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

TL;DR

The paper presents WideBNet, a deep learning architecture that efficiently and stably approximates inverse scattering maps from wide-band data, leveraging harmonic analysis tools for superior performance and super-resolution capabilities.

Contribution

Introduction of WideBNet, a novel neural network architecture combining harmonic analysis and multi-scale methods for stable, efficient inverse scattering reconstruction.

Findings

Requires fewer training points than standard architectures

Achieves stable training with standard initialization

Capable of super-resolving scatterers in scattering problems

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.