1,181 research outputs found
Reconstructing conductivities with boundary corrected D-bar method
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 inverse problem and calls for a special regularized
algorithm. One such algorithm, the so-called D-bar method, is improved in this
work by introducing new computational steps that remove the so far necessary
requirement that the conductivity should be constant near the boundary. The
numerical experiments presented suggest two conclusions. First, for most
conductivities arising in medical imaging, it seems the previous approach of
using a best possible constant near the boundary is sufficient. Second, for
conductivities that have high contrast features at the boundary, the new
approach produces reconstructions with smaller quantitative error and with
better visual quality
An Analysis of Finite Element Approximation in Electrical Impedance Tomography
We present a finite element analysis of electrical impedance tomography for
reconstructing the conductivity distribution from electrode voltage
measurements by means of Tikhonov regularization. Two popular choices of the
penalty term, i.e., -norm smoothness penalty and total variation
seminorm penalty, are considered. A piecewise linear finite element method is
employed for discretizing the forward model, i.e., the complete electrode
model, the conductivity, and the penalty functional. The convergence of the
finite element approximations for the Tikhonov model on both polyhedral and
smooth curved domains is established. This provides rigorous justifications for
the ad hoc discretization procedures in the literature.Comment: 20 page
Frequency dependence on image reconstruction for a buried conductor
[[abstract]]The frequency dependence of image reconstruction for a buried imperfectly conducting cylinder is investigated. A conducting cylinder of unknown shape and conductivity is buried in one half-space and scatters the incident wave from another half-space. By using the measured scattered field, the image problem is reformulated into an optimization problem and solved by the genetic algorithm. The frequency dependence of image reconstruction is investigated and numerical results show that the reconstruction is quite good in the resonant frequency range. On the contrary, if the frequency is too high or too low the reconstruction becomes bad. It is worth noting that the present work provides not only comparative information but quantitative information[[conferencetype]]ĺś‹éš›[[conferencedate]]20010521~20010523[[iscallforpapers]]Y[[conferencelocation]]Budapest, Hungar
Invisibility and Inverse Problems
This survey of recent developments in cloaking and transformation optics is
an expanded version of the lecture by Gunther Uhlmann at the 2008 Annual
Meeting of the American Mathematical Society.Comment: 68 pages, 12 figures. To appear in the Bulletin of the AM
Electromagnetic scattering by impedance structures
The scattering of electromagnetic waves from impedance structures is investigated, and current work on antenna pattern calculation is presented. A general algorithm for determining radiation patterns from antennas mounted near or on polygonal plates is presented. These plates are assumed to be of a material which satisfies the Leontovich (or surface impedance) boundary condition. Calculated patterns including reflection and diffraction terms are presented for numerious geometries, and refinements are included for antennas mounted directly on impedance surfaces. For the case of a monopole mounted on a surface impedance ground plane, computed patterns are compared with experimental measurements. This work in antenna pattern prediction forms the basis of understanding of the complex scattering mechanisms from impedance surfaces. It provides the foundation for the analysis of backscattering patterns which, in general, are more problematic than calculation of antenna patterns. Further proposed study of related topics, including surface waves, corner diffractions, and multiple diffractions, is outlined
Simultaneous reconstruction of outer boundary shape and admittivity distribution in electrical impedance tomography
The aim of electrical impedance tomography is to reconstruct the admittivity
distribution inside a physical body from boundary measurements of current and
voltage. Due to the severe ill-posedness of the underlying inverse problem, the
functionality of impedance tomography relies heavily on accurate modelling of
the measurement geometry. In particular, almost all reconstruction algorithms
require the precise shape of the imaged body as an input. In this work, the
need for prior geometric information is relaxed by introducing a Newton-type
output least squares algorithm that reconstructs the admittivity distribution
and the object shape simultaneously. The method is built in the framework of
the complete electrode model and it is based on the Fr\'echet derivative of the
corresponding current-to-voltage map with respect to the object boundary shape.
The functionality of the technique is demonstrated via numerical experiments
with simulated measurement data.Comment: 3 figure
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