Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks
Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks
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DOI：
10.1137/20m1383276
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发表时间：
2020-11
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通讯作者：
Matthew Li;L. Demanet;Leonardo Zepeda-N'unez
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作者：
Matthew Li;L. Demanet;Leonardo Zepeda-N'unez
我们引入了一种称为宽带蝴蝶网络（WideBNet）的端到端深度学习架构，用于根据宽带散射数据逼近逆散射图。该架构结合了计算调和分析（例如蝶形分解）和传统多尺度方法（例如 Cooley-Tukey FFT 算法）的工具，可大幅减少可训练参数的数量，以匹配问题的固有复杂性。因此，WideBNet 非常高效：它比现成的架构需要更少的训练点，并且具有稳定的训练动态，因此它可以依赖标准的权重初始化策略。该架构只需用户必须指定的几个超参数即可自动适应数据的维度。 WideBNet 能够生成与基于优化的方法相媲美的图像，但成本仅为其一小部分，而且我们还以数值方式证明了它能够在全孔径散射设置中学习超分辨散射体。
We introduce an end-to-end deep learning architecture called the wide-band butterfly network (WideBNet) for approximating the inverse scattering map from wide-band scattering data. This architecture incorporates tools from computational harmonic analysis, such as the butterfly factorization, and traditional multi-scale methods, such as the Cooley-Tukey FFT algorithm, to drastically reduce the number of trainable parameters to match the inherent complexity of the problem. As a result WideBNet is efficient: it requires fewer training points than off-the-shelf architectures, and has stable training dynamics, thus it can rely on standard weight initialization strategies. The architecture automatically adapts to the dimensions of the data with only a few hyper-parameters that the user must specify. WideBNet is able to produce images that are competitive with optimization-based approaches, but at a fraction of the cost, and we also demonstrate numerically that it learns to super-resolve scatterers in the full aperture scattering setup.