PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization.

Year:

2022

Publication:

Inverse Problems

Abstract:

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 maximum a posteriori 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.

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Additional Information

Brief introduction of the dida co-author(s) and relevance for dida's ML developments.

Fabian Altekrüger (PhD)

During his mathematics studies at TU Berlin, Fabian focused on functional analysis. In his subsequent doctoral research, he worked on the regularization and solution of Bayesian inverse problems in mathematical image processing, combining mathematical methods with neural networks. In this context, Fabian developed and applied conditional generative models, always with an emphasis on the stability and robustness of the methods. At dida, he contributes his skills as a machine learning scientist.