  This paper is devoted to the problem of sampling Gaussian fields in high
dimension. Solutions exist for two specific structures of inverse covariance :
sparse and circulant. The proposed approach is valid in a more general case and
especially as it emerges in inverse problems. It relies on a
perturbation-optimization principle: adequate stochastic perturbation of a
criterion and optimization of the perturbed criterion. It is shown that the
criterion minimizer is a sample of the target density. The motivation in
inverse problems is related to general (non-convolutive) linear observation
models and their resolution in a Bayesian framework implemented through
sampling algorithms when existing samplers are not feasible. It finds a direct
application in myopic and/or unsupervised inversion as well as in some
non-Gaussian inversion. An illustration focused on hyperparameter estimation
for super-resolution problems assesses the effectiveness of the proposed
approach.
