A survey on quaternion algebra and geometric algebra applications in engineering and computer science 1995–2020
E Bayro-Corrochano - IEEE Access, 2021 - ieeexplore.ieee.org
Geometric Algebra (GA) has proven to be an advanced language for mathematics, physics,
computer science, and engineering. This review presents a comprehensive study of works …
computer science, and engineering. This review presents a comprehensive study of works …
Fixed time synchronization of octonion valued neural networks with time varying delays
Octonion valued neural networks (OVNNs) does not fall into the category of Clifford valued
neural networks because of the non-associativity of OVNNs. The present article contains the …
neural networks because of the non-associativity of OVNNs. The present article contains the …
A generalization of the octonion Fourier transform to 3-D octonion-valued signals: properties and possible applications to 3-D LTI partial differential systems
Ł Błaszczyk - Multidimensional Systems and Signal Processing, 2020 - Springer
The paper is devoted to the development of the octonion Fourier transform (OFT) theory
initiated in 2011 in articles by Hahn and Snopek. It is also a continuation and generalization …
initiated in 2011 in articles by Hahn and Snopek. It is also a continuation and generalization …
Discrete octonion Fourier transform and the analysis of discrete 3-D data
Ł Błaszczyk - Computational and Applied Mathematics, 2020 - Springer
The purpose of this article is to further develop the theory of octonion Fourier transformations
(OFT), but from a different perspective than before. It follows the earlier work by Błaszczyk …
(OFT), but from a different perspective than before. It follows the earlier work by Błaszczyk …
Octonion Phase Retrieval
Signal processing over hypercomplex numbers arises in many optical imaging applications.
In particular, spectral image or color stereo data are often processed using octonion algebra …
In particular, spectral image or color stereo data are often processed using octonion algebra …
Preserving Spatio-Temporal Information in Machine Learning: A Shift-Invariant k-Means Perspective
In conventional machine learning applications, each data attribute is assumed to be
orthogonal to others. Namely, every pair of dimension is orthogonal to each other and thus …
orthogonal to others. Namely, every pair of dimension is orthogonal to each other and thus …
An invitation to hypercomplex phase retrieval: Theory and applications
Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle
multidimensional signals by harnessing intrinsic correlation of the signal dimensions …
multidimensional signals by harnessing intrinsic correlation of the signal dimensions …
An Invitation to Hypercomplex Phase Retrieval: Theory and applications [Hypercomplex Signal and Image Processing]
Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle
multidimensional signals by harnessing the intrinsic correlation of the signal dimensions …
multidimensional signals by harnessing the intrinsic correlation of the signal dimensions …
Hypercomplex Fourier transforms in the analysis of multidimensional linear time-invariant systems
Ł Błaszczyk - Progress in industrial mathematics at ECMI 2018, 2019 - Springer
The aim of this paper is to further investigate the properties of octonion Fourier transform
(OFT) of real-valued functions of three variables and its potential applications in signal and …
(OFT) of real-valued functions of three variables and its potential applications in signal and …
Global -stability and finite-time control of octonion-valued neural networks with unbounded delays
J Wang, X Liu - arXiv preprint arXiv:2003.11330, 2020 - arxiv.org
Octonion-valued neural networks (OVNNs) are a type of neural networks for which the states
and weights are octonions. In this paper, the global $\mu $-stability and finite-time stability …
and weights are octonions. In this paper, the global $\mu $-stability and finite-time stability …