  The Regularized D-bar method for Electrical Impedance Tomography 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
novel approach that combines the rigor of the D-bar approach with the
edge-preserving nature of Total Variation regularization is presented. The
method also includes a data-driven contrast adjustment technique guided by the
key functions (CGO solutions) of the D-bar method. The new TV-Enhanced D-bar
Method produces reconstructions with sharper edges and improved contrast while
still solving the full nonlinear problem. This is achieved by using the
TV-induced edges to increase the truncation radius of the scattering data in
the nonlinear frequency domain thereby increasing the radius of the low pass
filter. The algorithm is tested on numerically simulated noisy EIT data and
demonstrates significant improvements in edge preservation and contrast which
can be highly valuable for absolute EIT imaging.
