Accelerating proximal Markov chain Monte Carlo by using an explicit stabilised method

Luis Vargas Mieles, Marcelo Pereyra, Konstantinos C Zygalakis

Research output: Contribution to journalArticlepeer-review

Abstract

We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computa-tion in imaging problems. Similarly to previous proximal Monte Carlo approaches, the proposed method is derivedfrom an approximation of the Langevin diffusion. However, instead of the conventional Euler-Maruyama approx-imation that underpins existing proximal Monte Carlo methods, here we use a state-of-the-art orthogonal Runge-Kutta-Chebyshev stochastic approximation [2] that combines several gradient evaluations to significantly accelerateits convergence speed, similarly to accelerated gradient optimisation methods. The proposed methodology is demon-strated via a range of numerical experiments, including non-blind image deconvolution, hyperspectral unmixing, andtomographic reconstruction, with total-variation andℓ1-type priors. Comparisons with Euler-type proximal MonteCarlo methods confirm that the Markov chains generated with our method exhibit significantly faster convergencespeeds, achieve larger effective sample sizes, and producelower mean square estimation errors at equal computa-tional budget
Original languageEnglish
Number of pages28
JournalSiam journal on imaging sciences
Volume13
Issue number2
DOIs
Publication statusPublished - 26 May 2020

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