33 citations · 93 across the 15 of their papers we have counts for
23 papers
On the inverse problem of vibro-acoustography
Barbara Kaltenbacher
The aim of this paper is to put the problem of vibroacoustic imaging into the mathematical framework of inverse problems (more precisely, coefficient identification in PDEs) and re…
On an inverse problem of nonlinear imaging with fractional damping
Barbara Kaltenbacher, William Rundell
This paper considers the attenuated Westervelt equation in pressure formulation. The attenuation is by various models proposed in the literature and characterised by the inclusion…
On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements
Barbara Kaltenbacher, William Rundell
We consider an undetermined coefficient inverse problem for a non-\\linear partial differential equation occurring in high intensity ultrasound propagation as used in acoustic tomo…
On uniqueness and reconstruction of a nonlinear diffusion term in a parabolic equation
Barbara Kaltenbacher, William Rundell
The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time sca…
On the simultaneous recovery of the conductivity and the nonlinear reaction term in a parabolic equation
Barbara Kaltenbacher, William Rundell
This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity and the nonlinear reaction term in a reaction-diffusion equa…
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…