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.

翻译：电阻抗断层成像（EIT）是一种利用被测物体表面电流密度/电压数据的无创医学成像模态。卡尔德隆方法是近期发展的一种EIT成像算法，具有非迭代、速度快、能重建复值电阻抗的特点。然而，由于通过低通滤波和线性化进行正则化，重建图像存在严重的模糊现象，且对精确电导率值的估计不足。本研究开发了卡尔德隆方法的增强版本，利用深度卷积神经网络（即U-net）作为有效的针对性后处理步骤，将所得方法称为深度卡尔德隆方法。具体而言，我们训练了一个U-net对卡尔德隆方法生成的EIT图像进行后处理，以提高分辨率并更精确地估计电导率值。我们模拟了胸部构型，据此生成电流密度/电压边界测量数据及对应的卡尔德隆重建图像。利用配对训练数据训练深度神经网络，并基于真实水箱测量数据评估其性能。实验结果表明，所提方法确实提供了一种快速、直接（复值）的电阻抗断层成像技术，显著提升了标准卡尔德隆方法的能力。