Learned Regularization for Microwave Tomography

TL;DR

This paper introduces a physics-informed hybrid framework called SSD-Reg that uses diffusion models as learned regularizers within a variational scheme to improve microwave tomography reconstructions, especially for complex structures.

Contribution

It proposes a novel Single-Step Diffusion Regularization (SSD-Reg) method that integrates diffusion priors into iterative reconstruction without requiring paired training data.

Findings

SSD-Reg improves reconstruction accuracy and robustness.

It effectively captures complex anatomical structures.

The method enhances stability in ill-posed inverse problems.

Abstract

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.