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
this https URL

本文提出了一种基于最优传输理论的无监督去噪学习标准，该标准具有优秀的性质，能够实现近乎完全保留信号信息并实现感知重构。实验结果表明，该方法比监督方法具有更好的感知重构和更高的峰值信噪比，尤其在复杂噪声等恶劣实际条件下表现出卓越的优越性。