Related papers: Inhomogeneous Priors for Bayesian Inverse Problems

The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…

In Bayesian inverse problems, it is common to consider several hyperparameters that define the prior and the noise model that must be estimated from the data. In particular, we are interested in linear inverse problems with additive…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

Inverse problems, which are related to Maxwell's equations, in the presence of nonlinear materials is a quite new topic in the literature. The lack of contributions in this area can be ascribed to the significant challenges that such…

This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and…

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties,…

The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…

We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…

Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…

We propose a new learning-based approach to solve ill-posed inverse problems in imaging. We address the case where ground truth training samples are rare and the problem is severely ill-posed - both because of the underlying physics and…

We present a new technique, based on semivariogram methodology, for obtaining point estimates for use in prior modeling for solving Bayesian inverse problems. This method requires a connection between Gaussian processes with covariance…

This paper proposes a class of asymmetric priors to perform Bayesian wavelet shrinkage in the standard nonparametric regression model with Gaussian error. The priors are composed by mixtures of a point mass function at zero and one of the…

It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…

We present Bayesian techniques for solving inverse problems which involve mean-square convergent random approximations of the forward map. Noisy approximations of the forward map arise in several fields, such as multiscale problems and…

Generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals using a single fixed complexity or dimensionality. This can be limiting: depending on the problem, a…

Bayesian inference with deep generative prior has received considerable interest for solving imaging inverse problems in many scientific and engineering fields. The selection of the prior distribution is learned from, and therefore an…

We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by differential equations. We construct physics-informed…

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…