Related papers: Bayesian model selection for unsupervised image de…

Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…

In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…

Gaussian graphical models have been used to study intrinsic dependence among several variables, but the Gaussianity assumption may be restrictive in many applications. A nonparanormal graphical model is a semiparametric generalization for…

We solve the inverse problem of deblurring a pixelized image of Jupiter using regularized deconvolution and by sample-based Bayesian inference. By efficiently sampling the marginal posterior distribution for hyperparameters, then the full…

Gaussian graphical models, where it is assumed that the variables of interest jointly follow a multivariate normal distribution with a sparse precision matrix, have been used to study intrinsic dependence among variables, but the normality…

Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of the posterior…

We present a novel, general-purpose method for deconvolving and denoising images from gridded radio interferometric visibilities using Bayesian inference based on a Gaussian process model. The method automatically takes into account…

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…

We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…

We investigated the use of the Bayesian inference to restore noise-degraded images under conditions of spatially correlated noise. The generative statistical models used for the original image and the noise were assumed to obey…

We investigate an empirical Bayesian nonparametric approach to a family of linear inverse problems with Gaussian prior and Gaussian noise. We consider a class of Gaussian prior probability measures with covariance operator indexed by a…

A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone…

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

We develop a generative model-based approach to Bayesian inverse problems, such as image reconstruction from noisy and incomplete images. Our framework addresses two common challenges of Bayesian reconstructions: 1) It makes use of complex,…

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…

Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is…

The statistical inverse problem of estimating the probability distribution of an infinite-dimensional unknown given its noisy indirect observation is studied in the Bayesian framework. In practice, one often considers only…

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…