This work investigates the electrical impedance tomography (EIT) problem when only limited boundary measurements are available, which is known to be challenging due to the extreme ill-posedness. Based on the direct sampling method (DSM), we propose deep direct sampling methods (DDSMs) to locate inhomogeneous inclusions in which two types of deep neural networks (DNNs) are constructed to approximate the index function(functional): fully connected neural network(FNN) and convolutional neural network (CNN). The proposed DDSMs are easy to be implemented, capable of incorporating multiple Cauchy data pairs to achieve high-quality reconstruction and highly robust with respect to large noise. Additionally, the implementation of DDSMs adopts offline-online decomposition, which helps to reduce a lot of computational costs and makes DDSMs as efficient as the conventional DSM. The numerical experiments are presented to demonstrate the efficacy and show the potential benefits of combining DNN with DSM.

中文翻译：

---

基于直接采样方法构建深度神经网络解决电阻抗断层扫描

这项工作研究了当只有有限的边界测量可用时的电阻抗断层扫描 (EIT) 问题，众所周知，由于极端不适定性而具有挑战性。我们在直接采样方法 (DSM) 的基础上，提出了深度直接采样方法 (DDSM) 来定位非均匀包裹体，其中构建了两种类型的深度神经网络 (DNN) 来逼近索引函数（函数式）： 全连接神经网络（ FNN）和卷积神经网络（CNN）。所提出的 DDSM 易于实现，能够合并多个柯西数据对以实现高质量的重建，并且对于大噪声具有高度的鲁棒性。此外，DDSMs 的实现采用离线-在线分解，这有助于减少大量计算成本，并使 DDSM 与传统 DSM 一样高效。数值实验用于证明功效并展示将 DNN 与 DSM 相结合的潜在好处。