Novel computational signal and image analysis methodologies based on feature-rich mathematical/computational frameworks continue to push the limits of the technological envelope, thus providing optimized and efficient solutions. Hypercomplex signal and image processing is a fascinating field that extends conventional methods by using hypercomplex numbers in a unified framework for algebra and geometry. Methodologies that are developed within this field can lead to more effective and powerful ways to analyze signals and images. Processing audio, video, images, and other types of data in the hypercomplex domain allows for more complex and intuitive representations with algebraic properties that can lead to new insights and optimizations. Applications in image processing, signal filtering, and deep learning (just to name a few) have shown that working in the hypercomplex domain can lead to more efficient and robust outcomes. As research in this field progresses and software tools become more widely available, we can expect to see increasingly sophisticated applications in many areas of research, e.g., computer vision, machine learning, and so on.

中文翻译：

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超复杂信号和图像处理：第 1 部分 [来自客座编辑]


基于功能丰富的数学/计算框架的新型计算信号和图像分析方法不断突破技术极限，从而提供优化且高效的解决方案。超复数信号和图像处理是一个令人着迷的领域，它通过在代数和几何的统一框架中使用超复数来扩展传统方法。该领域开发的方法可以带来更有效、更强大的信号和图像分析方法。在超复杂域中处理音频、视频、图像和其他类型的数据可以使用代数属性进行更复杂和直观的表示，从而带来新的见解和优化。图像处理、信号过滤和深度学习（仅举几例）中的应用表明，在超复杂领域工作可以带来更高效、更稳健的结果。随着这一领域研究的进展和软件工具变得越来越广泛，我们可以预期在许多研究领域看到越来越复杂的应用，例如计算机视觉、机器学习等。