In this work, we develop an unsupervised method for the joint segmentation
and denoising of a single image. To this end, we combine the advantages of a
variational segmentation method with the power of a self-supervised,
single-image based deep learning approach. One major strength of our method
lies in the fact, that in contrast to data-driven methods, where huge amounts
of labeled samples are necessary, our model can segment an image into multiple
meaningful regions without any training database. Further, we introduce a novel
energy functional in which denoising and segmentation are coupled in a way that
both tasks benefit from each other. The limitations of existing single-image
based variational segmentation methods, which are not capable of dealing with
high noise or generic texture, are tackled by this specific combination with
self-supervised image denoising. We propose a unified optimisation strategy and
show that, especially for very noisy images available in microscopy, our
proposed joint approach outperforms its sequential counterpart as well as
alternative methods focused purely on denoising or segmentation. Another
comparison is conducted with a supervised deep learning approach designed for
the same application, highlighting the good performance of our approach.

我们开发了一种无监督的方法，用于单幅图像的联合分割和去噪。我们结合了变分分割方法的优势和自监督单幅图像的深度学习方法的能力。我们的方法的一个主要优点在于，与需要大量标记样本的数据驱动方法相比，我们的模型可以将图像分割为多个有意义的区域，而无需任何训练数据库。此外，我们引入了一种新的能量函数，其中去噪和分割被耦合在一起，使得两个任务相互受益。我们提出了一种统一的优化策略，并展示了在显微镜中可用的非常嘈杂的图像方面，我们提出的联合方法在性能上优于其顺序对应物以及纯粹针对去噪或分割的替代方法。我们还与设计用于相同应用的监督深度学习方法进行了比较，突出了我们方法的良好性能。