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.

翻译：我们引入了一种端到端深学习结构,称为宽带蝴蝶网络(WideBNet),以近似宽带散射数据的反散射图。这个结构包含来自计算和谐分析的工具,如蝴蝶因子化,以及传统的多尺度方法,如Cooley-Tukey FFFFT算法,以大幅降低可训练参数的数量,以适应问题的内在复杂性。结果,广域网是有效的:它需要的训练点比现成结构少,并且具有稳定的训练动态,因此它可以依赖标准的重量初始化战略。这个结构自动适应数据的尺寸,只有用户必须指定的几个超参数。广域网能够产生具有优化方法竞争力的图像,但成本的一小部分,我们还从数字上表明它在全孔散射装置中学习超级溶散射器。