Learning-based image reconstruction models, such as those based on the U-Net, require a large set of labeled images if good generalization is to be guaranteed. In some imaging domains, however, labeled data with pixel- or voxel-level label accuracy are scarce due to the cost of acquiring them. This problem is exacerbated further in domains like medical imaging, where there is no single ground truth label, resulting in large amounts of repeat variability in the labels. Therefore, training reconstruction networks to generalize better by learning from both labeled and unlabeled examples (called semi-supervised learning) is problem of practical and theoretical interest. However, traditional semi-supervised learning methods for image reconstruction often necessitate handcrafting a differentiable regularizer specific to some given imaging problem, which can be extremely time-consuming. In this work, we propose "supervision by denoising" (SUD), a framework that enables us to supervise reconstruction models using their own denoised output as soft labels. SUD unifies stochastic averaging and spatial denoising techniques under a spatio-temporal denoising framework and alternates denoising and model weight update steps in an optimization framework for semi-supervision. As example applications, we apply SUD to two problems arising from biomedical imaging -- anatomical brain reconstruction (3D) and cortical parcellation (2D) -- to demonstrate a significant improvement in the image reconstructions over supervised-only and stochastic averaging baselines.

翻译：基于学习的图像重建模型（如基于U-Net的模型）需要大量标注图像才能保证良好的泛化能力。然而，在某些成像领域，由于获取标注数据的成本高昂，像素级或体素级精确标注的数据十分稀缺。这一问题在医学成像等领域中更为严重，因为不存在单一的金标准标注，导致标注中存在大量重复变异性。因此，通过同时从标注和未标注样本中学习（称为半监督学习）来训练重建网络以提升泛化能力，是一个兼具实践和理论意义的问题。然而，传统的图像重建半监督学习方法通常需要针对特定成像问题手工设计可微正则化项，这一过程极为耗时。本文提出“基于去噪的监督”（SUD）框架，该框架能够利用重建模型自身的去噪输出作为软标签来监督模型训练。SUD在时空去噪框架下统一了随机平均和空间去噪技术，并在半监督优化框架中交替进行去噪和模型权重更新步骤。作为应用示例，我们将SUD应用于生物医学成像中的两个问题——解剖结构脑重建（3D）和皮层分区（2D）——结果表明，与纯监督和随机平均基线方法相比，图像重建性能得到显著提升。