; https://theses.hal.science/tel-01135180; https://theses.hal.science/tel-01135180/document; https://theses.hal.science/tel-01135180/file/VA2_ZHENG_YULING_04122014.pdf |
| الاتاحة: | https://theses.hal.science/tel-01135180 https://theses.hal.science/tel-01135180/document https://theses.hal.science/tel-01135180/file/VA2_ZHENG_YULING_04122014.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.4B2B4334 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |