Quaternion tensor decompositions have recently been the center of focus due to their wide potential applications in color data processing. In this paper, we establish a simultaneous decomposition for a quaternion tensor quaternity under Einstein prod...
To protect the copyright of the color image, a color image watermarking scheme based on quaternion discrete Fourier transform (QDFT) and tensor decomposition (TD) is presented. Specifically, the cover image is partitioned into non-overlapping blocks,...
This paper extends the theory of equivalence canonical forms from quaternion matrices to quaternion tensors under the Einstein product. Motivated by recent results on the simultaneous decomposition of two specific configurations of five quaternion ma...
With the rapid advancement of information technology, digital images such as medical images, grayscale images, and color images are widely used, stored, and transmitted. Therefore, protecting this type of information is a critical challenge. Meanwhil...
In this paper, we study the restricted singular-value decomposition (RSVD) for three quaternion tensors under the Einstein product, and give higher-order RSVD over the quaternion algebra, which can achieve simultaneous singular value decomposition of...
In this study, we developed a MATLAB 2024a toolbox that performs advanced algebraic calculations in the algebra of elliptic numbers and elliptic quaternions. Additionally, we introduce color image processing methods, such as principal component analy...
This article makes use of simultaneous decomposition of four quaternion matrixes to investigate some Sylvester-like quaternion matrix equation systems. We present some useful necessary and sufficient conditions for the consistency of the system of qu...
In this paper, we make use of the simultaneous decomposition of eight quaternion matrices to study the solvability conditions and general solutions to a system of two-sided coupled Sylvester-type quaternion matrix equations
In this study, we obtained results for the computation of eigen-pairs, singular value decomposition, pseudoinverse, and the least squares problem for elliptic quaternion matrices. Moreover, we established algorithms based on these results and provide...
This paper proposes a new method for calculating the quaternion discrete Fourier transform for one-dimensional data. Although the computational complexity of the proposed method still belongs to the
In view of the higher requirements of modern machinery for multi-sensor information acquisition and fusion technology, this paper proposes a novel multi-fusion analytic mode decomposition (MFAMD) method to separate and demodulate fault features in si...
Reduced biquaternion (RB) matrices provide a commutative algebraic framework for coupled multicomponent data, but their factorizations are usually formulated through complex or real representation matrices. The aim of this study is to develop and val...
Computer vision and deep learning are essential in diverse fields such as autonomous driving, medical imaging, face recognition, and object detection. However, enhancing low-light remote sensing images remains challenging for both research and real-w...
Color image decolorization can not only simplify the complexity of image processing and analysis, improving computational efficiency, but also help to preserve the key information of the image, enhance visual effects, and meet various practical appli...
Two algorithms are proposed for the superposition of assemblies of like molecules (e.g., peptide and proteins homooligomers and homoaggregates), which do not require examining all permutations of the molecules. Both start from searching the mutual or...
Quaternions are a non-commutative associative number system that extends complex numbers, first described by Hamilton in 1843. We present algorithms for solving the eigenvalue problem for arrowhead and DPRk (diagonal-plus-rank-k) matrices of quaterni...
Using the orbit decomposition, a new enumerative polynomial
This paper proposes a novel attitude control methodology for unmanned aerial vehicles (UAVs). The core of the approach is a decomposition of the vehicle’s orientation into a distinct horizontal tilt component and a yaw rotation. This reformulat...
Multi-focus image fusion is an important method used to combine the focused parts from source multi-focus images into a single full-focus image. Currently, to address the problem of multi-focus image fusion, the key is on how to accurately detect the...
This paper investigates the properties of the
Let
In the era of big data and multimedia communication, securing color images against unauthorized access and attacks is a pressing challenge. While quaternion-based models provide a unified representation for color images, most existing encryption sche...
Sixth-generation (6G) networks require advanced non-orthogonal multiple access (NOMA) schemes to support the technical requirements of dense massive machine-type communications (mMTC). While sparse-code multiple access (SCMA) improves uplink spectral...
In this paper, we present a Mirsky-type unitarily invariant norm inequality for dual quaternion matrices, which can be regarded as a singular value perturbation theorem for dual quaternion matrices. By using this unitarily invariant norm inequality,...
In this paper, a non-decomposition approach is adopted to study the robust stability of quaternion-valued neural networks (QVNNs) with leakage, discrete, and neutral time delays, and the parameter uncertainty is also considered. The existence and uni...
This paper investigates the problem of exponential synchronization for a class of quaternion-valued inertial neural networks with mixed time delays under aperiodic intermittent control. First, a neural network model incorporating both discrete and di...
