Wide-Band Butterfly Network: Stable and Efficient Inversion Via Multi-Frequency Neural Networks
Name
20m1383276.pdf
Description
Published version
Size
15.42 MB
Format
Adobe PDF
Checksum (MD5)
5cd762f4e947de984eefa25fbec24105
Author(s)
Li, Matthew
Demanet, Laurent
Zepeda-Núñez, Leonardo
Date Issued
December 31, 2022
Journal
Multiscale Modeling & Simulation
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Li, Matthew, Demanet, Laurent and Zepeda-Núñez, Leonardo. 2022. "Wide-Band Butterfly Network: Stable and Efficient Inversion Via Multi-Frequency Neural Networks." Multiscale Modeling & Simulation, 20 (4).
Version
Final published version
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 which are compatible with 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 with a full aperture configuration.
MIT Department
Massachusetts Institute of Technology. Center for Computational Science and Engineering
Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology. Earth Resources Laboratory
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/20M1383276
