Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks

• URL: http://arxiv.org/abs/2011.12413v2
• Date: Thu, 28 Oct 2021 22:07:09 GMT
• Title: Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks
• Authors: Matthew Li and Laurent Demanet and Leonardo Zepeda-N\'u\~nez
• Abstract summary: 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.
• Score: 1.2891210250935143
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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