Recent developments in quaternion-valued widely linear processing have established that the exploitation of complete second-order statistics requires consideration of both the standard covariance and the three complementary covariance matrices. Although such matrices have a tremendous amount of structure and their decomposition is a powerful tool in a variety of applications, the noncommutative...

In this paper, the quaternion Bessel-Fourier moments are introduced. The significance of phase information in quaternion Bessel-Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel-Fourier moments is derived. Experimental results sho...

The goal of this note is to give an elementary characterization of the well-known quaternion group Q8 by using its subgroup lattice.

We compute the number of symmetric r-colorings and the number of equivalence classes of symmetric r-colorings of the quaternion group.

Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms for channel equalization and beamforming. With most recent developments in quaternion-valued signal processing, in this work, we fill the gap to solve the p...

Lattices are a popular field of study in mathematical research, but also more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In theory, most often lattices over real numbers considered. However, communications, complex-valued processing is usually interest. Besides, by the use dual-polarized transmission as well combination two time slots frequencies, fou...

in this investigation, the effect of group cognitive-behavior therapy in reduction of anxiety and dysfunctional attitude were studied on patients with generalized anxiety disorder (gad). 20 female participants were recognized to have gad by the researcher through a clinical interview on the basis of dsm-iv-tr standards and invited to take part in the study. they first filled in the dysfunctiona...

The recently developed concepts of quaternion Fourier transform (QFT), quaternion convolution (QCV), and quaternion correlation, which are based on quaternion algebra, have been found to be useful for color image processing. However, the necessary computational algorithms and their complexity still need some attention. In this paper, we will develop efficient algorithms for QFT, QCV, and quater...

The generalized dynamic inversion control methodology is applied to the spacecraft attitude trajectory tracking problem. It is shown that the structure of the skew symmetric cross product matrix alleviates the need to include the inertia matrix in the control law. Accordingly, the proposed control law depends solely on attitude and angular velocity measurements, and it neither requires knowledg...