Quaternions are still largely misunderstood and often considered an “exotic” signal
representation without much practical utility despite the fact that they have been around the …

Complex-valued signals occur in many areas of science and engineering and are thus of
fundamental interest. In the past, it has often been assumed, usually implicitly, that complex …

The deviation of continuous and discrete complex random variables from the traditional
proper and symmetric assumption to a generalized improper and asymmetric …

Dual quaternions have wide applications in automatic differentiation, computer graphics,
mechanics, and others. Due to its application in control theory, matrix equation AXB= C has …

Few-shot segmentation (FSS) aims to segment unseen classes given only a few annotated
samples. Encouraging progress has been made for FSS by leveraging semantic features …

Vector-valued signals are crucial in science and engineering. The evolving field of
hypercomplex signal processing, particularly quaternion algebra, offers a concise and …

Real functions of quaternion variables are typical cost functions in quaternion valued
statistical signal processing, however, standard differentiability conditions in the quaternion …

This paper considers the Hermitian solutions of a new system of commutative quaternion
matrix equations, where we establish both necessary and sufficient conditions for the …

This book presents newly applied concepts for biomedical applications of singular spectrum
analysis (SSA) and introduces a new mathematical and signal processing technique for the …

This paper studies the eigenvalues of quaternion tensors and their applications. Firstly, we
investigate the definitions and properties of the left and right eigenvalues of the quaternion …