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.

翻译：我们提出了Self2Seg，一种用于单图像联合分割与去噪的自监督方法。为此，我们将变分分割与自监督深度学习的优势相结合。该方法的一个主要优势在于：与需要大量标注样本的数据驱动方法不同，Self2Seg无需任何训练数据库即可将图像分割为有意义的区域。此外，我们证明Self2Seg通过区域特定学习能显著提升自监督去噪性能。因此，我们引入了一种新型自监督能量泛函，其中去噪与分割以相互促进的方式耦合。我们提出了统一的优化策略，并通过数值实验表明，对于噪声显微图像，所提出的联合方法在性能上优于其序贯对应方法以及单纯专注于去噪或分割的其他方法。