We reconstruct the contrast of overfilled cavities by presenting an improved two-step learning method, which incorporates multi-frequency scattering fields and attention mechanism. The dataset of scattering fields is built with different frequencies by using Petrov–Galerkin finite element interface method based on non-body-fitted meshes. Since the shapes of various cavities and the interfaces of inhomogeneous media can share the same generating meshes, this mesh reduction method can effectively decrease the cost of mesh generation. In the proposed two-step learning method, the first step augments the data from single-frequency scattering field to multi-frequency scattering fields by a U-shaped fully connected network, which has higher accuracy and fewer computation cost. Then, we set the second step for searching the relationship between the scattering field and the property of the overfilled cavity, where the corresponding network is constructed by encoder parts and decoder parts with convolutional modules. Moreover, for demonstrating the feasibility in different situations, overfilled inhomogeneous cavities with isotropic and anisotropic media are examined in numerical examples. In comparison experiments, the proposed method can not only achieve the frequency extrapolation, but also effectively reconstruct the image contrast. In addition, when adding noise with the ratio of noise equaling 40%, the proposed method still can relatively accurately reconstruct the permittivity, which proves the anti-noise capability.

中文翻译：

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通过将多频散射场和注意力机制纳入两步学习方法来重建满腔的对比度


我们通过提出一种改进的两步学习方法来重建过度填充的空腔的对比度，该方法结合了多频散射场和注意力机制。采用基于非贴体网格的Petrov-Galerkin有限元界面法建立了不同频率的散射场数据集。由于各种型腔的形状和非均匀介质的界面可以共享相同的生成网格，因此这种网格缩减方法可以有效降低网格生成成本。在所提出的两步学习方法中，第一步通过U形全连接网络将数据从单频散射场增强到多频散射场，具有更高的精度和更少的计算成本。然后，我们设置第二步来搜索散射场与满腔特性之间的关系，其中相应的网络由带有卷积模块的编码器部分和解码器部分构建。此外，为了证明不同情况下的可行性，在数值示例中研究了各向同性和各向异性介质的过度填充非均匀空腔。在对比实验中，该方法不仅可以实现频率外推，而且可以有效地重建图像对比度。此外，当添加噪声比例为40%的噪声时，该方法仍能较准确地重建介电常数，证明了其抗噪声能力。