PatchNR: Learning from Small Data by Patch Normalizing Flow Regularization

Learning neural networks using only a small amount of data is an important ongoing research topic with tremendous potential for applications. In this paper, we introduce a regularizer for the variational modeling of inverse problems in imaging based on normalizing flows. Our regularizer, called patchNR, involves a normalizing flow learned on patches of very few images. The subsequent reconstruction method is completely unsupervised and the same regularizer can be used 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 variational model is indeed a MAP approach. Our model can be generalized to conditional patchNRs, if additional supervised information is available. Numerical examples for low-dose CT, limited-angle CT and superresolution of material images demonstrate that our method provides high quality results among unsupervised methods, but requires only few data.