Related papers: Multiresolution Approximation of a Bayesian Invers…

In this paper, we consider the problem of blind signal and image separation using a sparse representation of the images in the wavelet domain. We consider the problem in a Bayesian estimation framework using the fact that the distribution…

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…

We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…

We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors…

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 article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…

In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…

In this work, we contribute to the broader understanding of inverse problems by introducing a versatile multiscale modeling framework tailored to the challenges of sediment concentration estimation. Specifically, we propose a novel approach…

We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…

In petroleum well test analysis, deconvolution is used to obtain information about the reservoir system. This information is contained in the response function, which can be estimated by solving an inverse problem in the pressure and flow…

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or…

This work presents a model reduction approach to the inverse problem in the application of subsurface flows. For the Bayesian inverse problem, the forward model needs to be repeatedly computed for a large number of samples to get a…

In this work, we develop a Bayesian framework for solving inverse problems in which the unknown parameter belongs to a space of Radon measures taking values in a separable Hilbert space. The inherent ill-posedness of such problems is…

The Bayesian approach to solving inverse problems relies on the choice of a prior. This critical ingredient allows the formulation of expert knowledge or physical constraints in a probabilistic fashion and plays an important role for the…

Full waveform inversion is an ill-posed inverse problem whose solution non-uniqueness -- i.e., arising from band-limited, finite-aperture, noisy data -- calls for uncertainty quantification to avoid overconfident geological interpretations.…

Bathymetry reconstruction is an important problem in various fields, including oceanography and environmental monitoring. This paper presents a Bayesian inference approach to reconstructing bathymetries from point measurements of the water…

Inverse problems constrained by partial differential equations are often ill-conditioned due to noisy and incomplete data or inherent non-uniqueness. A prominent example is full waveform inversion, which estimates Earth's subsurface…

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…

The ability to image materials at the microscale from long-wavelength wave data is a major challenge to the geophysical, engineering and medical fields. Here, we present a framework to constrain microstructure geometry and properties from…

Bayesian inverse modeling is important for a better understanding of hydrological processes. However, this approach can be computationally demanding, as it usually requires a large number of model evaluations. To address this issue, one can…