# A Direct Sampling-Based Deep Learning Approach for Inverse Medium Scattering Problems

arXiv: https://arxiv.org/abs/2305.00250 · HTML: https://mlsanity.com/paper/2305.00250/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 56 references that are in the map.
- First posted on arXiv 29 Apr 2023.

## Builds on (most cited first, 11 of 11)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Solving ill-posed inverse problems using iterative deep neural networks](https://mlsanity.com/paper/1704.04058/) (2017)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [Wavelet neural operator: a neural operator for parametric partial differential equations](https://mlsanity.com/paper/2205.02191/) (2022)
- [SwitchNet: a neural network model for forward and inverse scattering problems](https://mlsanity.com/paper/1810.09675/) (2018)
- [Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problems](https://mlsanity.com/paper/2212.03130/) (2022)
- [A Neural Network Warm-Start Approach for the Inverse Acoustic Obstacle Scattering Problem](https://mlsanity.com/paper/2212.08736/) (2022)

## Built on by (most cited first, 4 of 4)

- [Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches](https://mlsanity.com/paper/2310.18636/) (2023)
- [Physics-aware deep learning framework for the limited aperture inverse obstacle scattering problem](https://mlsanity.com/paper/2403.19470/) (2024)
- [The learned range test method for the inverse inclusion problem](https://mlsanity.com/paper/2411.00463/) (2024)
- [Instance-Wise Adaptive Sampling for Dataset Construction in Approximating Inverse Problem Solutions](https://mlsanity.com/paper/2509.04583/) (2025)

## Abstract (arXiv)

In this work, we focus on the inverse medium scattering problem (IMSP), which aims to recover unknown scatterers based on measured scattered data. Motivated by the efficient direct sampling method (DSM) introduced in [23], we propose a novel direct sampling-based deep learning approach (DSM-DL)for reconstructing inhomogeneous scatterers. In particular, we use the U-Net neural network to learn the relation between the index functions and the true contrasts. Our proposed DSM-DL is computationally efficient, robust to noise, easy to implement, and able to naturally incorporate multiple measured data to achieve high-quality reconstructions. Some representative tests are carried out with varying numbers of incident waves and different noise levels to evaluate the performance of the proposed method. The results demonstrate the promising benefits of combining deep learning techniques with the DSM for IMSP.