153 citations · 545 across the 29 of their papers we have counts for
33 papers
Accelerated Bayesian imaging by relaxed proximal-point Langevin sampling
Teresa Klatzer, Paul Dobson, Yoann Altmann +3
This paper presents a new accelerated proximal Markov chain Monte Carlo methodology to perform Bayesian inference in imaging inverse problems with an underlying convex geometry. Th…
Proximal nested sampling with data-driven priors for physical scientists
Jason D. McEwen, Tobías I. Liaudat, Matthew A. Price +2
Proximal nested sampling was introduced recently to open up Bayesian model selection for high-dimensional problems such as computational imaging. The framework is suitable for mode…
Efficient Bayesian computation for low-photon imaging problems
Savvas Melidonis, Paul Dobson, Yoann Altmann +2
This paper studies a new and highly efficient Markov chain Monte Carlo (MCMC) methodology to perform Bayesian inference in low-photon imaging problems, with particular attention to…
The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distribution
Marcelo Pereyra, Luis A. Vargas-Mieles, Konstantinos C. Zygalakis
Developing efficient Bayesian computation algorithms for imaging inverse problems is challenging due to the dimensionality involved and because Bayesian imaging models are often no…
Learned reconstruction methods with convergence guarantees
Subhadip Mukherjee, Andreas Hauptmann, Ozan Öktem +2
In recent years, deep learning has achieved remarkable empirical success for image reconstruction. This has catalyzed an ongoing quest for precise characterization of correctness a…
On Maximum-a-Posteriori estimation with Plug & Play priors and stochastic gradient descent
Rémi Laumont, Valentin de Bortoli, Andrés Almansa +3
Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the…
Proximal nested sampling for high-dimensional Bayesian model selection
Xiaohao Cai, Jason D. McEwen, Marcelo Pereyra
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model…
Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithms
Matthew Holden, Marcelo Pereyra, Konstantinos C. Zygalakis
This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. Following t…
Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie
Rémi Laumont, Valentin de Bortoli, Andrés Almansa +3
Since the seminal work of Venkatakrishnan et al. in 2013, Plug & Play (PnP) methods have become ubiquitous in Bayesian imaging. These methods derive Minimum Mean Square Error (MMSE…
Bayesian model selection for unsupervised image deconvolution with structured Gaussian priors
Benjamin Harroué, Jean-François Giovannelli, Marcelo Pereyra
This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a su…
Maximum likelihood estimation of regularisation parameters in high-dimensional inverse problems: an empirical Bayesian approach. Part II: Theoretical Analysis
Valentin De Bortoli, Alain Durmus, Ana F. Vidal +1
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization pa…
Wasserstein Control of Mirror Langevin Monte Carlo
Kelvin Shuangjian Zhang, Gabriel Peyré, Jalal Fadili +1
Discretized Langevin diffusions are efficient Monte Carlo methods for sampling from high dimensional target densities that are log-Lipschitz-smooth and (strongly) log-concave. In p…
Maximum likelihood estimation of regularisation parameters in high-dimensional inverse problems: an empirical Bayesian approach. Part I: Methodology and Experiments
Ana F. Vidal, Valentin De Bortoli, Marcelo Pereyra +1
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation prob…
Accelerating proximal Markov chain Monte Carlo by using an explicit stabilised method
Luis Vargas, Marcelo Pereyra, Konstantinos C. Zygalakis
We present a highly efficient proximal Markov chain Monte Carlo methodology to perform Bayesian computation in imaging problems. Similarly to previous proximal Monte Carlo approach…
Efficient stochastic optimisation by unadjusted Langevin Monte Carlo. Application to maximum marginal likelihood and empirical Bayesian estimation
Valentin De Bortoli, Alain Durmus, Marcelo Pereyra +1
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in p…
Sparse Bayesian mass-mapping with uncertainties: local credible intervals
Matthew A. Price, Xiaohao Cai, Jason D. McEwen +2
Until recently mass-mapping techniques for weak gravitational lensing convergence reconstruction have lacked a principled statistical framework upon which to quantify reconstructio…
Quantifying Uncertainty in High Dimensional Inverse Problems by Convex Optimisation
Xiaohao Cai, Marcelo Pereyra, Jason D. McEwen
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their soluti…
Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimization
Audrey Repetti, Marcelo Pereyra, Yves Wiaux
We propose a Bayesian uncertainty quantification method for large-scale imaging inverse problems. Our method applies to all Bayesian models that are log-concave, where maximum-a-po…
Uncertainty quantification for radio interferometric imaging: II. MAP estimation
Xiaohao Cai, Marcelo Pereyra, Jason D. McEwen
Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry…
Uncertainty quantification for radio interferometric imaging: I. proximal MCMC methods
Xiaohao Cai, Marcelo Pereyra, Jason D. McEwen
Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry…
Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo
Nicolas Brosse, Alain Durmus, Éric Moulines +1
This paper presents a detailed theoretical analysis of the Langevin Monte Carlo sampling algorithm recently introduced in Durmus et al. (Efficient Bayesian computation by proximal…
Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau
Alain Durmus, Eric Moulines, Marcelo Pereyra
Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex opti…
Revisiting maximum-a-posteriori estimation in log-concave models
Marcelo Pereyra
Maximum-a-posteriori (MAP) estimation is the main Bayesian estimation methodology in imaging sciences, where high dimensionality is often addressed by using Bayesian models that ar…
Maximum-a-posteriori estimation with Bayesian confidence regions
Marcelo Pereyra
Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very ch…