Hypercomplex Signal and Image Processing: Part 2

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. The first part offered well-rounded coverage of the field, with seven articles that focused on overviews of current research, color image processing, signal filtering, and machine learning.

The second part of the special issue is also composed of seven articles, two that deal with hypercomplex signal processing, while the rest of the issue (five articles) leans heavily toward hypercomplex machine/deep learning, which is the most current trend in the signal and image processing literature.

The first two articles focus on the theory and applications of hypercomplex signal processing in the areas of phase retrieval and virtual representation of the ocean. More specifically, the first article, “An Invitation to Hypercomplex Phase Retrieval: Theory and Applications,” by Jacome et al. [A1], provides an introduction to the fundamental concepts of hypercomplex phase retrieval and corresponding sample problems in optical imaging. The authors show that phase retrieval in the hypercomplex domain yields better performance and novel theoretical guarantees compared to conventional complex-valued methods. The second article, “Hypercomplex Signal Processing in Digital Twin of the Ocean: Theory and Application,” by Yu et al. [A2], presents how hypercomplex signal processing can overcome several challenges in achieving the objectives of the digital twin of the ocean that include heterogeneous data integration, multidimensional data analysis, feature extraction, high-fidelity scene modeling, and so on. The digital twin of the ocean aims to create a comprehensive simulation platform that can unite digital replicas, forecasting, and what-if scenario simulations for assessing ocean conditions.