Abstract:
Electrical Impedance Tomography (EIT) is a relatively new
medical imaging technique in which electrodes are placed on the surface of the body, current is applied
on the electrodes, the
resulting voltage is measured on the electrodes, and an image is
formed from the reconstructed conductivity distribution.
One application is the real-time imaging of heart and lung function.
In this case, data is collected
on electrodes placed around the circumference of the patient's torso,
and the 2-D inverse conductivity problem
is solved numerically to form a cross-sectional image of the patient's chest.
The D-bar reconstruction algorithm is based on the uniqueness proof by
Nachman [Ann. of Math. 143 (1996)] for the 2-D inverse
conductivity problem and uses the D-bar method of inverse scattering
to solve the full nonlinear inverse problem.
In this talk we will outline the D-bar method for EIT, explain our
numerical solutions to the equations therein, and present
reconstructions of simulated and experimental data.
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