Full Quaternion Research Articles

Pyramid quaternion discrete cosine transform based ConvNet for cancelable face recognition

The current face scanning era can quickly and conveniently attain identity authentication, but face images imply sensitive information simultaneously. Under such context, we introduce a novel cancelable face recognition methodology by using quaternion transform based convolutional network. Firstly, face images in different modalities (e.g., RGB and depth or near-infrared) are encoded into full quaternion matrix for synchronous processing. Based on the designed multiresolution quaternion singular value decomposition, we can obtain pyramid representation. Then they are transformed through random projection for making the process noninvertible. Even if the feature template is compromised, a new one can be generated. Subsequently, a three-stream convolutional network is developed to learn features, where predefined filters are stemmed from quaternion two-dimensional discrete cosine transform basis. Extensive experiments on the TIII-D, NVIE and CASIA datasets have demonstrated that the proposed method obtains competitive performance, also satisfies redistributable and irreversible.

Quaternion-based 2D-DOST and stacked principal component analysis network for multimodal face recognition

Face recognition is widely utilized and has become a ubiquitous part of daily lives. However, original face images are often sensitive and unauthorized access could imperil personal information. To protect privacy and security of multimodal face data, we propose an original approach that integrates differential privacy and a lightweight convolutional neural network with unsupervised predefined quaternion-type filters. Firstly, different modalities of face images are banded together by means of full quaternion matrix representation for simultaneously processing. Then the proposed quaternion two-dimensional discrete orthogonal Stockwell transform is exploited for implementing difference privacy, which is disturbed by virtue of Laplace and exponential mechanism. Afterwards, we devise a stacked quaternion two-dimensional principal component analysis network with three-stages for learning representative features. The proposed network model can enhance the discriminative characteristics through inserting nonlinearity, together with union of feature maps in different levels to achieve information complementation. Experiments conducted on four multimodal face datasets unveil that the proposed method achieves superior recognition performance in comparison with other state-of-the-art approaches.

Prescribed-Time Spacecraft Attitude Control Using Time-Varying State Feedback

A time-varying feedback control law based on backstepping is proposed for the prescribed arbitrary time stabilization and tracking for a chain of integrators. Prescribed arbitrary time control permits the convergence time to be chosen regardless of the initial conditions or system parameters. The sufficient condition is used to demonstrate Lyapunov stability for the system. Analytical results and explanations are provided for the influence of convergence time on the maximum needed control torque. Sliding mode control is paired with the time-varying feedback approach to make the control law robust to reject the bounded disturbance. The control law is then applied to a spacecraft’s attitude motion that is susceptible to the bounded disturbance. A quaternion-based attitude representation is utilized to avoid mathematical singularity. The control law is written using a full quaternion with four components instead of only three in the vector part. Finally, promising numerical simulation results are presented.

Attitude estimation: with or without spacecraft dynamics?

Kalman filter based spacecraft attitude estimation has been used in many space missions and has been widely discussed in literature. While some models in spacecraft attitude estimation include spacecraft dynamics, most do not. To our best knowledge, there is no analysis to determine which model is a better choice. In this paper, we discuss the reasons why spacecraft dynamics should be considered in the Kalman filter based spacecraft attitude estimation problem. We also propose a reduced quaternion spacecraft dynamics model which admits additive noise. Geometry of the reduced quaternion model and the additive noise are discussed. This formulation makes computation easier than the one with full quaternion. Simulations are conducted to justify our claims.

Fully Quaternion-Valued Adaptive Beamforming Based on Crossed-Dipole Arrays

Based on crossed-dipole antenna arrays, quaternion-valued data models have been developed for both direction of arrival estimation and beamforming in the past. However, for almost all the models, and especially for adaptive beamforming, the desired signal is still complex-valued as in the quaternion-valued Capon beamformer. Since the complex-valued desired signal only has two components, while there are four components in a quaternion, only two components of the quaternion-valued beamformer output are used and the remaining two are simply discarded, leading to significant redundancy in its implementation. In this work, we consider a quaternion-valued desired signal and develop a fully quaternion-valued Capon beamformer which has a better performance and a much lower complexity. Furthermore, based on this full quaternion model, the robust beamforming problem is also studied in the presence of steering vector errors and a worst-case-based robust beamformer is developed. The performance of the proposed methods is verified by computer simulations.

