发表机构
Moscow Independent Research Institute of Artificial Intelligence; Applied AI Institute; Lomonosov Moscow State University; MIRIAI（莫斯科独立人工智能研究院; 应用人工智能研究所; 莫斯科国立罗蒙诺索夫大学; MIRIAI）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出同时最优传输问题，通过神经方法学习共享传输映射，在最小化平均传输成本的同时对齐多个源分布至共同目标，并应用于图像恢复中处理多种退化类型。
AI 中文摘要
最优传输（OT）为从未配对样本中学习概率分布之间变换提供了一个有原则的框架。然而，在许多应用中，单个变换必须将多个源分布映射到一个共同的目标分布。例如，图像恢复可能需要处理不同类型的退化，而在推理时不知道每个输入的具体退化类型。简单地对源分布进行池化仅鼓励在总体水平上与目标对齐，可能使个别源分布未对齐。在我们的论文中，我们考虑了同时最优传输问题，该问题形式化了学习一个共享传输映射的任务，该映射在使每个源分布与指定目标对齐的同时，最小化平均传输成本。我们提出了一种神经方法来解决同时最优传输问题，通过学习一个共享传输映射，在使每个源分布与指定目标对齐的同时，最小化平均传输成本。我们推导了一个最大-最小公式来学习该映射。我们展示了其在图像恢复中的应用，其中单个模型使用一组共同的干净目标图像来处理多种退化类型。
英文摘要
Optimal Transport (OT) provides a principled framework for learning transformations between probability distributions from unpaired samples. In many applications, however, a single transformation must map several source distributions to a common target distribution. For example, image restoration might require handling different types of degradation without knowing the degradation of each input at inference time. Simple approaches of pooling the source distributions only encourage alignment with the target at the aggregate level and may leave individual sources misaligned. In our paper, we consider the simultaneous OT problem which formalizes the task of learning a shared transport map that minimizes the average transport cost while aligning each source distribution with a prescribed target. We propose a neural method for solving the simultaneous OT problem by learning a shared transport map that minimizes the average transport cost while aligning each source distribution with a prescribed target. We derive a max-min formulation for learning this map. We illustrate its application to image restoration, where a single model handles multiple degradation types using a common collection of clean target images.
