Quaternionvalued wireless communication systems have been studied in the past. Morerecently,hypercomplexspectraltransformations and color images processing techniques have been introduced by ell and sangwine in 25 and pei and cheng in 6. Since animated motions comprise of signals, it is no surprise that the fourier trans. It is a context for learning fundamentals of computer programming within the context of the electronic arts. Color images can be treated as twodimensional quaternion functions. Pdf full 4d quaternion discrete fourier transform based. Adaptive beamforming based on complex quaternion processes.
Image disparity estimation is a hypercomplex, phase based technique, using quaternions, that can nd differences between subtlety varying images. Dividing a nonzero quaternion q by its norm produces a unit quaternion uq called the versor of q. The generalized quaternion fourier transform of the quaternion image q n,m is defined as 7 where the basic functions of the transform are the 2d qdft is parameterized, i. May 07, 2014 based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to quaternion fourier transforms.
Lti filtering theory of bivariate signals is proposed based on a tailored quaternion. Let us now introduce the rotation and involution operations. A signal processing based on quaternion for three axes. Feb 05, 2018 processings chirality, viewed in an orthographic camera from. Singular value decomposition ofquaternion matrices. Simulation results based on vector sensor arrays are presented as an example to demonstrate the effectiveness of the quaternion valued signal model and the derived signal processing algorithm. Introduction quaternion calculus has been introduced in signal process. Properties of a general quaternionvalued gradient operator. Quaternionbased kalman filtering on insgps yuhong yang, junchuan zhou and otmar loffeld center for sensorsystems zess, university of siegen siegen, germany abstract in this paper, two quaternionbased nonlinear filtering methods are applied on the processing of measurements from the lowcost microelectromechanical systems mems. I remember having lifted up a quaternion class i wrote a while ago, you can find it in. Problems where the unknown parameter is a quaternion matrix are wide ranging including array signal processing 12, spacetime coding 1618, and quaternion orthogonal designs 20.
Quaternion based edge detection and pattern matching are then implemented on segmentation results to locate glands. Image disparity estimation is a hypercomplex, phase based technique, using quaternions, that can find differences between subtlety varying images. Using quaternions to do a 3d rotation processing 2. Quaternions also admit the euler representation 6 where is a pure unit quaternion and is the angle or argument of the quaternion. Fourier inversion plays a crucial role in signal processing and. Efficient implementation of quaternion fourier transform. Full 4d quaternion discrete fourier transform based.
Pdf quaternionbased signal processing researchgate. Recently, three methods for obtaining the quaternion gradient have been. Processing is an electronic sketchbook for developing ideas. Quaternion based signal processing ben witten and jeff shragge abstract hypercomlex numbers, which have primarily been used for pattern recognition, offer many useful applications to geophysics. Pdf quaternionbased signal processing jeffrey shragge. Versatile quaternion multipliers based on distributed. Quaternion based optical flow tracking first letas introduce some quaternion notations used in this per. For analysis of quaternion images, a joint spacewavenumber localized quaternion s transform qs is presented in this study for a simultaneous determination of the local color image spectra. Pdf color image processing by using binary quaternion. Many fundamental algorithms can be realized by dft, such us the convolution, spectrum estimation and correlation. The quaternion gradient plays an important role in quaternion signal processing, and has undergone several modifications. Stott a clive cheong took b yili xia c sithan kanna a danilo p. Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to quaternion fourier transforms.
Mcghee, life fellow, ieee abstractorientation of a static or slowmoving rigid body can be determined from the measured gravity and local magnetic. Orthonormal vectors orthogonal and normalized, or perpendiculars of unit length are no less arbitrary for world space. Quaternion valued signal processing, neural networks, and machine learning. Quaternions and octonions in signal processing fundamentals and some. Quaternionvalued stochastic gradientbased adaptive. First, a complex quaternion leastmean squares cqlms algorithm is proposed and its performance is analyzed. Image disparity estimation is a hypercomplex, phasebased technique, using quaternions, that can find differences between subtlety varying images. Simultaneous diagonalisation of the covariance and. This paper introduces the idea of versatile circuits for multiplying 4dimensional hypercomplex numbers in hardware. Analytical formulas of the bqmp thresholding can thus be determined by using. The link includes a really good reference on the subject if you want to dig deeper.
Hypercomplex numbers are primarily used for pattern recognition, offer many useful applications to geophysics. Consequently, the quantitative analysis is available based on the extracted glands. During the recent years, signal processing research started investigating hypercomplex numbers and their usefulness in the modeling of systems. First, a quaternion model of linear symmetric array with twocomponent electromagnetic em vector sensors is presented. We then study the problem ofvectorsensor array signals, and introduce a subspace method for wave separation on such arrays. Partial encryption of color image using quaternion. Based on representing color data by the quaternions, the statistical parameters of color data can be expressed through the definition of quaternion moments. We propose the quaternion number system for numerical representation and further processing on dna sequences.
The 2d quaternion wavelets, like the 2d analytic signal described in. This paper presents a new momentpreserving thresholding technique, called the binary quaternionmomentpreserving bqmp thresholding, for color image data. Quaternions can be used as an alternative to model the fundamental patterns of electroencephalographic eeg signals in the time domain. Quaternion based segmentation for vanilla recognition ted shaneyfelt, sos agaian, mo jamshidi electrical and computer engineering the university of texas at san antonio san antonio, usa ted. Simulation results based on vector sensor arrays are presented as an example to demonstrate the effectiveness of the quaternionvalued signal model and the derived signal processing algorithm. With most recent developments in quaternionvalued signal. In this paper, we will develop efficient algorithms for. We present a new approach for vectorsensor signal modelling and processing, based on the use of quaternion algebra. Quaternionvalued stochastic gradientbased adaptive iir filtering, ieee transactions on signal processing, vol. The qwt forms a tight frame and can be efficiently com puted using a 2d dualtree tilter hank. The generalized sidelobe canceller based on quaternion widely.
