# Deep Injective Prior for Inverse Scattering

arXiv: https://arxiv.org/abs/2301.03092 · HTML: https://mlsanity.com/paper/2301.03092/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 85 references that are in the map.
- First posted on arXiv 8 Jan 2023.

## Builds on (most cited first, 30 of 40)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Deep Probabilistic Imaging: Uncertainty Quantification and Multi-modal Solution Characterization for Computational Imaging](https://mlsanity.com/paper/2010.14462/) (2020)
- [Composing Normalizing Flows for Inverse Problems](https://mlsanity.com/paper/2002.11743/) (2020)
- [Image-Adaptive GAN based Reconstruction](https://mlsanity.com/paper/1906.05284/) (2019)
- [Trumpets: Injective Flows for Inference and Inverse Problems](https://mlsanity.com/paper/2102.10461/) (2021)
- [SwitchNet: a neural network model for forward and inverse scattering problems](https://mlsanity.com/paper/1810.09675/) (2018)
- [DeepNIS: Deep Neural Network for Nonlinear Electromagnetic Inverse Scattering](https://mlsanity.com/paper/1810.03990/) (2018)
- [Solving Inverse Problems with a Flow-based Noise Model](https://mlsanity.com/paper/2003.08089/) (2020)
- [Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flows](https://mlsanity.com/paper/2106.05275/) (2021)
- [Prior Image-Constrained Reconstruction using Style-Based Generative Models](https://mlsanity.com/paper/2102.12525/) (2021)
- [Universal Joint Approximation of Manifolds and Densities by Simple Injective Flows](https://mlsanity.com/paper/2110.04227/) (2021)

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

- [Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Models](https://mlsanity.com/paper/2408.02866/) (2024)
- [LoFi: Neural Local Fields for Scalable Image Reconstruction](https://mlsanity.com/paper/2411.04995/) (2024)
- [Plug-and-Play Latent Diffusion for Electromagnetic Inverse Scattering with Application to Brain Imaging](https://mlsanity.com/paper/2509.04860/) (2025)

## Abstract (arXiv)

In electromagnetic inverse scattering, the goal is to reconstruct object permittivity using scattered waves. While deep learning has shown promise as an alternative to iterative solvers, it is primarily used in supervised frameworks which are sensitive to distribution drift of the scattered fields, common in practice. Moreover, these methods typically provide a single estimate of the permittivity pattern, which may be inadequate or misleading due to noise and the ill-posedness of the problem. In this paper, we propose a data-driven framework for inverse scattering based on deep generative models. Our approach learns a low-dimensional manifold as a regularizer for recovering target permittivities. Unlike supervised methods that necessitate both scattered fields and target permittivities, our method only requires the target permittivities for training; it can then be used with any experimental setup. We also introduce a Bayesian framework for approximating the posterior distribution of the target permittivity, enabling multiple estimates and uncertainty quantification. Extensive experiments with synthetic and experimental data demonstrate that our framework outperforms traditional iterative solvers, particularly for strong scatterers, while achieving comparable reconstruction quality to state-of-the-art supervised learning methods like the U-Net.