Related papers: Conductivity reconstruction from power density dat…
In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a…
We consider the problem of traffic density reconstruction using measurements from probe vehicles (PVs) with a low penetration rate. In other words, the number of sensors is small compared to the number of vehicles on the road. The model…
The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acoustic-optic data absorption distributions with bounded variation. The paper extends earlier results on smooth…
In this work we develop a novel approach using deep neural networks to reconstruct the conductivity distribution in elliptic problems from one measurement of the solution over the whole domain. The approach is based on a mixed reformulation…
This paper treats the inverse problem of retrieving the electrical conductivity of a material starting from boundary measurements in the framework of Electrical Resistance Tomography (ERT). In particular, the focus is on non-iterative…
Data scarcity is a fundamental barrier in Electrical Impedance Tomography (EIT), as undersampled Dirichlet-to-Neumann (DtN) measurements can substantially degrade conductivity reconstructions. We address this bottleneck by completing…
We derive an explicit method for reconstructing singularities of the initial data in a thermoacoustic tomography problem, in the case of variable sound speed and limited boundary data. In order to obtain this explicit formula we assume the…
Electrical impedance tomography aims at reconstructing the conductivity inside a physical body from boundary measurements of current and voltage at a finite number of contact electrodes. In many practical applications, the shape of the…
Measurements on a subset of the boundary are common in electrical impedance tomography, especially any electrode model can be interpreted as a partial boundary problem. The information obtained is different to full-boundary measurements as…
We present a comprehensive mathematical study of the Magneto-Telluric (MT) method, on bounded domain in $\mathbb{R}^3$. We show that electrical conductivity and magnetic permeability, assumed to be $C^2$, can be uniquely recovered from MT…
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…
A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the…
We provide a mathematical analysis and a numerical framework for magnetoacoustic tomography with magnetic induction. The imaging problem is to reconstruct the conductivity distribution of biological tissue from measurements of the Lorentz…
Electro-optic (EO) effects relate the change of optical constants by low-frequency electric fields. Thanks to the advent of Density Functional Perturbation Theory (DFPT), the EO properties of bulk three-dimensional (3D) materials can now be…
In this paper we propose a new joint model for the reconstruction of tomography data under limited angle sampling regimes. In many applications of Tomography, e.g. Electron Microscopy and Mammography, physical limitations on acquisition…
In a medium where the dielectric permittivity is perturbed in the presence of an acoustic wave, optical scattering generates frequency-shifted light. In this paper we consider the inverse problem of recovering the optical properties of this…
This short note modifies a reconstruction method by the author (Comm. PDE, 45(9):1118-1133, 2020), for reconstructing piecewise constant conductivities in the Calder\'on problem (electrical impedance tomography). In the former paper, a…
Magnetic resonance electrical property tomography is a recent medical imaging modality for visualizing the electrical tissue properties of the human body using radio-frequency magnetic fields. It uses the fact that in magnetic resonance…
The Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity tensor and potential in the body based on the measurement of the boundary voltages on the electrodes for a given electrode current is analyzed.…
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving…