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...

This paper proposesa new class of unit quaternion curves in SO(3). A general method is developed that transforms a curve in R3 (defined as a weighted sum of basis functions) into its unit quaternion analogue in SO(3). Applying the method to well-known spline curves (such as Bézier, Hermite, and B-spline curves), we are able to construct various unit quaternion curves which share many important ...

In this paper we introduce the continuous quaternion wavelet transform (CQWT). We express the admissibility condition in terms of the (right-sided) quaternion Fourier transform. We show that its fundamental properties, such as inner product, norm relation, and inversion formula, can be established whenever the quaternion wavelets satisfy a particular admissibility condition. We present several ...

Quaternion-valued signals along with quaternion Fourier transforms (QFT) provide an effective framework for vector-valued signal and image processing. However, the sampling theory of quaternion valued signals has not been well developed. In this paper, we present the generalized sampling expansions associated with QFT by using the generalized translation and convolution. We show that a σ-bandli...

Quaternion models have been developed for both direction of arrival estimation and beamforming based on crossed-dipole arrays in the past. However, for almost all the models, especially for adaptive beamforming, the desired signal is still complex-valued and one example is the quaternion-Capon beamformer. However, since the complex-valued desired signal only has two components, while there are ...

The field of deep learning has seen significant advancement in recent years. However, much of the existing work has been focused on real-valued numbers. Recent work has shown that a deep learning system using the complex numbers can be deeper for a fixed parameter budget compared to its real-valued counterpart. In this work, we explore the benefits of generalizing one step further into the hype...

The quaternion representation of colour is shown to be effective in the context of colour texture region segmentation in digital colour images. The advantage of using quaternion arithmetic is that a colour can be represented and analyzed as a single entity. A basis for the colour textures occurring in a given image is derived via quaternion principal component analysis of a training set of colo...

This paper presents a method to smoothly interpolate a given sequence of solid orientations using circular blending quaternion curves. Given three solid orientations, a circular quaternion curve is constructed that interpolates the three orientations. Therefore, given four orientations q i?1 ; q i ; q i+1 ; q i+2 , there are two circular quaternion curves C i and C i+1 which interpolate the tri...

Unit quaternion is an ideal parameterization for joint rotations. However, due to the complexity of the geometry of S group, it’s hard to specify meaningful joint constraints with unit quaternion. In this paper, we have proposed an effective and accurate method to specify the rotation limits for joints parameterized with the unit quaternion. Joint constrains constructed with our method are adeq...