A Novel Perceptual Hashing for Color Images Using a Full Quaternion Representation

A Novel Perceptual Hashing for Color Images Using a Full Quaternion Representation

A Novel Perceptual Hashing for Color Images Using a Full Quaternion Representation

Quaternions have been commonly employed in color image processing, but when the existing pure quaternion representation for color images is used in perceptual hashing, it would degrade the robustness performance since it is sensitive to image manipulations. To improve the robustness in color image perceptual hashing, in this paper a full quaternion representation for color images is proposed by introducing the local image luminance variances. Based on this new representation, a novel Full Quaternion Discrete Cosine Transform (FQDCT)-based hashing is proposed, in which the Quaternion Discrete Cosine Transform (QDCT) is applied to the pseudo-randomly selected regions of the novel full quaternion image to construct two feature matrices. A new hash value in binary is generated from these two matrices. Our experimental results have validated the robustness improvement brought by the proposed full quaternion representation and demonstrated that better performance can be achieved in the proposed FQDCT-based hashing than that in other notable quaternion-based hashing schemes in terms of robustness and discriminability.

High-precision full quaternion based finite-time cascade attitude control strategy considering a class of overactuated space systems

AbstractA high-precision full quaternion based finite-time three-axis cascade attitude control strategy is considered in the present research with respect to state-of-the-art to deal with a class of overactuated space systems. The main idea behind the subject is to design a new quaternion based proportional derivative approach, which is realized along with the linear quadratic regulator method. In a word, the control technique proposed here is organized based upon an inner closed loop control to handle the angular rates in the three axes and the corresponding outer closed loop to handle the rotational angles in the same three axes, as well. It aims us to cope with the present complex and complicated systems, in the productive and constructive manner, in a number of programmed space missions such as orbital, communicational, thermal and so on maneuvers. It can be shown that the proposed cascade control strategy is organized in association with a set of pulse-width pulse-frequency modulators to drive a number of on–off reaction thrusters. It should be noted that these ones could significantly be increased w. r. t. the investigated control efforts, in order to provide overall accurate performance of the present space systems. There is currently a control allocation realization to complete the process of the approach presentation and organization. At last, the investigated results are presented in comparison with some potential benchmarks to guarantee and verify the approach performance.

Full quaternion based finite-time cascade attitude control approach via pulse modulation synthesis for a spacecraft

In the aspect of further development of investigations in the area of spacecraft modeling and analysis of the control scheme, a new hybrid finite-time robust three-axis cascade attitude control approach is proposed via pulse modulation synthesis. The full quaternion based control approach proposed here is organized in association with both the inner and the outer closed loops. It is shown that the inner closed loop, which consists of the sliding mode finite-time control approach, the pulse width pulse frequency modulator, the control allocation and finally the dynamics of the spacecraft is realized to track the three-axis referenced commands of the angular velocities. The pulse width pulse frequency modulators are in fact employed in the inner closed loop to accommodate the control signals to a number of on–off thrusters, while the control allocation algorithm provides the commanded firing times for the reaction control thrusters in the overactuated spacecraft. Hereinafter, the outer closed loop, which consists of the proportional linear control approach and the kinematics of the spacecraft is correspondingly designed to deal with the attitude angles that are presented by quaternion vector. It should be noted that the main motivation of the present research is to realize a hybrid control method by using linear and nonlinear terms and to provide a reliable and robust control structure, which is able to track time varying three-axis referenced commands. Subsequently, a stability analysis is presented to verify the performance of the overall proposed cascade attitude control approach. To prove the effectiveness of the presented approach, a thorough investigation is presented compared to a number of recent corresponding benchmarks.

