19 research outputs found
Direct EIT Reconstructions of Complex Admittivities on a Chest-Shaped Domain in 2-D
Electrical impedance tomography (EIT) is a medical imaging technique in which current is applied on electrodes on the surface of the body, the resulting voltage is measured, and an inverse problem is solved to recover the conductivity and/or permittivity in the interior. Images are then formed from the reconstructed conductivity and permittivity distributions. In the 2-D geometry, EIT is clinically useful for chest imaging. In this work, an implementation of a D-bar method for complex admittivities on a general 2-D domain is presented. In particular, reconstructions are computed on a chest-shaped domain for several realistic phantoms including a simulated pneumothorax, hyperinflation, and pleural effusion. The method demonstrates robustness in the presence of noise. Reconstructions from trigonometric and pairwise current injection patterns are included
Incorporating a Spatial Prior into Nonlinear D-Bar EIT imaging for Complex Admittivities
Electrical Impedance Tomography (EIT) aims to recover the internal
conductivity and permittivity distributions of a body from electrical
measurements taken on electrodes on the surface of the body. The reconstruction
task is a severely ill-posed nonlinear inverse problem that is highly sensitive
to measurement noise and modeling errors. Regularized D-bar methods have shown
great promise in producing noise-robust algorithms by employing a low-pass
filtering of nonlinear (nonphysical) Fourier transform data specific to the EIT
problem. Including prior data with the approximate locations of major organ
boundaries in the scattering transform provides a means of extending the radius
of the low-pass filter to include higher frequency components in the
reconstruction, in particular, features that are known with high confidence.
This information is additionally included in the system of D-bar equations with
an independent regularization parameter from that of the extended scattering
transform. In this paper, this approach is used in the 2-D D-bar method for
admittivity (conductivity as well as permittivity) EIT imaging. Noise-robust
reconstructions are presented for simulated EIT data on chest-shaped phantoms
with a simulated pneumothorax and pleural effusion. No assumption of the
pathology is used in the construction of the prior, yet the method still
produces significant enhancements of the underlying pathology (pneumothorax or
pleural effusion) even in the presence of strong noise.Comment: 18 pages, 10 figure
Robust Computation in 2D Absolute EIT (A-EIT) Using D-Bar Methods with the “EXP” Approximation
Objective
Absolute images have important applications in medical Electrical Impedance Tomography (EIT) imaging, but the traditional minimization and statistical based computations are very sensitive to modeling errors and noise. In this paper, it is demonstrated that D-bar reconstruction methods for absolute EIT are robust to such errors. Approach
The effects of errors in domain shape and electrode placement on absolute images computed with 2-D D-bar reconstruction algorithms are studied on experimental data. Main Results
It is demonstrated with tank data from several EIT systems that these methods are quite robust to such modeling errors, and furthermore the artefacts arising from such modeling errors are similar to those occurring in classic time-difference EIT imaging. Significance
This study is promising for clinical applications where absolute EIT images are desirable, but previously thought impossible
A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D
A direct reconstruction algorithm for complex conductivities in
, where is a bounded, simply connected Lipschitz
domain in , is presented. The framework is based on the
uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating
the Dirichlet-to-Neumann to the scattering transform and the exponentially
growing solutions are not present in that work, and are derived here. The
algorithm constitutes the first D-bar method for the reconstruction of
conductivities and permittivities in two dimensions. Reconstructions of
numerically simulated chest phantoms with discontinuities at the organ
boundaries are included.Comment: This is an author-created, un-copyedited version of an article
accepted for publication in [insert name of journal]. IOP Publishing Ltd is
not responsible for any errors or omissions in this version of the manuscript
or any version derived from it. The Version of Record is available online at
10.1088/0266-5611/28/9/09500
Direct D-bar reconstruction algorithm for complex admittivities in W2,∞(Ω) for the 2-D EIT problem, A
2012 Summer.Includes bibliographical references.Electrical Impedance Tomography (EIT) is a fairly new, portable, relatively inexpensive, imaging system that requires no ionizing radiation. Electrodes are placed at the surface of a body and low frequency, low amplitude current is applied on the electrodes, and the resulting voltage value on each electrode is measured. By applying a basis of current patterns, one can obtain sufficient information to recover the complex admittivity distribution of the region in the plane of the electrodes. In 2000, Elisa Francini presented a nearly constructive proof that was the first approach using D-bar methods to solve the full nonlinear problem for twice-differentiable conductivities and permittivities. In this thesis the necessary formulas to turn her proof into a direct D-bar reconstruction algorithm that solves the full nonlinear admittivity problem in 2-D are described. Reconstructions for simulated Finite Element data for circular and non-circular domains are presented
Computational advancements in the D-bar reconstruction method for 2-D electrical impedance tomography
2016 Spring.Includes bibliographical references.We study the problem of reconstructing 2-D conductivities from boundary voltage and current density measurements, also known as the electrical impedance tomography (EIT) problem, using the D-bar inversion method, based on the 1996 global uniqueness proof by Adrian Nachman. We focus on the computational implementation and efficiency of the D-bar algorithm, its application to finite-precision practical data in human thoracic imaging, and the quality and spatial resolution of the resulting reconstructions. The main contributions of this work are (1) a parallelized computational implementation of the algorithm which has been shown to run in real-time, thus demonstrating the feasibility of the D-bar method for use in real-time bedside imaging, and (2) a modification of the algorithm to include \emph{a priori} data in the form of approximate organ boundaries and (optionally) conductivity estimates, which we show to be effective in improving spatial resolution in the resulting reconstructions. These computational advancements are tested using both numerically simulated data as well as experimental human and tank data collected using the ACE1 EIT machine at CSU. In this work, we provide details regarding the theoretical background and practical implementation for each advancement, we demonstrate the effectiveness of the algorithm modifications through multiple experiments, and we provide discussion and conclusions based on the results
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 Hybrid Segmentation and D-bar Method for Electrical Impedance Tomography
The Regularized D-bar method for Electrical Impedance Tomography provides a
rigorous mathematical approach for solving the full nonlinear inverse problem
directly, i.e. without iterations. It is based on a low-pass filtering in the
(nonlinear) frequency domain. However, the resulting D-bar reconstructions are
inherently smoothed leading to a loss of edge distinction. In this paper, a
novel approach that combines the rigor of the D-bar approach with the
edge-preserving nature of Total Variation regularization is presented. The
method also includes a data-driven contrast adjustment technique guided by the
key functions (CGO solutions) of the D-bar method. The new TV-Enhanced D-bar
Method produces reconstructions with sharper edges and improved contrast while
still solving the full nonlinear problem. This is achieved by using the
TV-induced edges to increase the truncation radius of the scattering data in
the nonlinear frequency domain thereby increasing the radius of the low pass
filter. The algorithm is tested on numerically simulated noisy EIT data and
demonstrates significant improvements in edge preservation and contrast which
can be highly valuable for absolute EIT imaging