Sampling High-Dimensional Gaussian Distributions for General Linear Inverse Problems
| Autor: | Olivier Féron, J-F Giovannelli, François Orieux |
|---|---|
| Přispěvatelé: | Institut d'Astrophysique de Paris (IAP), Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC), Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie (EDF R&D OSIRIS), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Laboratoire de l'intégration, du matériau au système (IMS), Université Sciences et Technologies - Bordeaux 1-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2012 |
| Předmět: |
high-dimensional sampling
Mathematical optimization myopic Gaussian Inverse 02 engineering and technology symbols.namesake [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] semi-blind 0202 electrical engineering electronic engineering information engineering unsupervised Applied mathematics Electrical and Electronic Engineering [STAT.CO]Statistics [stat]/Computation [stat.CO] Sparse matrix Mathematics Hyperparameter [STAT.AP]Statistics [stat]/Applications [stat.AP] Estimation theory Applied Mathematics Stochastic sampling 020206 networking & telecommunications [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Inverse problem Covariance [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] Signal Processing symbols inverse problem 020201 artificial intelligence & image processing Bayesian strategy [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing Gibbs sampling |
| Zdroj: | IEEE Signal Processing Letters IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, 2012, 19 (5), pp.251. ⟨10.1109/LSP.2012.2189104⟩ IEEE Signal Processing Letters, 2012, 19 (5), pp.251. ⟨10.1109/LSP.2012.2189104⟩ |
| ISSN: | 1558-2361 1070-9908 |
| DOI: | 10.1109/lsp.2012.2189104 |
| Popis: | International audience; This paper is devoted to the problem of sampling Gaussian distributions in high dimension. Solutions exist for two specific structures of inverse covariance: sparse and circulant. The proposed algorithm is valid in a more general case especially as it emerges in linear inverse problems as well as in some hierarchical or latent Gaussian models. It relies on a perturbation-optimization principle: adequate stochastic perturbation of a criterion and optimization of the perturbed criterion. It is proved that the criterion optimizer is a sample of the target distribution. The main motivation is in inverse problems related to general (non-convolutive) linear observation models and their solution in a Bayesian framework implemented through sampling algorithms when existing samplers are infeasible. It finds a direct application in myopic,unsupervised inversion methods as well as in some non-Gaussian inversion methods. An illustration focused on hyperparameter estimation for super-resolution method shows the interest and the feasibility of the proposed algorithm. |
| Databáze: | OpenAIRE |
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