A Novel Wasserstein Quaternion Generative Adversarial Network for Color Image Generation

TL;DR

This paper introduces a new quaternion Wasserstein distance and a corresponding GAN model that better captures color channel correlations, leading to improved color image generation quality.

Contribution

It develops a novel quaternion Wasserstein distance, its dual theory, and a Wasserstein quaternion GAN that enhances color image generation by considering channel correlations.

Findings

Outperforms existing GAN models in image quality

Achieves higher generation efficiency

Effectively models color channel correlations

Abstract

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.