  The mathematical problem for Electrical Impedance Tomography (EIT) is a
highly nonlinear ill-posed inverse problem requiring carefully designed
reconstruction procedures to ensure reliable image generation. D-bar methods
are based on a rigorous mathematical analysis and provide robust direct
reconstructions by using a low-pass filtering of the associated nonlinear
Fourier data. Similarly to low-pass filtering of linear Fourier data, only
using low frequencies in the image recovery process results in blurred images
lacking sharp features such as clear organ boundaries. Convolutional Neural
Networks provide a powerful framework for post-processing such convolved direct
reconstructions. In this study, we demonstrate that these CNN techniques lead
to sharp and reliable reconstructions even for the highly nonlinear inverse
problem of EIT. The network is trained on data sets of simulated examples and
then applied to experimental data without the need to perform an additional
transfer training. Results for absolute EIT images are presented using
experimental EIT data from the ACT4 and KIT4 EIT systems.
