Rotated quaternion valued algebra and its application to discrete time rotated quaternion valued Fourier transform based human signal processing

This paper proposes the concept of the rotated quaternion valued algebra and its application to the human signal processing. The conventional quaternion valued number consists of three pure imaginary components. They are the i component, the j component and the k component. These three components can be understood as these three standard principal axes in the Cartesian coordinate, in which they are orthogonal one another. In this paper, these three principal axes are rotated via multiplying to three rotational matrices. Here, these three rotational matrices perform the rotations with respect to these three principal axes, respectively. Now, the conventional discrete time quaternion valued Fourier transform is extended to the discrete time rotated quaternion valued Fourier transform based on the rotated quaternion valued system. For performing the denoising of the human signals, since the transform involves three rotational angles, the design of these three rotational angles is formulated as a nonconvex optimization problem. In particular, the objective is to minimize the total number of the transformed coefficients. In fact, this optimization problem is nonsmooth and nonconvex. To address these difficulties, an L ³ searching points algorithm is employed for finding the nearly global optimal solution of the optimization problem. To perform the regression, the features are extracted based on the various values of the rotational angles. Then, the random forest is employed for performing the feature selection. This technique is applied to perform the non-invasive blood glucose estimation. The computer numerical simulation results show that the estimation accuracy is significantly improved.