Hypercomplex signal and image processing extends upon conventional methods by using hypercomplex numbers in a unified framework for algebra and geometry. The special issue is divided into two parts and is focused on current advances and applications in computational signal and image processing in the hypercomplex domain.

Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing the intrinsic correlation of the signal dimensions through Clifford algebra. Recently, the hypercomplex representation of the phase retrieval (PR) problem, wherein a complex-valued signal is estimated through its intensity-only projections, has attracted significant interest.

In the first issue of 2024, we introduced the new lead editorial team of IEEE Signal Processing Magazine ( SPM ), composed of our four area editors. Their terms started with mine this January, and they oversee the Society e-newsletter and the three main components of our magazine: feature articles, special issues, and columns and forum articles.

This article aims to identify core research directions and provide a comprehensive overview of major advancements in the field of hypercomplex signal and image processing techniques using network graph theory. The methodology employs community detection algorithms on research networks to uncover relationships among researchers and topic fields in the hypercomplex domain.

For reasons beyond our control, the issues of IEEE Signal Processing Magazine arrive to you with delays this year. As you receive the current March issue, we are back from another edition of our flagship conference, the IEEE International Conference on Acoustic, Speech, and Signal Processing (ICASSP), which took place in Seoul, Korea, 14–19 April 2024.