In the real world, lacking paired training data makes image super-resolution (SR) be a tricky unsupervised task. Existing methods are mainly train models on synthetic datasets and achieve the tradeoff between detail restoration and noise artifact suppression based on a priori knowledge, which indicate it cannot be optimal in both aspects. To solve this problem, we propose OTSR, a single image super-resolution method based on optimal transport theory. OTSR aims to find the optimal solution to the ill-posed SR problem, so that the model can restore high-frequency detail accurately and also suppress noise and artifacts well. Our method consists of three stages: real-world images degradation estimation, LR images generation and model optimization based on quadratic Wasserstein distance. Through the first two stages, the problem of no paired image is solved. In the third stage, under the guidance of optimal transport theory, the optimal mapping from LR to HR image space is learned. Extensive experiments show that our method outperforms the state-of-the-art methods in terms of both detail repair and noise artifact suppression. The source code is available at https://github.com/cognaclee/OTSR.

在现实世界中，缺乏配对训练数据使得图像超分辨率（SR）成为一项棘手的无监督任务。现有方法主要是在合成数据集上训练模型，并基于先验知识在细节恢复和噪声伪影抑制之间进行权衡，这表明它不能在这两个方面都达到最优。为了解决这个问题，我们提出了OTSR，一种基于最优传输理论的单图像超分辨率方法。OTSR旨在寻找病态SR问题的最优解，使模型能够准确还原高频细节，同时很好地抑制噪声和伪影。我们的方法包括三个阶段：真实世界图像退化估计、LR 图像生成和基于二次 Wasserstein 距离的模型优化。通过前两个阶段，解决了没有成对图像的问题。第三阶段，在最优传输理论的指导下，学习从LR到HR图像空间的最优映射。大量实验表明，我们的方法在细节修复和噪声伪影抑制方面都优于最先进的方法。源代码可在 https://github.com/cognaclee/OTSR 获得。