Related papers: Solving High-dimensional Inverse Problems Using Am…

When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated…

We address functional uncertainty quantification for ill-posed inverse problems where it is possible to evaluate a possibly rank-deficient forward model, the observation noise distribution is known, and there are known parameter…

In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…

Many statistical problems include model parameters that are defined as the solutions to optimization sub-problems. These include classical approaches such as profile likelihood as well as modern applications involving flow networks or…

In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…

The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

The fate of scientific hypotheses often relies on the ability of a computational model to explain the data, quantified in modern statistical approaches by the likelihood function. The log-likelihood is the key element for parameter…

In Bayesian inverse problems, one aims at characterizing the posterior distribution of a set of unknowns, given indirect measurements. For non-linear/non-Gaussian problems, analytic solutions are seldom available: Sequential Monte Carlo…

We propose a new probabilistic method for unsupervised recovery of corrupted data. Given a large ensemble of degraded samples, our method recovers accurate posteriors of clean values, allowing the exploration of the manifold of possible…

We address the numerical solution of infinite-dimensional inverse problems in the framework of Bayesian inference. In the Part I companion to this paper (arXiv.org:1308.1313), we considered the linearized infinite-dimensional inverse…

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 common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…

Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…

Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

Recovering a signal from its degraded measurements is a long standing challenge in science and engineering. Recently, zero-shot diffusion based methods have been proposed for such inverse problems, offering a posterior sampling based…

Existing score-based methods for inverse problems often resort to approximate minimization of the KL divergence between the inversion distribution and the Bayesian posterior. Such an approximation leads to severe mode collapse and…

In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…

In many applications, Bayesian inverse problems can give rise to probability distributions which contain complexities due to the Hessian varying greatly across parameter space. This complexity often manifests itself as lower dimensional…