Dna sequence representation and comparison based on. As an important tool of multidimensional signal processing, the quaternion algebra has been applied to parameter estimation of 2d harmonic signals, doa estimation of polarized signals 24, image processing, spacetimepolarization block codes, kalman filter, adaptive filter 8, 9, independent component analysis ica algorithm, widely linear modeling and. Pdf quaternion filtering based on quaternion involutions. Ell 1992 introduced the quaternionic fourier transform qft for twodimensional signals, fqu d z r2 e i2. Quaternion fourier transforms for signal and image processing. We investigate the problem of quaternion beamforming based on widely linear processing. To illustrate the potential of the qaut in rank reduction of quaternion data, a 2d quaternion process, x 1, x 2, was generated where x 1 and x 2 were highly correlated as shown in fig.
A quaternionbased sparse tight frame qstf is proposed with the help of quaternion matrix and tight frame analyses, which can be. Quaternionvalued adaptive signal processing and its. Quaternion fourier transform for character motions ben kenwrighty abstract the fourier transform plays a crucial role in a broad range of signal processing applications, including enhancement, restoration, analysis, and compression. To this end, based on the isomorphism with real vectors and the use of quaternion involutions, we. In this paper, we will develop efficient algorithms for qft, qcv, and quaternion correlation.
There are different ways of combining the signal processing approach and the cfd approach to obtain a more effective and ef. Pdf quaternions and octonions in signal processing. We introduce the concept ofquaternionic signal and give some primary tools to characterize it. For any complex number, z d a cib, the argument or phaseangle is dened as atan2b,a. Image disparity estimation is a hypercomplex, phasebased technique, using quaternions that can find differences between subtly varying. The books attention to mathematical concepts, imaging applications, and matlab compatibility render it an irreplaceable. Pathological signal quantitative analysis using quaternion. Article pdf available in digital signal processing 281.
Multiplierless circuits based on distributed arithmetic da are. Local quaternion fourier transform and color image texture. The proposed socalled quaternion based signal analysis qsa method described in algorithm 1 table 2 can be used to model multichannel eeg signals using quaternions, taking a set of input signals as a single entity, and converting it into a pure quaternion. Rather than reading a large number of medical images all by themselves, doctors can provide diagnosis more efficiently and more accurately using. A concept manipulating multiple signals from three axes sensors flexibly is presented. Using conjugation and the norm makes it possible to define the reciprocal of a nonzero quaternion.
Our quaternion wavelet transform is similar to the quaternion fourier transform qft in the use of quaternion algebra 5. Motivated by the benefits of array signal processing in quaternion domain, we investigate the problem of adaptive beamforming based on complex quaternion processes in this paper. Although progress has been made in this promising area, a crucial missing link is lack of effective and ef. The cqlms algorithm is suitable for adaptive beamforming of vectorsensor array. Quaternion based optical flow estimation for robust object. The advantage of using quaternion based operations to manipulate color. In the combined method, the signal processing part employs the qlms algorithm, while for the cfd part, large eddy simulation les based on the smagorinsky. The high cost of vanilla has led to the problem of. Full 4d quaternion discrete fourier transform based watermarking for color images. Qft is a central component of processing color images and complex valued signals. However, the necessary computational algorithms and their complexity still need some attention. Recently, however, quaternions have been applied to signal processing, most notably pattern recogni tion. Quaternionbased signal processing will be considered to be 0 since only 2d images are discussed in this paper. Depending on the settings of such a device, a variable quaternion can be left or rightmultiplied by a constant coefficient or by its conjugate, as various operations are useful in transformtype algorithms.
In the proposed method, the quaternion crosscorrelation operation can. To begin with, the expression form based on a quaternion is applied to the three channel measurement signals from a sensor in order to stand for those scalar signals with a single signal channel in real system. Quaternionbased signal processing stanford university. Thus, this article presents a new quaternionbased technique known as quaternionbased signal analysis qsa to represent eeg signals obtained using a braincomputer interface bci device to detect and interpret cognitive activity. Quaternionbased signal analysis for motor imagery classification. In signal processing, it is only in the last decade that quaternionbased algorithms were proposed1. A complete framework for linear filtering of bivariate signals arxiv. A hypercomplex version of the multidimensional complex. The qwt and the 2d complex wavclet transform cwt are related by a unitary trans formation. The product of a quaternion with its reciprocal should equal 1, and the. This technique relies on applying a quaternionic fourier transform, a quaternionic gabor filter and exploits the symmetries inherent in the quaternion. Quaternion fourier and linear canonical inversion theorems. Recently, the topic of generalization of the ft to the quaternion algebra called the quaternion fourier transform qft has received considerable attention. Thus, this article presents a new quaternionbased technique known as quaternionbased signal analysis qsa to represent eeg signals.
800 188 705 1075 67 693 551 811 1286 697 966 597 1177 795 733 1068 1397 536 433 1265 20 1020 355 1068 1412 1481 702 926 137 1194 901 183 1365 756 1102