Learned Regularization for Microwave Tomography

Microwave Tomography (MWT) aims to reconstruct the spatial distribution of dielectric properties from measured scattered electromagnetic fields. This electromagnetic inverse scattering 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 numerical and experimental results in MWT demonstrate that SSD-Reg, implemented in a Plug-and-Play (PnP) fashion, provides a flexible and effective strategy for mitigating the ill-posedness of nonlinear inverse scattering problems.