- Keywords: score-based generative modeling, inverse problems, sparse-view CT, undersampled MRI, metal artifact removal, diffusion
- Abstract: Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions from machine learning typically train a model to directly map measurements to medical images, with a training dataset comprising paired images and measurements. These measurements are synthesized from images using a fixed physical model of the measurement process, which consequently limits the generalization capability of models to unknown measurement processes. To address this issue, we propose a fully unsupervised technique for inverse problem solving, leveraging the recently introduced score-based generative models. Specifically, we train a score-based generative model on medical images to capture their prior distribution. Given a measurement and a physical model of the measurement process, we propose a sampling method to reconstruct an image consistent with both the prior and the observed measurement. Our method does not assume a fixed measurement process during training, and can thus be flexibly adapted to different measurement processes at test time. Empirically, we observe comparable or better performance to supervised learning techniques in several medical imaging tasks, including sparse-view CT and undersampled MRI, while demonstrating remarkably better generalization to unknown measurement processes.