论文标题
SOM网络：展开基于子空间的优化，以求解全波反散射问题
SOM-Net: Unrolling the Subspace-based Optimization for Solving Full-wave Inverse Scattering Problems
论文作者
论文摘要
在本文中，提出了基于迭代子空间的优化方法（SOM）的展开算法，以解决全波逆散射问题（ISP）。名为SOM-NET的展开网络固有地将Lippmann-Schwinger物理模型嵌入到网络结构的设计中。 SOM网络将确定性诱导的电流和从后传播（BP）获得的原始介电常数作为输入。然后，它通过模仿SOM的迭代，在SOM的子网络块中依次更新引起的电流和介电常数。 SOM-NET的最终输出是完整的预测电流，也可以通过分析推导散射场和介电效率图像。 SOM-NET的参数以监督方式优化，总损失同时确保诱导电流，散射场和管理方程中的介电性的一致性。对合成数据和实验数据的数值测试验证了所提出的SOM-NET的出色性能。诸如具有强硬概况或高介电常数的散射器之类的具有挑战性的例子的结果证明了SOM-NET的良好概括能力。通过使用深层展开的技术，这项工作建立了传统迭代方法与解决ISP的深度学习方法之间的桥梁。
In this paper, an unrolling algorithm of the iterative subspace-based optimization method (SOM) is proposed for solving full-wave inverse scattering problems (ISPs). The unrolling network, named SOM-Net, inherently embeds the Lippmann- Schwinger physical model into the design of network structures. The SOM-Net takes the deterministic induced current and the raw permittivity image obtained from back-propagation (BP) as the input. It then updates the induced current and the permittivity successively in sub-network blocks of the SOM- Net by imitating iterations of the SOM. The final output of the SOM-Net is the full predicted induced current, from which the scattered field and the permittivity image can also be deduced analytically. The parameters of the SOM-Net are optimized in a supervised manner with the total loss to simultaneously ensure the consistency of the induced current, the scattered field, and the permittivity in the governing equations. Numerical tests on both synthetic and experimental data verify the superior performance of the proposed SOM-Net over typical ones. The results on challenging examples like scatterers with tough profiles or high permittivity demonstrate the good generalization ability of the SOM-Net. With the use of deep unrolling technology, this work builds a bridge between traditional iterative methods and deep learning methods for solving ISPs.
