# Accurate and Robust Deep Learning Framework for Solving Wave-Based Inverse Problems in the Super-Resolution Regime

arXiv: https://arxiv.org/abs/2106.01143 · HTML: https://mlsanity.com/paper/2106.01143/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 58 references that are in the map.
- First posted on arXiv 2 Jun 2021.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks](https://mlsanity.com/paper/1901.06523/) (2019)
- [SwitchNet: a neural network model for forward and inverse scattering problems](https://mlsanity.com/paper/1810.09675/) (2018)
- [Solving Inverse Wave Scattering with Deep Learning](https://mlsanity.com/paper/1911.13202/) (2019)
- [High Resolution 3D Ultrasonic Breast Imaging by Time-Domain Full Waveform Inversion](https://mlsanity.com/paper/2102.00755/) (2021)
- [Solving Traveltime Tomography with Deep Learning](https://mlsanity.com/paper/1911.11636/) (2019)
- [Wide-band butterfly network: stable and efficient inversion via multi-frequency neural networks](https://mlsanity.com/paper/2011.12413/) (2020)
- [Limited-angle tomographic reconstruction of dense layered objects by dynamical machine learning](https://mlsanity.com/paper/2007.10734/) (2020)
- [Butterfly-Net: Optimal Function Representation Based on Convolutional Neural Networks](https://mlsanity.com/paper/1805.07451/) (2018)
- [Butterfly-Net2: Simplified Butterfly-Net and Fourier Transform Initialization](https://mlsanity.com/paper/1912.04154/) (2019)

## Built on by (most cited first, 3 of 3)

- [Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach](https://mlsanity.com/paper/2506.03979/) (2025)
- [Reinforced Inverse Scattering](https://mlsanity.com/paper/2206.04186/) (2022)
- [A physically-informed Deep-Learning approach for locating sources in a waveguide](https://mlsanity.com/paper/2208.04938/) (2022)

## Abstract (arXiv)

We propose an end-to-end deep learning framework that comprehensively solves the inverse wave scattering problem across all length scales. Our framework consists of the newly introduced wide-band butterfly network coupled with a simple training procedure that dynamically injects noise during training. While our trained network provides competitive results in classical imaging regimes, most notably it also succeeds in the super-resolution regime where other comparable methods fail. This encompasses both (i) reconstruction of scatterers with sub-wavelength geometric features, and (ii) accurate imaging when two or more scatterers are separated by less than the classical diffraction limit. We demonstrate these properties are retained even in the presence of strong noise and extend to scatterers not previously seen in the training set. In addition, our network is straightforward to train requiring no restarts and has an online runtime that is an order of magnitude faster than optimization-based algorithms. We perform experiments with a variety of wave scattering mediums and we demonstrate that our proposed framework outperforms both classical inversion and competing network architectures that specialize in oscillatory wave scattering data.