  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.
