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Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems using MCMC

Abstract : The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. Based on the reversible jump Markov chain framework, this paper proposes an efficient Gaussian sampling algorithm having a reduced computation cost and memory usage, as compared to classical methods based on Cholesky factorization. The main feature of the algorithm is to perform an approximate resolution of a linear system with a truncation level adjusted using a self-tuning adaptive scheme allowing to achieve the minimal computation cost. The connection between this algorithm and some existing strategies is discussed and its efficiency is illustrated on a linear inverse problem of image resolution enhancement.
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Submitted on : Sunday, August 31, 2014 - 11:56:32 AM
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Clément Gilavert, Saïd Moussaoui, Jérôme Idier. Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems using MCMC. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2015, 63 (01), pp.70-80. ⟨10.1109/TSP.2014.2367457⟩. ⟨hal-01059414⟩

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