Related papers: Regularized Ensemble Kalman Methods for Inverse Pr…
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…
Many imaging problems require solving an inverse problem that is ill-conditioned or ill-posed. Imaging methods typically address this difficulty by regularising the estimation problem to make it well-posed. This often requires setting the…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Ensemble Kalman Inversion (EKI) methods are a family of iterative methods for solving weighted least-squares problems, especially those arising in scientific and engineering inverse problems in which unknown parameters or states are…
Data assimilation combines dynamical models with observations to improve state estimates. Ensemble filters sequentially assimilate observations by updating a set of samples over time, alternating between a forecast and an analysis step.…
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,…
We introduce a practical method for incorporating equality and inequality constraints in global optimization methods based on stochastic interacting particle systems, specifically consensus-based optimization (CBO) and ensemble Kalman…
The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an…
Many inverse problems can be described by a PDE model with unknown parameters that need to be calibrated based on measurements related to its solution. This can be seen as a constrained minimization problem where one wishes to minimize the…
We study an iterative regularization method of optimal control problems with control constraints. The regularization method is based on generalized Bregman distances. We provide convergence results under a combination of a source condition…
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 paper analyzes a popular computational framework to solve infinite-dimensional Bayesian inverse problems, discretizing the prior and the forward model in a finite-dimensional weighted inner product space. We demonstrate the benefit of…
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…
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…
Stochastic parameterizations are increasingly being used to represent the uncertainty associated with model errors in ensemble forecasting and data assimilation. One of the challenges associated with the use of these parameterizations is…
Bayesian uncertainty quantification (UQ) is of interest to industry and academia as it provides a framework for quantifying and reducing the uncertainty in computational models by incorporating available data. For systems with very high…
The Ensemble Kalman filter and Ensemble square root filters are data assimilation methods used to combine high dimensional nonlinear models with observed data. These methods have proved to be indispensable tools in science and engineering…
The iterative ensemble Kalman filter (IEnKF) is widely used in inverse problems to estimate system parameters from limited observations. However, the IEnKF, when applied to nonlinear systems, can be plagued by poor convergence. Here we…
In this paper, we extend the previous method for solving inverse problems for steady-state equations using the Generalized Collage Theorem by searching for an approximation that not only minimizes the collage error but also maximizes the…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…