Posterior Sampling with Latent Diffusion for Microwave Brain Imaging

Microwave imaging, whose measurements are collected from portable and non-invasive devices, is a promising tool for detecting and monitoring strokes. The imaging process is a highly ill-posed problem, where incorporating prior information regarding the target is necessary. Classical methods with hand-crafted priors cannot fully exploit the prior knowledge, leading to limited image resolution. To address the challenge, we propose a physics-data-driven method that samples from the posterior distribution of head electrical properties. It includes a data consistency sampler to generate samples consistent with the measurements, and a latent diffusion model combined with a variational auto-encoder employed as an expressive prior. This method bypasses local minima that often occur in deterministic inversion and achieves a high resolution of electrical property distribution. Our method is validated on a two-dimensional microwave dataset simulated from heads with and without hemorrhagic or ischemic strokes, showing the the smallest model misfit (0.067 vs. ≥ 0.085 ) and highest structure similarity index measure (SSIM) (0.936 vs. ≤ 0.906) compared to other existing methods.