相关论文: A Bayesian approach to inverse problems in spaces …

Inverse problems lend themselves naturally to a Bayesian formulation, in which the quantity of interest is a posterior distribution of state and/or parameters given some uncertain observations. For the common case in which the forward…

We deal with the solution of a generic linear inverse problem in the Hilbert space setting. The exact right hand side is unknown and only accessible through discretised measurements corrupted by white noise with unknown arbitrary…

Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…

This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering…

Inverse scattering problems have many important applications. In this paper, given limited aperture data, we propose a Bayesian method for the inverse acoustic scattering to reconstruct the shape of an obstacle. The inverse problem is…

We consider an acoustic obstacle reconstruction problem with Poisson data. Due to the stochastic nature of the data, we tackle this problem in the framework of Bayesian inversion. The unknown obstacle is parameterized in its angular form.…

In this work, the Bayesian approach to inverse problems is formulated in an all-at-once setting. The advantages of the all-at-once formulation are known to include the avoidance of a parameter-to-state map as well as numerical improvements,…

The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these…

Geoscientists often solve inverse problems to estimate values of parameters of interest given relevant data sets. Bayesian inference solves these problems by combining probability distributions that describe uncertainties in both…

We consider the statistical linear inverse problem of making inference on an unknown source function in an elliptic partial differential equation from noisy observations of its solution. We employ nonparametric Bayesian procedures based on…

In inverse problems, it is widely recognized that the incorporation of a sparsity prior yields a regularization effect on the solution. This approach is grounded on the a priori assumption that the unknown can be appropriately represented…

Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaussian noise. The measurement model for an unknown Gaussian…

In many inverse problems, the unknown is composed of multiple components with different regularities, for example, in imaging problems, where the unknown can have both rough and smooth features. We investigate linear Bayesian inverse…

We consider the efficient inference of finite dimensional parameters arising in the context of inverse problems. Our setup is the observation of a transformation of an unknown infinite dimensional signal $f$ corrupted by statistical noise,…

We consider the statistical inverse problem of estimating a background flow field (e.g., of air or water) from the partial and noisy observation of a passive scalar (e.g., the concentration of a solute), a common experimental approach to…

The article considers the nonlinear inverse problem of identifying the material parameters in viscoelastic structures based on a generalized Maxwell model. The aim is to reconstruct the model parameters from stress data acquired from a…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

The subject of this article is the introduction of a new concept of well-posedness of Bayesian inverse problems. The conventional concept of (Lipschitz, Hellinger) well-posedness in [Stuart 2010, Acta Numerica 19, pp. 451-559] is difficult…

A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…

We study Bayesian inference in statistical linear inverse problems with Gaussian noise and priors in Hilbert space. We focus our interest on the posterior contraction rate in the small noise limit. Existing results suffer from a certain…