To address the non-negativity dropout problem of quaternion models, a novel quasi non-negative matrix factorization (QNQMF) model is presented for color image processing. implement QNQMF, projected gradient algorithm and alternating direction method multipliers are proposed via formulating QNQMF as non-convex constraint optimization problems. Some properties algorithms studied. The numerical ex...

Let Hmxn be the set of all m x n matrices over real quaternion algebra. We call that A ? Hnxn is ?-Hermitian if = A?* where -?A*?,? {i,j,k},i,j,k are units. In this paper, we derive some solvability conditions and general solution to a system matrix equations. As an application, present necessary sufficient for existence systems also give expressions solutions these when they solvable. Some num...

Abstract The solvability of several new constrained quaternion matrix equations is investigated, and their unique solutions are presented in terms the weighted MPD inverse DMP suitable matrices. It interesting to consider some exceptional cases these corresponding solutions. Determinantal representations for as mentioned earlier established sums appropriate minors. In order illustrate obtained ...

In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion B∗-algebras are equivalent to the category of real vector spaces, the category of real Hilbert spaces and the category of real C∗-algebras respectively. We will also give a Riesz representation theorem for quaternion...

New, efficient, 8-D rotation CORDIClike algorithms for matrix computations are presented. These algorithms are a natural extension to 8 dimensions of Quaternion CORDIC algorithms, offered by J.M. Delosme and S.F. Hsiao. This leads to significantly reduced computations in contrast to 8-D Householder CORDIC algorithms given by the same authors. Such algorithms may be utilized for designing VLSI a...

In this paper, we have proposed a novel VLSI-oriented approach to computing the rotation matrix entries from the quaternion coefficients. The advantage of this approach is the complete elimination of multiplications and replacing them by less costly squarings. Our approach uses Logan's identity, which proposes to replace the calculation of the product of two numbers on summing the squares via t...

Reducible matrices are closely associated with the connection of directed graph and can be used in stochastic processes, biology others. In this paper, we investigate reducible solution to a system matrix equations over Hamilton quaternion algebra. We establish necessary sufficient conditions for have derive formula general when it is solvable. Finally, present numerical example illustrate main...

An extension of the FastICA algorithm is proposed for the blind separation of both Q-proper and Q-improper quaternionvalued signals. This is achieved by maximising a negentropy-based cost function, and is implemented using the Newton method in the augmented quaternion statistics framework. It is shown that the use of augmented statistics and the associated widely linear modeling provide theoret...