# SOM-Net: Unrolling the Subspace-based Optimization for Solving Full-wave Inverse Scattering Problems

arXiv: https://arxiv.org/abs/2209.03567 · HTML: https://mlsanity.com/paper/2209.03567/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2022.

## Built on by (most cited first, 12 of 12)

- [Physics-Driven Neural Network for Solving Electromagnetic Inverse Scattering Problems](https://mlsanity.com/paper/2507.16321/) (2025)
- [Deep Injective Prior for Inverse Scattering](https://mlsanity.com/paper/2301.03092/) (2023)
- [Multi-frequency Neural Born Iterative Method for Solving 2-D Inverse Scattering Problems](https://mlsanity.com/paper/2409.01315/) (2024)
- [Improved Physics-Driven Neural Network to Solve Inverse Scattering Problems](https://mlsanity.com/paper/2512.09333/) (2025)
- [Fast Physics-Driven Untrained Network for Highly Nonlinear Inverse Scattering Problems](https://mlsanity.com/paper/2602.13805/) (2026)
- [VBIM-Net: Variational Born Iterative Network for Inverse Scattering Problems](https://mlsanity.com/paper/2405.18731/) (2024)
- [A Differentiable Framework for Full and Phaseless Data Inversion Using Neural Implicit Contrast-Source Representation](https://mlsanity.com/paper/2508.10555/) (2025)
- [A Physics-Informed Hierarchical Neural Network for Microwave Scattering Analysis of 3D PEC Targets](https://mlsanity.com/paper/2508.03774/) (2025)
- [Contrast-Source-Based Physics-Driven Neural Network for Inverse Scattering Problems](https://mlsanity.com/paper/2601.19243/) (2026)
- [ScoreField: Neural Inverse Scattering with Score-Based Generative Priors](https://mlsanity.com/paper/2608.02937/) (2026)
- [Coordinate-Residual Physics-Driven Neural Network for Inverse Scattering Imaging](https://mlsanity.com/paper/2608.09382/) (2026)
- [Structured Multi-Level-Set Inversion for 3-D Electromagnetic Inverse Scattering](https://mlsanity.com/paper/2609.08594/) (2026)

## Abstract (arXiv)

In this paper, an unrolling algorithm of the iterative subspace-based optimization method (SOM) is proposed for solving full-wave inverse scattering problems (ISPs). The unrolling network, named SOM-Net, inherently embeds the Lippmann- Schwinger physical model into the design of network structures. The SOM-Net takes the deterministic induced current and the raw permittivity image obtained from back-propagation (BP) as the input. It then updates the induced current and the permittivity successively in sub-network blocks of the SOM- Net by imitating iterations of the SOM. The final output of the SOM-Net is the full predicted induced current, from which the scattered field and the permittivity image can also be deduced analytically. The parameters of the SOM-Net are optimized in a supervised manner with the total loss to simultaneously ensure the consistency of the induced current, the scattered field, and the permittivity in the governing equations. Numerical tests on both synthetic and experimental data verify the superior performance of the proposed SOM-Net over typical ones. The results on challenging examples like scatterers with tough profiles or high permittivity demonstrate the good generalization ability of the SOM-Net. With the use of deep unrolling technology, this work builds a bridge between traditional iterative methods and deep learning methods for solving ISPs.