Related papers: Quaternion-Valued Single-Phase Model for Three-Pha…
This paper addresses the color image completion problem in accordance with low-rank quatenrion matrix optimization that is characterized by sparse regularization in a transformed domain. This research was inspired by an appreciation of the…
Quaternion-valued signals along with quaternion Fourier transforms (QFT)provide an effective framework for vector-valued signal and image processing. However, the sampling theory of quaternion valued signals has not been well developed. In…
In this paper we propose and demonstrate the potential for unifying models and algorithms for the steady state and transient simulation of single-phase and three-phase power systems. At present, disparate algorithms and models are used for…
Recently, the connectionist temporal classification (CTC) model coupled with recurrent (RNN) or convolutional neural networks (CNN), made it easier to train speech recognition systems in an end-to-end fashion. However in real-valued models,…
This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…
In this article, we introduce the notion of Quaternion Boostlet Transform (QBT), a hypercomplex framework designed to unify the analysis of multi-component wavefields by merging the algebraic richness of quaternions with the relativistic,…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from…
Color in an image is resolved into 3 or 4 color components and 2-Dimages of these components are stored in separate channels. Most of the color image enhancement algorithms are applied channel-by-channel on each image. But such a system of…
We investigate the effects of including the full three-loop QCD correction to the static short distance $1/r$ potential on the spectroscopy and decays in the charmonium and upsilon systems. We use a variational technique with the full…
The increasing integration of power electronic devices is driving the development of more advanced tools and methods for the modeling, analysis, and control of modern power systems to cope with the different time-scale oscillations. In this…
A novel single-frame quaternion estimator processing two vector observations is introduced. The singular cases are examined, and appropriate rotational solutions are provided. Additionally, an alternative method involving sequential…
This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…
We introduce Contrastive Multivariate Singular Spectrum Analysis, a novel unsupervised method for dimensionality reduction and signal decomposition of time series data. By utilizing an appropriate background dataset, the method transforms a…
A novel method for distributed estimation of the frequency of power systems is introduced based on the cooperation between multiple measurement nodes. The proposed distributed widely linear complex Kalman filter (D-ACKF) and the distributed…
This paper describes the passage of light through a system of waveplates mathematically in terms of quaternions, an extension of the complex numbers, instead of the more usual Jones vectors and Jones matrices. Both the light beam and the…
The concept of complex frequency has been recently introduced on the IEEE Transactions on Power Systems to study bus voltage variations in magnitude and frequency and their link with complex power injections of a power system. In this…
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…
We measure the joint Q-function of a multi-spatial-mode field using a charge-coupled device array detector in an unbalanced heterodyne configuration. The intensity pattern formed by interference between a weak signal field and a strong…
There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has…