Related papers: Reconstructing conductivities with boundary correc…
We develop a linearized boundary control method for the inverse boundary value problem of determining the damping coefficient in the damped wave equation. The objective is to reconstruct an unknown perturbation in a known background damping…
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…
The aim of this research is to reconstruct the 3D X-ray refractive index gradient maps by the proposed vector Radon transform and its inverse, assuming that the small-angle deviation condition is met. Theoretical analyses show that the…
Electrical Impedance Imaging would suffer a serious obstruction if for two different conductivities the potential and current measured at the boundary were the same. The Calder\'on's problem is to decide whether the conductivity is indeed…
This report extends our recent progress in tackling a challenging 3D inverse scattering problem governed by the Helmholtz equation. Our target application is to reconstruct dielectric constants, electric conductivities and shapes of front…
Electrical capacitance tomography (ECT) has been investigated in many fields due to its advantages of being non-invasive and low cost. Sparse algorithms with l1-norm regularization are used to reduce the smoothing effect and obtain sharp…
The article suggests a new approach what is called a consistency method for the inversion of the spherical Radon transform in 2D with detectors on a line. It is known that there is not an exact inversion formula in 2D. By means of the…
Non-destructive X-ray imaging of thruster parts and assemblies down to the scale of several micrometers is a key technology for electric propulsion research and engineering. It allows for thorough product assurance, rapid state acquisition…
A direct three dimensional EIT reconstruction algorithm based on complex geometrical optics solutions and a nonlinear scattering transform is presented and implemented for spherically symmetric conductivity distributions. The scattering…
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…
Hybrid imaging techniques utilize couplings of physical modalities -- they are called hybrid, because, typically, the excitation and measurement quantities belong to different modalities. Recently there has been an enormous research…
This paper introduces a new approach for solving electrical impedance tomography (EIT) problems using deep neural networks. The mathematical problem of EIT is to invert the electrical conductivity from the Dirichlet-to-Neumann (DtN) map.…
Computational image reconstruction algorithms generally produce a single image without any measure of uncertainty or confidence. Regularized Maximum Likelihood (RML) and feed-forward deep learning approaches for inverse problems typically…
We treat the inverse problem of determining material losses, such as cavities, in a conducting body, by performing electrostatic measurements at the boundary. We develop a numerical approach, based on variational methods, to reconstruct the…
We develop a boundary integral equation-based numerical method to solve for the electrostatic potential in two dimensions, inside a medium with piecewise constant conductivity, where the boundary condition is given by the complete electrode…
This paper presents an improved technique for solving the inverse problem in magnetic induction tomography (MIT) by considering skin and proximity effects in coils. MIT is a non-contact, noninvasive, and low-cost imaging modality for…
Electrical impedance tomography (EIT) plays a crucial role in non-invasive imaging, with both medical and industrial applications. In this paper, we present three data-driven reconstruction methods for EIT imaging. These three approaches…
Electrical impedance tomography (EIT) uses current-voltage measurements on the surface of an imaging subject to detect conductivity changes or anomalies. EIT is a promising new technique with great potential in medical imaging and…
Objective: The strengths of Electrical Impedance Tomography (EIT) are its capability of imaging the internal body by using a noninvasive, radiation safe technique, and the absence of known hazards. In this paper we introduce a novel idea of…
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…