无配对图像逆问题是实际应用中的常见难题，UOTIP 用非平衡最优传输优雅地解决了数据不配对和噪声鲁棒性问题，做医学成像或遥感图像恢复的团队值得关注。
UOTIP 提出了一种基于非平衡最优传输（UOT）的新方法，用于解决无配对图像逆问题。该方法通过引入基于似然的代价函数，学习从噪声测量分布到干净信号分布的传输映射，无需配对训练数据。UOT 框架通过放松精确边际约束，使模型对多级观测噪声、类别不平衡和多种噪声类型具有鲁棒性。理论分析表明，加入二次代价项可确保传输映射的存在性和唯一性。实验结果显示，UOTIP 在线性和非线性逆问题基准上均达到最先进性能。
UOTIP: Unbalanced Optimal Transport Map for Unpaired Inverse Problems
We investigate unpaired image inverse problems, a challenging setting where only independent, non-paired sets of noisy measurements and clean target signals are available for training. We propose a novel inverse problem solver based on Unbalanced Optimal Transport, called Unbalanced Optimal Transport Map for Inverse Problems (UOTIP). Our method formulates the reconstruction task, predicting clean target signals from noisy measurements, as learning a UOT Map from noisy measurement distribution to clean signal distribution by incorporating a likelihood-based cost function. By relaxing the exact marginal constraint, the UOT framework provides key advantages to our model: robustness to multi-level observation noise, adaptability to class imbalance between noisy and clean datasets, and generalizability to diverse noise-type scenarios. Furthermore, we theoretically demonstrate that incorporating a quadratic cost term ensures the existence and uniqueness of the transport map by satisfying the twist condition, even for ill-posed inverse problems. Our experiments demonstrate that UOTIP achieves state-of-the-art performance on unpaired image inverse problem benchmarks, across linear and nonlinear inverse problems.