Sampling type method combined with deep learning for inverse scattering with one incident wave
Sampling type method combined with deep learning for inverse scattering with one incident wave
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DOI：
10.48550/arxiv.2207.10011
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发表时间：
2022-07
期刊：
影响因子：
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通讯作者：
Thu Le;Dinh-Liem Nguyen;V. Nguyen;TrungDung Truong
中科院分区：
文献类型：
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作者：
Thu Le;Dinh-Liem Nguyen;V. Nguyen;TrungDung Truong
我们考虑的逆问题确定的几何形状的可穿透的物体从散射数据所产生的一个入射波在一个固定的频率。我们首先研究了一种正交采样类型的方法，该方法快速，易于实现，并且对数据中的噪声具有鲁棒性。该采样方法具有新的成像函数，适用于近场或远场测量数据。成像泛函的分辨率分析进行了分析，其中明确的衰变率的功能建立。本文还研究了与Potthast正交抽样法的关系。然后将采样方法与深度神经网络相结合来解决逆散射问题。这种组合方法可以被理解为一种网络，它使用通过第一层的采样方法计算的图像，然后是其余层的U-net架构。快速计算和来自采样方法的结果的知识有助于加快网络的训练。该组合导致在最初通过采样方法获得的重建结果中的显著改善。该组合方法还能够反演一些有限孔径的实验数据，而无需任何额外的传输训练。
We consider the inverse problem of determining the geometry of penetrable objects from scattering data generated by one incident wave at a fixed frequency. We first study an orthogonality sampling type method which is fast, simple to implement, and robust against noise in the data. This sampling method has a new imaging functional that is applicable to data measured in near field or far field regions. The resolution analysis of the imaging functional is analyzed where the explicit decay rate of the functional is established. A connection with the orthogonality sampling method by Potthast is also studied. The sampling method is then combined with a deep neural network to solve the inverse scattering problem. This combined method can be understood as a network using the image computed by the sampling method for the first layer and followed by the U-net architecture for the rest of the layers. The fast computation and the knowledge from the results of the sampling method help speed up the training of the network. The combination leads to a significant improvement in the reconstruction results initially obtained by the sampling method. The combined method is also able to invert some limited aperture experimental data without any additional transfer training.