Color image compression is a commonly used process to represent image data as few bits as possible, which removes redundancy in the data while maintaining an appropriate level of quality for the user. Color image compression algorithms based on quaternion are very common in recent years. In this paper, we propose a color image compression scheme, based on the real SVD, named real compression sc...

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, we offer and discuss three efficient structural solutions for the hardware-oriented implementation of discrete quaternion Fourier transform basic operations with reduced implementation complexities. The first solution a scheme for calculating sq product, the second solution – a scheme for calculating qt product, and the third solution – a scheme for calculating sqt product, where...

Hamiltonian matrices with respect to a nondegenerate skewsymmetric or skewhermitian indefinite inner product in finite dimensional real, complex, or quaternion vector spaces are studied. Subspaces that are simultaneously invariant for the matrices and neutral in the indefinite inner product are of special interest. The dimension of maximal (by inclusion) such subspaces is identified in terms of...

The strictly linear quaternion valued affine projection algorithm (QAPA) and its widely linear counterpart (WLQAPA) are introduced, in order to provide fast converging stochastic gradient learning in the quaternion domain, for the processing of both second order circular (proper) and second order noncircular (improper) signals. This is achieved based on the recent advances in augmented quaterni...

The modeling of human emotion expression in speech signals is an important, yet challenging task. high resource demand recognition models, combined with the general scarcity emotion-labelled data are obstacles to development and application effective solutions this field. In paper, we present approach jointly circumvent these difficulties. Our method, named RH-emo, a novel semi-supervised archi...

we derive the formulas of the maximal andminimal ranks of four real matrices $x_{1},x_{2},x_{3}$ and $x_{4}$in common solution $x=x_{1}+x_{2}i+x_{3}j+x_{4}k$ to quaternionmatrix equations $a_{1}x=c_{1},xb_{2}=c_{2},a_{3}xb_{3}=c_{3}$. asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. we give the exp...

Hamiltonian matrices with respect to a nondegenerate skewsymmetric or skewhermitian indefinite inner product in finite dimensional real, complex, or quaternion vector spaces are studied. Subspaces that are simultaneously invariant for the matrices and neutral in the indefinite inner product are of special interest. The dimension of maximal (by inclusion) such subspaces is identified in terms of...

ABSTRACT : Quaternion Dirac equation has been obtained from the square root of Klein-Gordon equation in compact and consistent way. Dirac matrices are described as quaternion valued and the Dirac Hamiltonian is considered as Hermitian with real eigenvalues of energy. Dirac spinors and free particle energy solution has been obtained in terms of one component, two-component and four-component Dir...