The D-bar method for electrical impedance tomography—demystified
نویسندگان
چکیده
منابع مشابه
D-Bar Method for Electrical Impedance Tomography with Discontinuous Conductivities
The effects of truncating the (approximate) scattering transform in the D-bar reconstruction method for 2-D electrical impedance tomography are studied. The method is based on Nachman’s uniqueness proof [Ann. of Math. 143 (1996)] that applies to twice differentiable conductivities. However, the reconstruction algorithm has been successfully applied to experimental data, which can be characteriz...
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The importance of the solution of the boundary integral equation for the exponentially growing solutions to the Schrödinger equation arising from the 2-D inverse conductivity problems is demonstrated by a study of reconstructions of simple piecewise constant conductivities on a disk from two methods of approximating the scattering transform in the Dbar method and from Calderón’s linearization m...
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A practical D-bar algorithm for reconstructing conductivity changes from EIT data taken on electrodes in a 2D geometry is described. The algorithm is based on the global uniqueness proof of Nachman (1996 Ann. Math. 143 71-96) for the 2D inverse conductivity problem. Results are shown for reconstructions from data collected on electrodes placed around the circumference of a human chest to recons...
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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 re...
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The regularized D-bar method for electrical impedance tomography (EIT) 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 no...
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ژورنال
عنوان ژورنال: Inverse Problems
سال: 2020
ISSN: 0266-5611,1361-6420
DOI: 10.1088/1361-6420/aba2f5