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Sampling high-dimensional Gaussian distributions for general linear inverse problems

Abstract : 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.
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Submitted on : Tuesday, January 22, 2013 - 2:46:42 PM
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François Orieux, Olivier Féron, Jean-François Giovannelli. Sampling high-dimensional Gaussian distributions for general linear inverse problems. IEEE Signal Processing Letters, Institute of Electrical and Electronics Engineers, 2012, 19 (5), pp.251. ⟨10.1109/LSP.2012.2189104⟩. ⟨hal-00779449⟩

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