Regularization of the D-bar method for electrical impedance tomography
Samuli Siltanen

Abstract: In electrical impedance tomography (EIT) one applies electric voltages on the surface of an unknown conducting body and measures the resulting current distributions. The goal is to reconstruct the spatially varying conductivity distribution inside the body from the boundary measurements. This is a nonlinear and ill-posed inverse problem that has applications in geophysical sensing, medical imaging and nondestructive testing. In dimension two one can take the seminal uniqueness result of A. Nachman [Ann. of Math. 1996] as the starting point of a direct EIT reconstruction algorithm based on the solution of a D-bar equation. That approach has been shown to give useful images when applied to data measured from laboratory phantoms and from a living human subject. In this talk it is shown how the D-bar method can be regularized in the classical sense by truncating the scattering transform at a radius determined explicitly from measurement noise level.