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We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
We present a study of the numerical solution of the two dimensional electrical impedance tomography problem, with noisy measurements of the Dirichlet to Neumann map. The inversion uses parametrizations of the conductivity on optimal grids.…
In tomographic reconstruction, the goal is to reconstruct an unknown object from a collection of line integrals. Given a complete sampling of such line integrals for various angles and directions, explicit inverse formulas exist to…
The aim of electrical impedance tomography is to form an image of the conductivity distribution inside an unknown body using electric boundary measurements. The computation of the image from measurement data is a non-linear ill-posed…
This work considers the inclusion detection problem of electrical impedance tomography with stochastic conductivities. It is shown that a conductivity anomaly with a random conductivity can be identified by applying the Factorization Method…
In this paper, we consider an inverse conductivity problem on a bounded domain $\Omega\subset\mathbb{R}^n$, $n\geq2$, also known as Electrical Impedance Tomography (EIT), for the case where unknown impenetrable obstacles are embedded into…
The objective of electrical impedance tomography (EIT) is to reconstruct the internal conductivity of a physical body based on current and voltage measurements at the boundary of the body. In many medical applications the exact shape of the…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
In this paper we investigate the problem of identifying conductivity in electrical impedance tomography from one boundary measurement. A variational method with total variation regularization is here proposed to tackle this problem. We…
This paper considers the non-linear inverse problem of reconstructing an electric conductivity distribution from the interior power density in a bounded domain. Applications include the novel tomographic method known as acousto-electric…
We focus on a geometrical inverse problem that involves recovering discontinuities in electrical conductivity based on boundary measurements. This problem serves as a model to introduce a shape recovery technique that merges the…
This paper proposes a novel approach to reconstruct changes in a target conductivity from electrical impedance tomography measurements. As in the conventional difference imaging, the reconstruction of the conductivity change is based on…
We treat an inverse electrical conductivity problem which deals with the reconstruction of nonlinear electrical conductivity starting from boundary measurements in steady currents operations. In this framework, a key role is played by the…
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…
This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…
We show how to eliminate the error caused by an incorrectly modeled boundary in electrical impedance tomography (EIT). In practical measurements, one usually lacks the exact knowledge of the boundary. Because of this the numerical…
Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…
We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction…
We propose a new numerical method to reconstruct the isotropic electrical conductivity from measured restricted Dirichlet-to-Neumann map data in electrical impedance tomography (EIT) model. "Restricted Dirichlet-to-Neumann (DtN) map data"…
This work considers using reduced basis techniques in connection to (smoothened) total variation regularization in electrical impedance tomography, but analogous ideas can also be used for other inverse elliptic boundary value problems. It…