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We study an inverse problem associated with an eddy current model. We first address the ill-posedness of the inverse problem by proving the compactness of the forward map with respect to the conductivity and the non-uniqueness of the…
We propose a tomographic method to reconstruct the optical properties of a highly-scattering medium from incoherent acousto-optic measurements. The method is based on the solution to an inverse problem for the diffusion equation and makes…
We propose a method to reconstruct the electrical current density inside a conducting medium from acoustically-modulated boundary measurements of the electric potential. We show that the current can be uniquely reconstructed with Lipschitz…
The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…
Electrical Impedance Tomography (EIT) is a non-invasive imaging technique that reconstructs conductivity distributions within a body from boundary measurements. However, EIT reconstruction is hindered by its ill-posed nonlinear inverse…
We look at continuum solutions in optimisation problems associated to linear inverse problems $y = Ax$ with non-negativity constraint $x \geq 0$. We focus on the case where the noise model leads to maximum likelihood estimation through…
This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedance tomography (EIT), which is known to be a nonlinear and…
In this article, we propose a novel regularization method for a class of nonlinear inverse problems that is inspired by an application in quantitative magnetic resonance imaging (qMRI). The latter is a special instance of a general…
The goal in acousto-electric tomography (AET) is to reconstruct an image of the unknown electric conductivity in an object from exterior electrostatic currents and voltages that are measured on the boundary of the object while the object is…
The monotonicity-based approach has become one of the fundamental methods for reconstructing inclusions in the inverse problem of electrical impedance tomography. Thus far the method has not been proven to be able to handle extreme…
Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…
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…
We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art…
This paper concerns the reconstruction of an anisotropic conductivity tensor in an elliptic second-order equation from knowledge of the so-called power density functionals. This problem finds applications in several coupled-physics medical…
We consider Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity and potential in the body based on the measurement of the boundary voltages on the $m$ electrodes for a given electrode current. The…
Electrical impedance tomography (EIT) is a non-invasive imaging method in which an unknown physical body is probed with electric currents applied on the boundary, and the internal conductivity distribution is recovered from the measured…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
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 evaluation of a parameter-to-state map. We do so by rephrasing…
An efficient computational approach for optimal reconstruction of binary-type images suitable for models in various applications including biomedical imaging is developed and validated. The methodology includes derivative-free optimization…
This paper focuses on the acousto-electromagnetic tomography, a recently introduced hybrid imaging technique. In a previous work, the reconstruction of the electric permittivity of the medium from internal data was achieved under the Born…