33 citations · 303 across the 46 of their papers we have counts for
30 papers · 1 filter
Regularising the Cauchy problem for Laplace's equation by fractional operators
Barbara Kaltenbacher an William Rundell
In this paper we revisit the classical Cauchy problem for Laplace's equation as well as two further related problems in the light of regularisation of this highly ill-conditioned p…
Simultaneous reconstruction of sound speed and nonlinearity parameter in a paraxial model of vibro-acoustography in frequency domain
Barbara Kaltenbacher ans teresa Rauscher
In this paper we consider the inverse problem of vibro-acoustography, a technique for enhancing ultrasound imaging by making use of nonlinear effects. It amounts to determining two…
Nonlinearity parameter imaging in the frequency domain
Barbara Kaltenbacher, William Rundell
Nonlinearity parameter tomography leads to the problem of identifying a coefficient in a nonlinear wave equation (such as the Westervelt equation) modeling ultrasound propagation.…
On the simultanenous identification of the nonlinearity coefficient and the sound speed in the Westervelt equation
Barbara Kaltenbacher, William Rundell
This paper considers the Westervelt equation, one of the most widely used models in nonlinear acoustics, and seeks to recover two spatially-dependent parameters of physical importa…
Convergence guarantees for coefficient reconstruction in PDEs from boundary measurements by variational and Newton type methods via range invariance
Barbara Kaltenbacher
A key observation underlying this paper is the fact that the range invariance condition for convergence of regularization methods for nonlinear ill-posed operator equations -- such…
Discretization of parameter identification in PDEs using Neural Networks
Barbara Kaltenbacher, Tram Thi Ngoc Nguyen
We consider the ill-posed inverse problem of identifying a nonlinearity in a time-dependent PDE model. The nonlinearity is approximated by a neural network, and needs to be determi…
Determining the nonlinearity in an acoustic wave equation
Barbara Kaltenbacher, William Rundell
We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high intensity ultrasound propagation as widely used in medical ima…
Fractional time stepping and adjoint based gradient computation in an inverse problem for a fractionally damped wave equation
Barbara Kaltenbacher, Anna Schlintl
In this paper we consider the inverse problem of identifying the initial data in a fractionally damped wave equation from time trace measurements on a surface, as relevant in photo…
All-at-once formulation meets the Bayesian approach: A study of two prototypical linear inverse problems
Anna Schlintl, Barbara Kaltenbacher
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…
Iterative regularization for constrained minimization formulations of nonlinear inverse problems
Barbara Kaltenbacher, Kha Van Huynh
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analys…
On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations
J. Baumeister, B. Kaltenbacher, A. Leitao
In this article a modified Levenberg-Marquardt method coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations is invest…
Some application examples of minimization based formulations of inverse problems and their regularization
Kha Van Huynh, Barbara Kaltenbacher
In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluat…
The Inverse Problem of Reconstructing Reaction-Diffusion Systems
Barbara Kaltenbacher, William Rundell
This paper considers the inverse problem of recovering state-dependent source terms in a reaction-diffusion system from overposed data consisting of the values of the state variabl…
All-at-once versus reduced iterative methods for time dependent inverse problems
Barbara Kaltenbacher
In this paper we investigate all-at-once versus reduced regularization of dynamic inverse problems on finite time intervals . In doing so, we concentrate on iterative method…
Regularization of a backwards parabolic equation by fractional operators
Barbara Kaltenbacher, William Rundell
The backwards diffusion equation is one of the classical ill-posed inverse problems, related to a wide range of applications, and has been extensively studied over the last 50 year…
The Ivanov regularized Gauss-Newton method in Banach space with an a posteriori choice of the regularization radius
Barbara Kaltenbacher, Andrej Klassen, Mario Luiz Previatti de Souza
In this paper we consider the iteratively regularized Gauss-Newton method, where regularization is achieved by Ivanov regularization, i.e., by imposing a priori constraints on the…
Recovery of multiple coefficients in a reaction-diffusion equation
Barbara Kaltenbacher, William Rundell
This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity and the potential in a parabolic equation from overposed dat…
On the identification of a nonlinear term in a reaction-diffusion equation
Barbara Kaltenbacher, William Rundell
Reaction-diffusion equations are one of the most common partial differential equations used to model physical phenomenon. They arise as the combination of two physical processes: a…
Regularization of ill-posed problems with non-negative solutions
Christian Clason, Barbara Kaltenbacher, Elena Resmerita
This survey reviews variational and iterative methods for reconstructing non-negative solutions of ill-posed problems in infinite-dimensional spaces. We focus on two classes of met…
On convergence and convergence rates for Ivanov and Morozov regularization and application to some parameter identification problems in elliptic PDEs
Barbara Kaltenbacher, Andrej Klassen
In this paper we provide a convergence analysis of some variational methods alternative to the classical Tikhonov regularization, namely Ivanov regularization (also called method o…
Convergence and adaptive discretization of the IRGNM Tikhonov and the IRGNM Ivanov method under a tangential cone condition in Banach space
Barbara Kaltenbacher, Mario Luiz Previatti de Souza
In this paper we consider the Iteratively Regularized Gauss-Newton Method (IRGNM) in its classical Tikhonov version and in an Ivanov type version, where regularization is achieved…
Regularization based on all-at-once formulations for inverse problems
Barbara Kaltenbacher
Parameter identification problems typically consist of a model equation, e.g. a (system of) ordinary or partial differential equation(s), and the observation equation. In the conve…
Computing quasisolutions of nonlinear inverse problems via efficient minimization of trust region problems
Barbara Kaltenbacher, Franz Rendl, Elena Resmerita
In this paper we present a method for the regularized solution of nonlinear inverse problems, based on Ivanov regularization (also called method of quasi solutions or constrained l…
Functional error estimators for the adaptive discretization of inverse problems
Christian Clason, Barbara Kaltenbacher, Daniel Wachsmuth
So-called functional error estimators provide a valuable tool for reliably estimating the discretization error for a sum of two convex functions. We apply this concept to Tikhonov…