Recently, much progress has been made in unsupervised denoising learning. However, existing methods more or less rely on some assumptions on the signal and/or degradation model, which limits their practical performance. How to construct an optimal criterion for unsupervised denoising learning without any prior knowledge on the degradation model is still an open question. Toward answering this question, this work proposes a criterion for unsupervised denoising learning based on the optimal transport theory. This criterion has favorable properties, e.g., approximately maximal preservation of the information of the signal, whilst achieving perceptual reconstruction. Furthermore, though a relaxed unconstrained formulation is used in practical implementation, we prove that the relaxed formulation in theory has the same solution as the original constrained formulation. Experiments on synthetic and real-world data, including realistic photographic, microscopy, depth, and raw depth images, demonstrate that the proposed method even compares favorably with supervised methods, e.g., approaching the PSNR of supervised methods while having better perceptual quality. Particularly, for spatially correlated noise and realistic microscopy images, the proposed method not only achieves better perceptual quality but also has higher PSNR than supervised methods. Besides, it shows remarkable superiority in harsh practical conditions with complex noise, e.g., raw depth images. Code is available at https://github.com/wangweiSJTU/OTUR.

翻译：最近,在未经监督的去污学习方面取得了很大进展,然而,现有方法或多或少依赖于对信号和(或)退化模型的一些假设,这些假设限制了它们的实际性能。如何为未经监督的去污学习制定最佳标准而无需事先对退化模型有任何了解,仍然是一个尚未解决的问题。在回答这一问题时,这项工作提出了一个基于最佳运输理论的未经监督的去污学习标准。这一标准具有有利的特性,例如,在概念重建的同时,对信号信息进行最充分的保存。此外,虽然在实际执行中采用了宽松的、不受限制的配方,但我们证明,在理论上的较宽松的配方与最初的受限制的配方具有相同的解决办法。关于合成和现实世界数据的实验,包括现实的摄影、显微镜、深度和原始深度图像,表明拟议方法甚至优于受监督的方法,例如,接近受监督方法的PSNRRR,同时提高感知质量。特别是,对于与空间相关噪音和现实的显微镜图像,拟议的方法不仅具有较高的甚高度,而且具有高度的RIS/底底线,还显示,而且具有较先进的甚高度的RVR,还具有较高度。