Collaborative representation-based classification (CRC) and sparse RC (SRC) have recently achieved great success in face recognition (FR). Previous CRC SRC are originally designed the real setting for grayscale image-based FR. They separately represent color channels of a query image ignore structural correlation information among channels. To remedy this limitation, paper, we propose two novel methods FR, namely, quaternion (QCRC) (QSRC) using ℓ1 minimization. By modeling each as...

This paper investigates the disturbance decoupling problem (DDP) of Boolean control networks (BCNs) by event-triggered control. Using semi-tensor product matrices, algebraic forms BCNs can be achieved, based on which, controllers are designed to solve DDP BCNs. In addition, partial is also derived Finally, two illustrative examples demonstrate effectiveness proposed methods.

We generalize the linear canonical transform (LCT) to quaternion-valued signals, known as quaternionic (QLCT). Using properties of LCT we establish an uncertainty principle for QLCT. This prescribes a lower bound on product effective widths signals in spatial and frequency domains. It is shown that only 2D Gaussian signal minimizes uncertainty.

Abstract Quaternion‐valued differential equations (QDEs) are a new kind of which have many applications in physics and life sciences. The largest difference between QDEs ordinary (ODEs) is the algebraic structure. Due to noncommutativity quaternion algebra, set all solutions linear homogenous completely different from ODEs. It actually right‐free module, not vector space . This paper establishes systematic frame work for theory , can be applied quantum mechanics, fluid Frenet geometry,...

As a new color image representation tool, quaternion has achieved excellent results in processing problems. In this paper, we propose novel low-rank matrix completion algorithm to recover missing data of image. Motivated by two kinds approximation approaches (low-rank decomposition and nuclear norm minimization) traditional matrix-based methods, combine the our model. Furthermore, is replaced sum Frobenius its factor matrices. Based on relationship between equivalent complex matrix, problem...

In this paper, we address the Clifford-valued distributed optimization subject to linear equality and inequality constraints. The objective function of problems is composed sum convex functions defined in Clifford domain. Based on generalized gradient, a system multiple recurrent neural networks (RNNs) proposed for solving problems. Each RNN minimizes local individually, with interactions others. convergence rigorously proved based Lyapunov theory. Two illustrative examples are delineated...

Prolate spheroidal wave functions (PSWFs) possess many remarkable properties. They are orthogonal basis of both square integrable space finite interval and the Paley–Wiener bandlimited on real line. No other system classical is known to obey this unique property. This raises question whether they these properties in Clifford analysis. The aim article answer extend results more flexible integral transforms, such as offset linear canonical transform. We also illustrate how use generalized...

In a recent paper, the authors have introduced windowed linear canonical transform and shown its good properties together with some applications such as Poisson summation formulas, sampling interpolation, series expansion. this we prove Paley–Wiener theorems uncertainty principles for (inverse) transform. They are new in literature has consequences that now under investigation. Copyright © 2012 John Wiley & Sons, Ltd.

In the present paper, we generalize linear canonical transform (LCT) to quaternion‐valued signals, known as quaternionic LCT (QLCT). Using properties of LCT, establish an uncertainty principle for two‐sided QLCT. This prescribes a lower bound on product effective widths signals in spatial and frequency domains. It is shown that only Gaussian signal minimizes uncertainty. Copyright © 2016 John Wiley & Sons, Ltd.

The theory of real quaternion differential equations has recently received more attention, but significant challenges remain the non‐commutativity structure. They have numerous applications throughout engineering and physics. In present investigation, Laplace transform approach to solve linear is achieved. Specifically, process solving a different equation transformed an algebraic problem. makes ODEs related initial value problems much easier. It two major advantages over methods discussed...

The theory of two-dimensional linear quaternion-valued differential equations (QDEs) was recently established (see Kou and Xia, SAPM). Some profound differences between QDEs ODEs were observed. Also, an algorithm to evaluate the fundamental matrix by employing eigenvalues eigenvectors presented in [Kou SAPM]. However, can be constructed providing that are simple. If system has multiple eigenvalues, how construct matrix? In particular, if number independent might less than dimension system....

As a new color image representation tool, quaternion has achieved excellent results in the processing, because it treats as whole rather than separate space component, thus can make full use of high correlation among RGB channels. Recently, low-rank matrix completion (LRQMC) methods have proven very useful for inpainting. In this paper, we propose three novel LRQMC based on quaternion-based bilinear factor (QBF) norm minimization models. Specifically, define double Frobenius (Q-DFN), nuclear...