Computational aspects of the continuum quaternionic wave functions for hydrogen

Over the past few years considerable attention has been given to the role played by the Hydrogen Continuum Wave Functions (HCWFs) in quantum theory. The HCWFs arise via the method of separation of variables for the time-independent Schrödinger equation in spherical coordinates. The HCWFs are composed of products of a radial part involving associated Laguerre polynomials multiplied by exponential factors and an angular part that is the spherical harmonics. In the present paper we introduce the continuum wave functions for hydrogen within quaternionic analysis ((R)QHCWFs), a result which is not available in the existing literature. In particular, the underlying functions are of three real variables and take on either values in the reduced and full quaternions (identified, respectively, with R3 and R4). We prove that the (R)QHCWFs are orthonormal to one another. The representation of these functions in terms of the HCWFs are explicitly given, from which several recurrence formulae for fast computer implementations can be derived. A summary of fundamental properties and further computation of the hydrogen-like atom transforms of the (R)QHCWFs are also discussed. We address all the above and explore some basic facts of the arising quaternionic function theory. As an application, we provide the reader with plot simulations that demonstrate the effectiveness of our approach.(R)QHCWFs are new in the literature and have some consequences that are now under investigation.

ON CONVERGENCE PROPERTIES OF 3D SPHEROIDAL MONOGENICS

Morais has recently introduced certain complete orthogonal sets of monogenic polynomials over 3D prolate spheroids with remarkable properties. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with ℝ3and ℝ4), and are generally assumed to be nullsolutions of the well known Riesz and Moisil–Théodoresco systems in ℝ3. In continuation of these studies, we recall some fundamental properties of the polynomials, and prove some recursive formulae between them. As a consequence, we obtain a two-term type recurrence relation satisfied by those basis polynomials. These results are then employed to investigate a rather wide class of approximation properties for monogenic functions over 3D prolate spheroids in terms of spheroidal monogenics.

Comparison of space launcher equations of translation using a full quaternion

This paper extends the nonstandard full quaternion formulation of the orbital motion to the propelled motion of a space launcher. The main goal of this paper is to compare the resulting equations with two classic formulations using polar coordinates and Cartesian coordinates. The mathematical development of the full quaternion scheme is presented as it explains the absence of discontinuities over the poles. This paper also introduces the equations linking the polar coordinates scheme to the full quaternion scheme. These equations are important for discontinuity avoidance purposes as they define the relations between the two representations. The full quaternion, the polar coordinates, and the Cartesian coordinates formulations are then compared using three basis: accuracy, discontinuity avoidance, and computation time. As the three schemes are equally accurate, this analysis concludes that, based on computation time, the standard polar coordinates scheme is the best for nearly all desirable orbits. However, because of a discontinuity, it is not recommended for high inclination orbits. In that case, the full quaternion scheme should be considered as the first alternative.

THE LORF ORBIT EQUATION WITH FULL QUATERNIONS

The Local Orbital Reference Frame (LORF) is a Cartesian frame tangential to the trajectory of an orbiting satellite. The orbital motion of the satellite entrains the movement of the LORF around an Inertial Reference Frame (IRF). In this paper, the classical orbit equations (written in terms of inertial position and velocity vectors) are transformed into the LORF orbit equations, by means of full quaternions. Simple application examples are presented.

Orbit Dynamics and Kinematics with Full Quaternions

Full quaternions constitute a compact notation for describing the motion of a body in the space. An important result about full quaternions is that they can be partitioned into a unit quaternion (which describes the orientation with respect to a suitable reference), and a modulus (which represents the translational motion along the direction indicated by the unit quaternion). Since vectors and scalars are also fullquaternions, the equations of body motion can be rewritten in quaternion form. In this paper the orbit dynamics and kinematics of a point mass moving in the space are transformed in quaternion form. Simple application examples are presented.