Related papers: Inhomogeneous Priors for Bayesian Inverse Problems

While diffusion priors generate high-quality posterior samples across many inverse problems, they are often trained on limited training sets or purely simulated data, thus inheriting the errors and biases of these underlying sources.…

Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree…

The availability of data from multiple heterogeneous environments has motivated methods that remain reliable under distributional shifts. When the joint distribution of response and predictors varies across environments, the response may…

To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have…

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

Datasets in engineering applications are often limited and contaminated, mainly due to unavoidable measurement noise and signal distortion. Thus, using conventional data-driven approaches to build a reliable discriminative model, and…

In this article, we investigate the problem of estimating a spatially inhomogeneous function and its derivatives in the white noise model using Besov-Laplace priors. We show that smoothness-matching priors attains minimax optimal posterior…

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…

This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…

In a fissile material, the inherent multiplicity of neutrons born through induced fissions leads to correlations in their detection statistics. The correlations between neutrons can be used to trace back some characteristics of the fissile…

In recent years, the transformer has established itself as a workhorse in many applications ranging from natural language processing to reinforcement learning. Similarly, Bayesian deep learning has become the gold-standard for uncertainty…

We consider solving ill-posed imaging inverse problems without access to an image prior or ground-truth examples. An overarching challenge in these inverse problems is that an infinite number of images, including many that are implausible,…

We consider a class of inverse problems characterized by forward operators that are partially specified, non-smooth, and non-differentiable. Although generative inverse solvers have made significant progress, we find that these forward…

We consider the problem of constructing Bayesian based confidence sets for linear functionals in the inverse Gaussian white noise model. We work with a scale of Gaussian priors indexed by a regularity hyper-parameter and apply the…

The structure of the nonlinear inverse problem arising from capillarity-driven imbibition in porous media is investigated, considering a degenerate parabolic PDE with compactly supported diffusivity and boundary-driven fluxes as the…

When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…

Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…

The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…

The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…

Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of…