  Electrical impedance tomography (EIT) is a noninvasive medical imaging
modality utilizing the current-density/voltage data measured on the surface of
the subject. Calder\'on's method is a relatively recent EIT imaging algorithm
that is non-iterative, fast, and capable of reconstructing complex-valued
electric impedances. However, due to the regularization via low-pass filtering
and linearization, the reconstructed images suffer from severe blurring and
under-estimation of the exact conductivity values. In this work, we develop an
enhanced version of Calder\'on's method, using {deep} convolution neural
networks (i.e., U-net) {as an effective targeted post-processing step, and term
the resulting method by deep Calder\'{o}n's method.} Specifically, we learn a
U-net to postprocess the EIT images generated by Calder\'on's method so as to
have better resolutions and more accurate estimates of conductivity values. We
simulate chest configurations with which we generate the
current-density/voltage boundary measurements and the corresponding
reconstructed images by Calder\'on's method. With the paired training data, we
learn the deep neural network and evaluate its performance on real tank
measurement data. The experimental results indicate that the proposed approach
indeed provides a fast and direct (complex-valued) impedance tomography imaging
technique, and substantially improves the capability of the standard
Calder\'on's method.
