Sampling High-Dimensional Gaussian Distributions for General Linear Inverse Problems

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...

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Bibliographic Details
Published in:IEEE signal processing letters 2012-05, Vol.19 (5), p.251-254
Main Authors: Orieux, F., Feron, O., Giovannelli, J-F
Format: Article
Language:English
Subjects:
Applications
Bayesian methods
Bayesian strategy
Computation
Computer Science
Engineering Sciences
Gaussian distribution
high-dimensional sampling
Image Processing
Image resolution
inverse problem
Inverse problems
Mathematics
myopic
Optimization
Signal and Image processing
Signal processing algorithms
Statistics
Statistics Theory
Stochastic processes
stochastic sampling
unsupervised
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Summary: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.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2012.2189104