Format of Original
A direct reconstruction algorithm for complex conductivities in W2, ∞(Ω), where Ω is a bounded, simply connected Lipschitz domain in R2 , is presented. The framework is based on the uniqueness proof by Francini (2000 Inverse Problems 6 107–19), 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.
Hamilton, Sarah J.; Herrera, C. N. L.; Mueller, J. L.; and Von Herrmann, A., "A Direct D-bar Reconstruction Algorithm for Recovering a Complex Conductivity in 2D" (2012). Mathematics, Statistics and Computer Science Faculty Research and Publications. 468.