  Learning neural networks using only few available information is an important
ongoing research topic with tremendous potential for applications. In this
paper, we introduce a powerful regularizer for the variational modeling of
inverse problems in imaging. Our regularizer, called patch normalizing flow
regularizer (patchNR), involves a normalizing flow learned on small patches of
very few images. In particular, the training is independent of the considered
inverse problem such that the same regularizer can be applied for different
forward operators acting on the same class of images. By investigating the
distribution of patches versus those of the whole image class, we prove that
our model is indeed a MAP approach. Numerical examples for low-dose and
limited-angle computed tomography (CT) as well as superresolution of material
images demonstrate that our method provides very high quality results. The
training set consists of just six images for CT and one image for
superresolution. Finally, we combine our patchNR with ideas from internal
learning for performing superresolution of natural images directly from the
low-resolution observation without knowledge of any high-resolution image.
