Associate Professor, Heriot-Watt University and Maxwell Institute for Mathematical Sciences, UK
Visiting Professor 2022-23 - April 8 to 29, 2023
Inviting Researcher: Julián Tachella Marcelo Pereyra is Associate Professor of Statistics in the School of Mathematics and Computer Science at Heriot-Watt University and at the Maxwell Institute for Mathematical Sciences. His research focuses on new mathematical theories, methods and algorithms for solving complex inverse problems related to mathematical and computational imaging. His work focuses on new Bayesian analysis and computational approaches for imaging, and on the synergy between statistical paradigms, variational analysis and machine learning for imaging methodology development.
He studied electronic engineering in Buenos Aires (Argentina) and Toulouse (France) and completed his PhD in signal processing at the Université de Toulouse in 2012. From 2012 to 2016, he has been Research Fellow in Statistics at the School of Mathematics, University of Bristol, funded by a Marie Curie Intra-European Career Development Fellowship, a Brunel Postdoctoral Fellowship in Statistics, a French Ministry of Defense Postdoctoral Research Fellowship. In 2019, he held a visiting professorship at the Institut Henri Poincaré in Paris during the "Mathematics of Imaging" term.
Dr. Pereyra’s stay in the Signals, Systems and Physics (SiSyPh) team at the Physics Laboratory of ENS de Lyon will be beneficial to all team members, as he has significant experience in several of the areas where SiSyPh conducts research activities. One of the objectives of his visit will be to study new methods that combine Bayesian inference with deep learning to solve inverse imaging problems that are blind or semi-blind (i.e. when the observational model representing the instrument and the acquisition system is not fully known). Specifically, Julián Tachella and Nelly Pustelnik will work with Marcelo Pereyra on new unsupervised learning approaches that exploit Bayesian strategies to handle situations with uncertainty in the image observation model, and for which it is necessary to quantify the uncertainty in the solutions provided.
In addition, SiSyPh has recently produced several works related to Covid-19 reproduction number estimation (N. Pustelnik, P. Abry, S. Roux), a typical case of inference problem that informs important decisions and conclusions and where it is crucial to characterize the uncertainty in the solution. The work developed by SiSyPh considers estimation strategies based on convex optimization as well as Monte Carlo sampling. This line of research can benefit significantly from some of Dr. Pereyra’s work on uncertainty quantification for convex optimization problems, as well as his work on Bayesian inference by Monte Carlo sampling using proximal Markov chains.
Wednesday, April 26. 1:00 pm - 2:00 pm
Machine Learning and Signal Processing Seminar session R. Laumont, V. de Bortoli, A. Almansa, J. Delon, A. Durmus, and M. Pereyra, "Bayesian imaging using Plug and Play priors: when Langevin meets Tweedie", to appear in SIAM Journal on Imaging Sciences. [Preprint https://arxiv.org/abs/2103.04715 ].
V. De Bortoli, A. Durmus, A. F. Vidal, M. Pereyra, "Maximum Likelihood Estimation of Regularization Parameters in High-Dimensional Inverse Problems: An Empirical Bayesian Approach Part II: Theoretical Analysis", SIAM Journal on Imaging Sciences, vol. 13, no. 4, pp. 1990-2028, 2020. [ https://doi.org/10.1137/20M1339842 ].
A. F. Vidal, V. De Bortoli, M. Pereyra, A. Durmus, "Maximum Likelihood Estimation of Regularization Parameters in High-Dimensional Inverse Problems: An Empirical Bayesian Approach Part I: Methodology and Experiments", SIAM Journal on Imaging Sciences, vol. 13, no. 4, pp. 1945-1989, 2020. [ https://doi.org/10.1137/20M1339829 ].
M. A. Price, X. Cai, J.D. McEwen, M. Pereyra, T. D. Kitching, "Sparse Bayesian massmapping with uncertainties: local credible intervals", Monthly Notices of the Royal Astronomical Society, vol. 492, no. 1, 2020, pp. 394’404 . [ https://doi.org/10.1093/mnras/stz3453 ].