Gradient Scan Gibbs Sampler: An Efficient Algorithm for High-Dimensional Gaussian Distributions. Féron, O., Orieux, F., & Giovannelli, J. IEEE Journal of Selected Topics in Signal Processing, PP(2):343–352, 2015.
Gradient Scan Gibbs Sampler: An Efficient Algorithm for High-Dimensional Gaussian Distributions [link]Paper  doi  abstract   bibtex   
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.
@article{feron_gradient_2015,
	title = {Gradient {Scan} {Gibbs} {Sampler}: {An} {Efficient} {Algorithm} for {High}-{Dimensional} {Gaussian} {Distributions}},
	volume = {PP},
	copyright = {All rights reserved},
	issn = {1932-4553},
	shorttitle = {{IEEE} journal of selected topics in signal processi},
	url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7362115},
	doi = {10.1109/JSTSP.2015.2510961},
	abstract = {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.},
	number = {2},
	journal = {IEEE Journal of Selected Topics in Signal Processing},
	author = {Féron, Olivier and Orieux, François and Giovannelli, Jean-François},
	year = {2015},
	keywords = {Convergence, Gaussian distribution, Inverse problems, Markov processes, Mathematics, Monte Carlo methods, Optimization, Signal processing algorithms, Signal resolution, belief networks, general linear observation models, gradient scan Gibbs sampler, hierarchical Bayesian framework, high-dimensional Gaussian distributions, image resolution, nonGaussian methods, optimization methods, super-resolution methods, unsupervised estimation, unsupervised learning},
	pages = {343--352}
}

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