105 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
Nonlinear Inversion from Partial EIT Data: Computational Experiments
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 boundary voltage data. The reconstruction task is a nonlinear and
ill-posed inverse problem, whose solution calls for special regularized
algorithms, such as D-bar methods which are based on complex geometrical optics
solutions (CGOs). In many applications of EIT, such as monitoring the heart and
lungs of unconscious intensive care patients or locating the focus of an
epileptic seizure, data acquisition on the entire boundary of the body is
impractical, restricting the boundary area available for EIT measurements. An
extension of the D-bar method to the case when data is collected only on a
subset of the boundary is studied by computational simulation. The approach is
based on solving a boundary integral equation for the traces of the CGOs using
localized basis functions (Haar wavelets). The numerical evidence suggests that
the D-bar method can be applied to partial-boundary data in dimension two and
that the traces of the partial data CGOs approximate the full data CGO
solutions on the available portion of the boundary, for the necessary small
frequencies.Comment: 24 pages, 12 figure
A Data-Driven Edge-Preserving D-bar Method for Electrical Impedance Tomography
In Electrical Impedance Tomography (EIT), the internal conductivity of a body
is recovered via current and voltage measurements taken at its surface. The
reconstruction task is a highly ill-posed nonlinear inverse problem, which is
very sensitive to noise, and requires the use of regularized solution methods,
of which D-bar is the only proven method. The resulting EIT images have low
spatial resolution due to smoothing caused by low-pass filtered regularization.
In many applications, such as medical imaging, it is known \emph{a priori} that
the target contains sharp features such as organ boundaries, as well as
approximate ranges for realistic conductivity values. In this paper, we use
this information in a new edge-preserving EIT algorithm, based on the original
D-bar method coupled with a deblurring flow stopped at a minimal data
discrepancy. The method makes heavy use of a novel data fidelity term based on
the so-called {\em CGO sinogram}. This nonlinear data step provides superior
robustness over traditional EIT data formats such as current-to-voltage
matrices or Dirichlet-to-Neumann operators, for commonly used current patterns.Comment: 24 pages, 11 figure
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