Marcelo Pereyra | Heriot-Watt University

Marcelo Pereyra | Welcome

Maxwell Insitute for Mathematical Sciences
School of Mathematical and Computer Sciences, Heriot-Watt University

News

Conference I will chair the next IMA conference on Inverse Problems, which will take place in Edinburgh at the ICMS from 3 to 5 May 2022. Please see the conference webpage for more details.

New paper I am glad to report that the paper "Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks" with Matthew Holdan and Kostas Zygalakis has been accepted for publication in SIAM Journal on Imaging Sciences. Pre-print https://arxiv.org/abs/2103.10182.

Two new companion papers Following several years of intense work, Remi Laumont, Valentin De Bortoli, Julie Delon, Andres Almansa, Alain Durmus and I have produced these two companion papers on a Bayesian treatment of inference with "plug-and-play" priors, with special attention to foundational questions such as the existence and well-posedness of the models and key quantities of interest, as well as the convergence properties of plug-and-play stochastic algorithms:
1) 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.
2) R. Laumont, V. de Bortoli, A. Almansa, J. Delon, A. Durmus, and M. Pereyra, “On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descent”, 2021. Preprint https://hal.archives-ouvertes.fr/hal-03348735/.

EPSRC Project BLOOM I am delighted to report that the project BLOOM Bayesian computation for low-photon imaging with Dr Yoann Altmann and Kostas Zygalakis, funded by EPSRC UKRI, has started! This is a 4-year project to develop new computational imaging methodology for low-photon imaging problems, with special attention to quantum-enhanced approaches that seek to exploit the quantum nature of light in order to dramatically advance imaging sciences. In collaboration with the UK Quantum Enhanced Imaging Hub (QUANTIC), the University of Illinois, Ecole Normale Superieure Paris-Saclay, and the aerospace company Leonardo. More details here.

UKRI Project LEXCI Our UKRI EPSRC research grant proposal Learned Exascale Computational Imaging (LEXCI) with Prof. Jason McEwen, Prof. Marta Betcke, Rev. Dr Jeremy Yates, and Dr Jonas Latz has been successful! This is a 3-year project to develop novel highly parallelized and distributed hybrid algorithms that blend model-based and deep learning computational imaging approaches, with special attention to scalability, uncertainty quantification, and applications in radio astronomy. In collaboration with the Curtin Institute for Computation, University of Toronto, UC Davis, and Kagenova.

EPSRC Project BOLT I have started an exciting three-year project, funded by EPSRC, to develop new Bayesian methodology for blind and semi-blind bilinear inverse problems in imaging sciences, in collaboration with colleagues at Ecole Normale Superieure Cachan and at UCL Mullard Space Science Laboratory. The aim is to develop new computational and analysis methods for objectively comparing, selecting, and calibrating computational imaging models directly from the observed data in a fully unsupervised way. More details here.

Three new companion papers Following several years of intense work, Ana F. Vidal, Valentin De Bortoli, Alain Durmus and I have produced these three long companion papers on new computation methodology for empirical Bayesian estimation in high-dimentional inverse problems, with special attention to imaging applications:
1) 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.
2) 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.
3) V. De Bortoli, A. F. Vidal, A. Durmus, M. Pereyra, "Efficient stochastic optimisation by unadjusted Langevin Monte Carlo. Application to maximum marginal likelihood and empirical Bayesian estimation", Statistics and Computing, to appear. Pre-print https://arxiv.org/abs/1906.12281.