PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization.
von Fabian Altekrüger, Alexander Denker, Paul Hagemann, Johannes Hertrich, Peter Maass, Gabriele Steidl
Jahr:
2022
Publikation:
Inverse Problems
Abstrakt:
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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Dr. Fabian Altekrüger
Fabian legte während seines Mathematikstudiums an der TU Berlin seinen Fokus auf Themen der Funktionalanalysis. In seiner anschließenden Promotion beschäftigte er sich mit der Regularisierung und Lösung Bayesscher inverser Probleme in der mathematischen Bildverarbeitung, wobei er mathematische Methoden mit neuronalen Netzen kombinierte. Dabei entwickelte und nutzte Fabian unter anderem bedingte generative Modelle, stets mit Blick auf die Stabilität und Robustheit der Methoden. Bei dida bringt er seine Fähigkeiten als Machine Learning Scientist ein.