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 underestimation of the exact conductivity values. In this work, we develop an enhanced version of Calder\'on's method, using convolution neural networks (i.e., U-net) via a postprocessing step. 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 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：电阻抗层析成像（EIT）是一种利用被测物体表面电流密度/电压数据的非侵入式医学成像技术。卡尔德隆方法作为较新的EIT成像算法，具有非迭代、快速且能重构复值电阻抗的优点。然而，由于采用低通滤波的正则化处理与线性化策略，其重构图像存在严重模糊与电导率低估的问题。本研究通过卷积神经网络（即U-net）后处理步骤，开发了卡尔德隆方法的增强版本。具体而言，我们训练U-net对卡尔德隆方法生成的EIT图像进行后处理，以提升图像分辨率并获得更精确的电导率估计值。通过模拟胸部结构生成边界电流密度/电压测量数据及对应重构图像，利用配对训练数据学习神经网络，并在真实水箱测量数据上评估其性能。实验结果表明，所提方法确实提供了快速直接的（复值）电阻抗成像技术，并显著提升了标准卡尔德隆方法的成像能力。