The success of applying generalized complex orthogonal designs as space-time block codes recently motivated the definition of quaternion orthogonal designs as potential building blocks for space-time-polarization block codes. Since complex orthogonal designs with no zero entries have proven important in applications, this paper offers a construction for an infinite family of restricted quaterni...

The quaternion wavelet transform is a new multiscale analysis tool. Firstly, this paper studies the standard orthogonal basis of scale space and wavelet space of quaternion wavelet transform in spatial L2 R2 , proves and presents quaternion wavelet’s scale basis function and wavelet basis function concepts in spatial scale space L2 R2;H , and studies quaternion wavelet transform structure. Fina...

Nomenclature = normalized Euler rotation axis i<1-3> = indices of first, second and third Euler rotation, e.g. if rotation sequence is 3-2-1, i1 is 3, i2 is 2, and i3 is 1 i<1-3>n = next circular index following i<1-3>, e.g. if i2 = 3, i2n = 1 i<1-3>nn = next circular index following i<1-3>n, e.g. if i2n = 3, i2nn = 2 = Quaternion = = operator: rotation of vector by a quaternion vi = unit vecto...

In this paper, cyclic codes are established over some finite quaternion integer rings with respect to the quaternion Mannheim distance, and decoding algorithm for these codes is given. 2000 AMS Classification: 94B05, 94B15, 94B35, 94B60

In this article, we obtain sharp estimate of the Ricci curvature of quaternion slant, bi-slant and semi-slant submanifolds in a quaternion space form, in terms of the squared mean curvature.

We describe a fast algorithm for the 2-D left-side QDFT which is based on the concept of the tensor representation when the color or four-componnrnt quaternion image is described by a set of 1-D quaternion signals and the 1-D left-side QDFTs over these signals determine values of the 2-D left-side QDFT at corresponding subset of frequency-points. The efficiency of the tensor algorithm for calcu...

A split quaternion learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of three- and four-dimensional signals is proposed. The derivation takes into account the non-commutativity of the quaternion product, an aspect neglected in the derivation of the existing learning algorithms. It is shown that the additional information taken into acco...

The 2D Quaternionic Fourier Transform (QFT), applied to a real 2D image, produces an invertible quaternionic spectrum. If we conserve uniquely the first quadrant of this spectrum, it is possible, after inverse transformation, to obtain, not the original image, but a 2D quaternion image, which generalize in 2D the classical notion of 1D analytical image. From this quaternion image, we compute th...

The Fourier transforms plays a critical role in broad range of image processing applications, including enhancement, restoration, analysis and compression. For filtering of gray scale images 2D Fourier transform is an important tool which converts the image from spatial domain to frequency domain and then by applying filtering mask filtering is done. To filter color images, a new approach is im...