We develop detailed quaternionic and octonionic frameworks for quantum computation grounded on normed division algebras. Our central result is to prove the polynomial computational equivalence of quaternionic and complex quantum models: Computation o...
Images used in real-world applications such as image or video retrieval, outdoor surveillance, and autonomous driving suffer from poor weather conditions. When designing robust computer vision systems, removing adverse weather such as haze, rain, and...
This paper presents a high dynamic range (HDR) image zero watermarking method based on dual tree complex wavelet transform (DT-CWT) and quaternion. In order to be against tone mapping (TM), DT-CWT is used to transform the three RGB color channels of...
Obtaining precise attitude information is essential for aircraft navigation and control. This paper presents the results of the attitude determination using an in-house designed low-cost MEMS-based flight information measurement unit. This study prop...
In this paper, the adaptive synchronization problem of quaternion-valued Cohen–Grossberg neural networks (QVCGNNs), with and without known parameters, is investigated. On the basis of constructing an appropriate Lyapunov function, and utilizing...
To address the limitations of the traditional long-vector model, which cannot adequately preserve the inherent orthogonal structure among channels in the signal processing of a single vector hydrophone, three minimum variance distortionless response...
Despite the popularity of electroencephalograms (EEGs) as tools for assessing brain health, they can sometimes be abstract and prone to noise, making them difficult to interpret. The following work aims to implement a Quaternion Convolutional Neural...
The need to estimate the orientation between frames of reference is crucial in spacecraft navigation. Robust algorithms for this type of problem have been built by following algebraic approaches, but data-driven solutions are becoming more appealing...
Polarimetric synthetic aperture radar (PolSAR) image classification plays an important role in various PolSAR image application. And many pixel-wise, region-based classification methods have been proposed for PolSAR images. However, most of the pixel...
Wireless capsule endoscopy (WCE) offers a non-invasive diagnostic alternative for the gastrointestinal tract using a battery-powered capsule. Despite advantages, WCE encounters issues with video quality and diagnostic accuracy, often resulting in mis...
This paper proposes a two dimensional quaternion valued singular spectrum analysis based method for enhancing the hyperspectral image. Here, the enhancement is for performing the object recognition, but neither for improving the visual quality nor su...
Unbiased Finite Impulse Response (UFIR) filters are widely used in engineering applications, such as vehicle attitude estimation, due to their advantages, including independence from initial conditions and insensitivity to noise. However, the perform...
Color constancy, the ability to perceive consistent object colors under varying illumination, is a core function of the human visual system and a persistent challenge in machine vision. Retinex theory models this process by decomposing an image
This survey provides a review of the theoretical research on the classic system of matrix equations
This paper develops a direct analytical framework for synchronizing and controlling fractional-order octonion-valued fuzzy bidirectional associative memory neural networks (FOOVFBAMNNs). Octonion algebra is neither commutative nor associative, which...
In this work, we investigate analytically the solutions of a nonlinear div-curl system with fractional derivatives of the Riemann–Liouville or Caputo types. To this end, the fractional-order vector operators of divergence, curl and gradient are ident...
This paper builds upon a previous study suggesting an optimization procedure for rotation sequences by introducing a fourth factor in Euler-type decompositions, thus allowing for an additional degree of freedom used both as a variational parameter an...
Laser scanning allows for the rapid acquisition of three-dimensional data in the form of 3D point clouds. However, due to the accumulation of errors in the registration of multiple pairs of point clouds along the sensor’s trajectory, the genera...
This paper primarily investigates the solutions to the system of equations
This paper proposes a screen-shooting resilient watermarking scheme via learned invariant keypoints and QT; that is, if the watermarked image is displayed on the screen and captured by a camera, the watermark can be still extracted from the photo. A...
Due to the high complexity of geo-spatial entities and the limited field of view of LiDAR equipment, pairwise registration is a necessary step for integrating point clouds from neighbouring LiDAR stations. Considering that accurate extraction of poin...
Wearable exoskeletons can help people with mobility impairments by improving their rehabilitation. As electromyography (EMG) signals occur before movement, they can be used as input signals for the exoskeletons to predict the body’s movement in...
Let \(\mathbf{H}\) be the quaternion algebra. Let \(\mathfrak{g}\) be a complex Lie algebra and let \(U(\mathfrak{g})\) be the enveloping algebra of \(\mathfrak{g}\). The quaternification \(\mathfrak{g}^{\mathbf{H}}=\)\(\,(\,\mathbf{H}\otimes U(\math...