SIGEST

Abstract

SIAM Review, Volume 64, Issue 4, Page 989-989, November 2022.
The SIGEST article in this issue is “A Proximal Markov Chain Monte Carlo Method for Bayesian Inference in Imaging Inverse Problems: When Langevin Meets Moreau,” by Alain Durmus, Éric Moulines, and Marcelo Pereyra. The authors provide new algorithms to sample from high-dimensional log-concave probability measures, where they combine Moreau--Yosida envelopes with the Euler--Maruyama discretization of Langevin diffusions. This allows for an efficient Markov chain Monte Carlo methodology that is applicable to inverse problems arising in imaging sciences. Asymptotic and nonasymptotic convergence results are provided, along with extensive computational experiments on realistic imaging problems involving deconvolution and tomographic reconstruction. The original article, which appeared in the SIAM Journal on Imaging Sciences in 2018, has attracted substantial interest. In preparing this highlighted SIGEST version, the authors have expanded the introduction to make it accessible to a wide audience. The final section also discusses follow-up work arising from the original publication.