Quaternions are still largely misunderstood and often considered an “exotic” signal representation without much practical utility despite the fact that they have been around the signal and image processing community for more than 30 years now. The main aim of this article is to counter this misconception and to demystify the use of quaternion algebra for solving problems in signal and image processing. To this end, we propose a comprehensive and objective overview of the key aspects of quaternion representations, models, and methods and illustrate our journey through the literature with flagship applications. We conclude this work by an outlook on the remaining challenges and open problems in quaternion signal and image processing.

中文翻译：

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信号和图像处理中的四元数：全面客观的概述

尽管四元数已经在信号和图像处理社区存在了 30 多年，但它仍然在很大程度上被误解，并且经常被认为是一种“奇异”的信号表示形式，没有太多实际用途。本文的主要目的是反驳这种误解，并揭开使用四元数代数解决信号和图像处理问题的神秘面纱。为此，我们对四元数表示、模型和方法的关键方面提出了全面、客观的概述，并通过旗舰应用说明了我们的文献之旅。我们通过对四元数信号和图像处理中剩余挑战和未解决问题的展望来结束这项工作。