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 [Inverse Problems 20 2000], 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.Comment: This is an author-created, un-copyedited version of an article
accepted for publication in [insert name of journal]. IOP Publishing Ltd is
not responsible for any errors or omissions in this version of the manuscript
or any version derived from it. The Version of Record is available online at
10.1088/0266-5611/28/9/09500