Construct Deep Neural Networks Based on Direct Sampling Methods for Solving Electrical Impedance Tomography
Construct Deep Neural Networks Based on Direct Sampling Methods for Solving Electrical Impedance Tomography
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DOI：
10.1137/20m1367350
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发表时间：
2020-09
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影响因子：
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通讯作者：
Ruchi Guo;Jiahua Jiang
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文献类型：
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作者：
Ruchi Guo;Jiahua Jiang
本文研究了电阻抗断层成像（EIT）问题时，只有有限的边界测量，这是已知的是具有挑战性的，由于极端不适定性。在直接采样方法（DSM）的基础上，我们提出了深度直接采样方法（DDSMs）来定位非均匀夹杂物，其中构造了两种类型的深度神经网络（DNN）来逼近指标函数（泛函）：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和相对于大噪声的高度鲁棒性。此外，DDSM的实现采用离线-在线分解，这有助于减少大量的计算成本，使DDSM的效率与传统的DSM。数值实验证明了DNN与DSM相结合的有效性和潜在的好处。
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.