Quaternion Neural Networks: A physics-incorporated intelligence framework [Hypercomplex Signal and Image Processing]

Why quaternions in neural networks (NNs)? Are there quaternions in the human brain? “No” may be an ordinary answer. However, quaternion NNs (QNNs) are a powerful framework that strongly connects artificial intelligence (AI) and the real world. In this article, we deal with NNs based on quaternions and describe their basics and features. We also detail the underlying ideas in their engineering applications, especially when we adaptively process the polarization information of electromagnetic waves. We focus on their role in remote sensing, such as Earth observation radar mounted on artificial satellites or aircraft and underground radar, as well as mobile communication. There, QNNs are a class of NNs that know physics, especially polarization, composing a framework by fusing measurement physics with adaptive-processing mathematics. This fusion realizes a seamless integration of measurement and intelligence, contributing to the construction of a human society having harmony between AI and real human lives.