论文标题
基于直接采样方法构建深神网络，以解决电阻抗
Construct Deep Neural Networks Based on Direct Sampling Methods for Solving Electrical Impedance Tomography
论文作者
论文摘要
这项工作研究了仅有限的边界测量值时，就研究了电阻抗断层扫描（EIT）问题，这是由于极端不良的性能而挑战的。基于直接采样方法（DSM），我们提出了深度直接采样方法（DDSM）来定位不均匀的包含物，其中构建了两种类型的深神经网络（DNN），以近似索引函数（功能性）：完全连接的神经网络（FNN）和卷积神经网络（CNN）。提出的DDSM易于实现，能够结合多个cauchy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的实施采用了离线在线分解，这有助于降低许多计算成本，并使DDSM与常规DSM一样有效。提出了数值实验以证明功效，并显示了将DNN与DSM相结合的潜在优势。
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.
