Reconstructing medical images from partial measurements is an important inverse problem in Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). Existing solutions based on machine learning typically train a model to directly map measurements to medical images, leveraging a training dataset of paired images and measurements. These measurements are typically synthesized from images using a fixed physical model of the measurement process, which hinders 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 first train a score-based generative model on medical images to capture their prior distribution. Given measurements and a physical model of the measurement process at test time, we introduce a sampling method to reconstruct an image consistent with both the prior and the observed measurements. 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 in CT and MRI, while demonstrating significantly better generalization to unknown measurement processes.
翻译:从部分测量中重建医疗图像是计算地形学(CT)和磁共振成像(MRI)的一个重要反向问题。基于机器学习的现有解决方案通常培训一种模型,直接将测量图绘制为医疗图像,利用对齐图像和测量的培训数据集。这些测量通常使用测量过程固定物理模型从图像中合成,这妨碍模型向未知测量过程的普及能力。为了解决这一问题,我们提出一种完全不受监督的反向解决问题技术,利用最近引进的基于分数的基因化模型。具体地说,我们首先对医学图像进行基于分数的基因化模型,以捕捉其先前的分布。鉴于测量过程的测量结果和物理模型,我们引入了一种抽样方法,以重建与先前和观察的测量过程相一致的图像。我们的方法在培训期间不采用固定的测量过程,因此可以灵活地适应测试时的不同测量过程。我们观察到,在CT和MRI的若干医学成像任务中,在监督的学习技术方面,可以比较或改进性,同时展示出显著的不为未知的测量过程。