Color image generation has a wide range of applications, but the existing generation models ignore the correlation among color channels, which may lead to chromatic aberration problems. In addition, the data distribution problem of color images has not been systematically elaborated and explained, so that there is still the lack of the theory about measuring different color images datasets. In this paper, we define a new quaternion Wasserstein distance and develop its dual theory. To deal with the quaternion linear programming problem, we derive the strong duality form with helps of quaternion convex set separation theorem and quaternion Farkas lemma. With using quaternion Wasserstein distance, we propose a novel Wasserstein quaternion generative adversarial network. Experiments demonstrate that this novel model surpasses both the (quaternion) generative adversarial networks and the Wasserstein generative adversarial network in terms of generation efficiency and image quality.

翻译：彩色图像生成具有广泛的应用，但现有生成模型忽略了颜色通道间的相关性，可能导致色差问题。此外，彩色图像的数据分布问题尚未得到系统阐述与解释，导致目前仍缺乏衡量不同彩色图像数据集的理论基础。本文定义了一种新的四元数Wasserstein距离并发展了其对偶理论。为处理四元数线性规划问题，我们借助四元数凸集分离定理和四元数Farkas引理推导出其强对偶形式。基于四元数Wasserstein距离，我们提出了一种新型Wasserstein四元数生成对抗网络。实验表明，该新型模型在生成效率和图像质量方面均超越了（四元数）生成对抗网络和Wasserstein生成对抗网络。