Gradient Scan Gibbs Sampler: An Efficient Algorithm for High-Dimensional Gaussian Distributions

This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set of directions. The algorithm is proved to converge, i.e., th...

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Bibliographic Details
Published in:IEEE journal of selected topics in signal processing 2016-03, Vol.10 (2), p.343-352
Main Authors: Feron, Olivier, Orieux, Franois, Giovannelli, Jean-Francois
Format: Article
Language:English
Subjects:
Algorithms
Applications
Asymptotic properties
Bayesian analysis
Computer Science
Convergence
Engineering Sciences
Gaussian
Gaussian distribution
Image Processing
Inverse problems
Markov processes
Mathematics
Monte Carlo methods
Normal distribution
Optimization
optimization methods
Samplers
Sampling
Signal and Image Processing
Signal processing algorithms
Signal resolution
Statistics
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Summary:This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set of directions. The algorithm is proved to converge, i.e., the drawn samples are asymptotically distributed according to the target distribution. Our main motivation is in inverse problems related to general linear observation models and their solution in a hierarchical Bayesian framework implemented through sampling algorithms. It finds direct applications in semi-blind/unsupervised methods as well as in some non-Gaussian methods. The paper provides an illustration focused on the unsupervised estimation for super-resolution methods.
ISSN:1932-4553
1941-0484
DOI:10.1109/JSTSP.2015.2510961