Solving Inverse Problems in Medical Imaging with Score-Based Generative Models

Yang Song, Liyue Shen, Lei Xing, Stefano Ermon

Keywords: inverse problems, sparse-view CT, undersampled MRI, score-based generative modeling, diffusion

TL;DR: We propose a new method to solve linear inverse problems with score-based generative models.

Abstract: Solving inverse problems with a small number of measurements has important applications in medical imaging, including image reconstruction for undersampled MRI and sparse-view CT. With the progress of machine learning, traditional image reconstruction methods have been outperformed by models that learn to directly map measurements to medial images. However, these models require both ground truth medical images and their measurements for training, which complicates data collection and harms their generalization performance to unknown measurement processes. To address these issues, 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 to capture the prior distribution of medical images, which is subsequently combined with a given physical measurement process to sample images consistent with measurements at the test time. Our method makes no assumption on the measurement process during training, and can be flexibly adapted to any linear measurement processes. Empirically, we observe comparable or better performance to supervised learning techniques, with better generalization to unknown measurement processes on several MRI/CT datasets.