Related papers: On convergence rates of adaptive ensemble Kalman i…

The ensemble Kalman filter is a well-known and celebrated data assimilation algorithm. It is of particular relevance as it used for high-dimensional problems, by updating an ensemble of particles through a sample mean and covariance…

Ensemble Kalman inversion (EKI) is a technique for the numerical solution of inverse problems. A great advantage of the EKI's ensemble approach is that derivatives are not required in its implementation. But theoretically speaking, EKI's…

This manuscript derives locally weighted ensemble Kalman methods from the point of view of ensemble-based function approximation. This is done by using pointwise evaluations to build up a local linear or quadratic approximation of a…

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…

We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…

This paper is focused on the optimization approach to the solution of inverse problems. We introduce a stochastic dynamical system in which the parameter-to-data map is embedded, with the goal of employing techniques from nonlinear Kalman…

We present a regularization method to approach a solution of the pessimistic formulation of ill -posed bilevel problems . This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and…

In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…

The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in…

In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class…

This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…

This work is concerned with linear inverse problems where a distributed parameter is known a priori to only take on values from a given discrete set. This property can be promoted in Tikhonov regularization with the aid of a suitable convex…

We investigate a level-set type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable…

This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant components. To solve such problems we consider regularizers consisting of two terms that must be…

This work unifies the analysis of various randomized methods for solving linear and nonlinear inverse problems by framing the problem in a stochastic optimization setting. By doing so, we show that many randomized methods are variants of a…

Conditional stability estimates are a popular tool for the regularization of ill-posed problems. A drawback in particular under nonlinear operators is that additional regularization is needed for obtaining stable approximate solutions if…

Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the ensemble Kalman filter to reconstruct an elastic rigid…

State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…

Many parameter estimation problems arising in applications are best cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates.…

Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here…