Deep D-Bar: Real-Time Electrical Impedance Tomography Imaging With Deep Neural Networks

The mathematical problem for electrical impedance tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features, such as clear organ boundaries. Convolutional neural networks provide a powerful framework for post-processing such convolved direct reconstructions. In this paper, we demonstrate that these CNN techniques lead to sharp and reliable reconstructions even for the highly nonlinear inverse problem of EIT. The network is trained on data sets of simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems

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

Comparing D-Bar and Common Regularization-Based Methods for Electrical Impedance Tomography

Objective: To compare D-bar difference reconstruction with regularized linear reconstruction in electrical impedance tomography. Approach: A standard regularized linear approach using a Laplacian penalty and the GREIT method for comparison to the D-bar difference images. Simulated data was generated using a circular phantom with small objects, as well as a \u27Pac-Man\u27 shaped conductivity target. An L-curve method was used for parameter selection in both D-bar and the regularized methods. Main results: We found that the D-bar method had a more position independent point spread function, was less sensitive to errors in electrode position and behaved differently with respect to additive noise than the regularized methods. Significance: The results allow a novel pathway between traditional and D-bar algorithm comparison

A Direct D-Bar Method for Partial Boundary Data Electrical Impedance Tomography With a Priori Information

Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that uses surface electrical measurements to determine the internal conductivity of a body. The mathematical formulation of the EIT problem is a nonlinear and severely ill-posed inverse problem for which direct D-bar methods have proved useful in providing noise-robust conductivity reconstructions. Recent advances in D-bar methods allow for conductivity reconstructions using EIT measurement data from only part of the domain (e.g., a patient lying on their back could be imaged using only data gathered on the accessible part of the body). However, D-bar reconstructions suffer from a loss of sharp edges due to a nonlinear low-pass filtering of the measured data, and this problem becomes especially marked in the case of partial boundary data. Including a priori data directly into the D-bar solution method greatly enhances the spatial resolution, allowing for detection of underlying pathologies or defects, even with no assumption of their presence in the prior. This work combines partial data D-bar with a priori data, allowing for noise-robust conductivity reconstructions with greatly improved spatial resolution. The method is demonstrated to be effective on noisy simulated EIT measurement data simulating both medical and industrial imaging scenarios

EIT Imaging of Admittivities with a D-Bar Method and Spatial Prior: Experimental Results for Absolute and Difference Imaging

Electrical impedance tomography (EIT) is an emerging imaging modality that uses harmless electrical measurements taken on electrodes at a body\u27s surface to recover information about the internal electrical conductivity and or permittivity. The image reconstruction task of EIT is a highly nonlinear inverse problem that is sensitive to noise and modeling errors making the image reconstruction task challenging. D-bar methods solve the nonlinear problem directly, bypassing the need for detailed and time-intensive forward models, to provide absolute (static) as well as time-difference EIT images. Coupling the D-bar methodology with the inclusion of high confidence a priori data results in a noise-robust regularized image reconstruction method. In this work, the a priori D-bar method for complex admittivities is demonstrated effective on experimental tank data for absolute imaging for the first time. Additionally, the method is adjusted for, and tested on, time-difference imaging scenarios. The ability of the method to be used for conductivity, permittivity, absolute as well as time-difference imaging provides the user with great flexibility without a high computational cost

Vulnerability and the Erosion of Seismic Culture in Mountainous Central Asia

Vulnerability to earthquake disasters in mountainous regions frequently escapes investigation and analysis. The tragic and costly earthquake disasters that have recently occurred in Central Asia have spurred important questions among local, regional, and international policymakers, scientists, and social activists regarding the root causes of earthquake vulnerability. Drawing on an analysis of recent earthquake disasters in Kyrgyzstan, Tajikistan, Afghanistan, and Pakistan, this article explores the concept of “seismic culture” (Degg and Homan 2005) in relation to vulnerability. Specifically, it argues that diminishing levels of indigenous hazard knowledge, demographic shifts, gendered livelihood transformations, and the lack of public access to science- based earthquake information have contributed to overall low levels of seismic cultures of prevention in the region. A major finding of the study points to the particular role of women in helping to redress the erosion of seismic culture, thereby bolstering local resilience, earthquake preparedness, and disaster risk reduction

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 novel weighting method for satellite magnetic data and a new global magnetic field model

A new data weighting scheme is introduced for satellite geomagnetic survey data. Data weights for individual satellite samples at 20-s spacing are derived from two ‘noise’ (or unmodelled signal) estimators for the sample. First, the standard deviation along the 20 s of satellite track, centred on each sample, is computed as a measure of local magnetic activity. Second a larger-scale noise estimator is defined in terms of a ‘local area vector activity’ (LAVA) index for the sample. This is derived from activity measured at the geographically nearest magnetic observatories to the sample point. Weighting of the satellite data by the inverse-sum-of-squares of these noise estimators then leads to a robust model of the field, the ‘Model of Earth’s Magnetic Environment 2008’, or MEME08, to about spherical harmonic degree 60. Our approach allows vector samples of the field to be used at all magnetic latitudes and, for example, results in a lithospheric magnetic field model with low spectral noise, comparable with other recent global models. We also do not require a particularly complex model parametrization, regularization, or prior data correction to remove estimates of unmodelled source fields

C4: The New Hampshire Spherulitic Rhyolites: Rocks of Importance to Prehistoric Native Americans

Guidebook for field trips in Western Maine and Northern New Hampshire: New England Intercollegiate Geological Conference, p. 305-316