Sampling High-Dimensional Gaussian Distributions for General Linear Inverse Problems
Orieux, François; Féron, Olivier; Giovannelli, Jean-François (2012), Sampling High-Dimensional Gaussian Distributions for General Linear Inverse Problems, IEEE Signal Processing Letters, 19, 5, p. 251-254. http://dx.doi.org/10.1109/LSP.2012.2189104
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00779449
Journal nameIEEE Signal Processing Letters
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Abstract (EN)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 (nonconvolutive) 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.
Subjects / KeywordsStochastic sampling; high-dimensional sampling; inverse problem; Bayesian strategy; unsupervised; myopic; semi-blind
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