# Learned Regularization for Microwave Tomography

arXiv: https://arxiv.org/abs/2508.08114 · HTML: https://mlsanity.com/paper/2508.08114/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- Builds on 15 of its 47 references that are in the map.
- First posted on arXiv 11 Aug 2025.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Builds on (most cited first, 15 of 15)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [A Variational Perspective on Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2305.04391/) (2023)
- [Adaptive Diffusion Priors for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.05876/) (2022)
- [DMPlug: A Plug-in Method for Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2405.16749/) (2024)
- [PET image denoising based on denoising diffusion probabilistic models](https://mlsanity.com/paper/2209.06167/) (2022)
- [Diffusion Probabilistic Priors for Zero-Shot Low-Dose CT Image Denoising](https://mlsanity.com/paper/2305.15887/) (2023)
- [Imaging Interiors: An Implicit Solution to Electromagnetic Inverse Scattering Problems](https://mlsanity.com/paper/2407.09352/) (2024)
- [SEAGLE: Sparsity-Driven Image Reconstruction under Multiple Scattering](https://mlsanity.com/paper/1705.04281/) (2017)
- [Cross-correlated Contrast Source Inversion](https://mlsanity.com/paper/1906.10864/) (2019)
- [Diff-INR: Generative Regularization for Electrical Impedance Tomography](https://mlsanity.com/paper/2409.04494/) (2024)

## Abstract (arXiv)

Microwave Tomography (MWT) aims to reconstruct the dielectric properties of tissues from measured scattered electromagnetic fields. This inverse problem is highly nonlinear and ill-posed, posing significant challenges for conventional optimization-based methods, which, despite being grounded in physical models, often fail to recover fine structural details. Recent deep learning strategies, including end-to-end and post-processing networks, have improved reconstruction quality but typically require large paired training datasets and may struggle to generalize. To overcome these limitations, we propose a physics-informed hybrid framework that integrates diffusion models as learned regularization within a data-consistency-driven variational scheme. Specifically, we introduce Single-Step Diffusion Regularization (SSD-Reg), a novel approach that embeds diffusion priors into the iterative reconstruction process, enabling the recovery of complex anatomical structures without the need for paired data. SSD-Reg maintains fidelity to both the governing physics and learned structural distributions, improving accuracy, stability, and robustness. Extensive experiments demonstrate that SSD-Reg, implemented as a Plug-and-Play (PnP) module, provides a flexible and effective solution for tackling the ill-posedness inherent in functional image reconstruction.