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This paper is devoted to the problem of sampling Gaussian fields in highdimension. Solutions exist for two specific structures of inverse covariance :sparse and circulant. The proposed approach is valid in a more general case andespecially as it emerges in inverse problems. It relies on aperturbation-optimization principle: adequate stochastic perturbation of acriterion and optimization of the perturbed criterion. It is shown that thecriterion minimizer is a sample of the target density. The motivation ininverse problems is related to general (non-convolutive) linear observationmodels and their resolution in a Bayesian framework implemented throughsampling algorithms when existing samplers are not feasible. It finds a directapplication in myopic and/or unsupervised inversion as well as in somenon-Gaussian inversion. An illustration focused on hyperparameter estimationfor super-resolution problems assesses the effectiveness of the proposedapproach.

Efficient sampling of high-dimensional Gaussian fields: the non-stationary / non-sparse case