  We develop Self2Seg, a self-supervised method for the joint segmentation and
denoising of a single image. To this end, we combine the advantages of
variational segmentation with self-supervised deep learning. One major benefit
of our method lies in the fact, that in contrast to data-driven methods, where
huge amounts of labeled samples are necessary, Self2Seg segments an image into
meaningful regions without any training database. Moreover, we demonstrate that
self-supervised denoising itself is significantly improved through the
region-specific learning of Self2Seg. Therefore, we introduce a novel
self-supervised energy functional in which denoising and segmentation are
coupled in a way that both tasks benefit from each other. We propose a unified
optimisation strategy and numerically show that for noisy microscopy images our
proposed joint approach outperforms its sequential counterpart as well as
alternative methods focused purely on denoising or segmentation.
