Hypercomplex Signal and Image Processing: Part 1 [From the Guest Editors]

Abstract

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.