Image splicing detection is of fundamental importance in digital forensics and therefore has attracted increasing attention recently. In this paper, a color image splicing detection approach is proposed based on Markov transition probability of quaternion component separation in quaternion discrete cosine transform (QDCT) domain and quaternion wavelet transform (QWT) domain. Firstly, Markov fea...

The performances of three attitude determination algorithms are compared in this paper. The three methods are the Complementary Filter, a Quaternion-based Kalman Filter and a Quaternion-based Gradient Descent Algorithm. An analysis of their performance based on an experimental investigation was undertaken. This paper shows that the Complementary Filter requires the least computational power; Qu...

Hadamard matrices with a subjacent algebraic structure have been deeply studied as well as the links with other topics in algebraic combinatorics [1]. An important and pioneering paper about this subject is [5], where it is introduced the concept of Hadamard group. In addition, we find beautiful equivalences between Hadamard groups, 2-cocyclic matrices and relative difference sets [4], [7]. Fro...

We use the quaternion Kähler reduction technique to study old and new selfdual Einstein metrics of negative scalar curvature with at least a two-dimensional isometry group, and relate the quotient construction to the hyperbolic eigenfunction Ansatz. We focus in particular on the (semi-)quaternion Kähler quotients of (semi-)quaternion Kähler hyperboloids, analysing the completeness and topology,...

An efficient widely linear prediction algorithm is introduced for the class of wide-sense stationary quaternion signals. Specifically, using second order statistics information in the quaternion domain, a multivariate Durbin–Levison-like algorithm is derived. The proposed solution can be applied under a very general formulation of the problem, allowing for the estimation of a function of the qu...

—The l 1-norm minimization problem plays an important role in the compressed sensing (CS) theory. We present in this letter an algorithm for solving the problem of l 1 Index Terms—L-norm minimization for quaternion signals by converting it to second-order cone programming. An application example of the proposed algorithm is also given for practical guidelines of perfect recovery of quaternion s...

Three and four parameter representations of 3x3 orthogonal matrices are extended to the general case of proper NxN orthogonal matrices. These developments generalize the classical Rodrigues parameter, the Euler parameters, and the recently introduced modified Rodrigues parameters to higher dimensions. The developments presented generalize and extend the classical result known as the Cayley tran...

Attitude quaternion [1] is the attitude parameterization of choice for spacecraft attitude estimation for several reasons: 1) it is free of singularities, 2) the attitude matrix is quadratic in the quaternion components, and 3) the kinematics equations is bilinear and an analytic solution exists for the propagation. However, the components of the attitude quaternion are not independent of each ...