2011/05/30 by François Orieux, F. Orieux, O. Féron +6
Computer Science · Mathematics · #Advanced Image Processing Techniques #Applications (stat.AP) #Computation (stat.CO) #FOS: Computer and information sciences #Image and Signal Denoising Methods #Machine Learning (cs.LG) #Statistical Methods and Inference #cs.LG #stat.AP #stat.CO
paper · pdf · doi:10.48550/arxiv.1105.5887
arxiv created 2011/05/30 · openalex publication_date 2011/05/30 · arxiv updated 2011/05/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.