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.

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