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.

中文翻译：

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无监督去噪学习的最佳传输


最近，无监督去噪学习取得了很大进展。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，这限制了它们的实际性能。如何在没有任何退化模型先验知识的情况下构建无监督去噪学习的最佳标准仍然是一个悬而未决的问题。为了回答这个问题，这项工作提出了基于最优传输理论的无监督去噪学习的标准。该标准具有有利的特性，例如，在实现感知重建的同时，近似最大程度地保留信号信息。此外，尽管在实际实现中使用了松弛的无约束公式，但我们证明了理论上的松弛公式与原始约束公式具有相同的解。对合成数据和真实世界数据（包括真实摄影、显微镜、深度和原始深度图像）的实验表明，所提出的方法甚至可以与监督方法相媲美，例如，接近监督方法的 PSNR，同时具有更好的感知质量。特别是，对于空间相关噪声和真实的显微镜图像，所提出的方法不仅能够实现更好的感知质量，而且比监督方法具有更高的 PSNR。此外，它在具有复杂噪声的恶劣实际条件下（例如原始深度图像）显示出显着的优越性。代码可在 https://github.com/wangweiSJTU/OTUR 获取。