May 23, 2012 quaternion based adaptive output feedback attitude control of spacecraft using chebyshev neural networks ieee transactions on neural networks, vol. Quaternionbased encryptiondecryption of audio signal using. 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. The proposed socalled quaternionbased 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. We have developed a quaternion based sparse tight frame qstf with the help of quaternion matrix and tight frame analyses, which can be used to process the vectorvalued multicomponent data by following a vectorial processing workflow. Thus, this article presents a new quaternion based technique known as quaternion based signal analysis qsa to represent eeg signals obtained using a braincomputer interface bci device to detect and interpret cognitive activity. Mandic, the quaternion lms algorithm for adaptive filtering of hypercomplex processes, ieee trans. Different kinds of quaternion signal detection problems in continuoustime by using a widely linear processing are dealt with. Quaternionbased signal processing ben witten and jeff shragge abstract hypercomlex numbers, which have primarily been used for pattern recognition, offer many useful applications to geophysics. Quaternionic rankreduction methods for vectorfield seismic data. The cqlms algorithm is suitable for adaptive beamforming of vectorsensor array. Quaternions and octonions in signal processing fundamentals and some new results. The book s attention to mathematical concepts, imaging applications, and matlab compatibility render it an irreplaceable.
A novel perceptual hashing for color images using a full quaternion representation. During the recent years, signal processing research started investigating hypercomplex numbers and their usefulness in the modeling of systems. The ideas of instantaneous amplitude and phase are well understood for signals with realvalued samples, based on the analytic signal which is a complex signal with onesided fourier transform. Beamformer based on quaternion processes intechopen.
Steve sangwine 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. Many books discuss about quaternions and their properties. Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results. Recently, three methods for obtaining the quaternion gradient have been proposed based on generalized hr calculus, the quaternion product, and. Sensors free fulltext quaternionbased signal analysis. Singular value decomposition of quaternion matrices. The book s attention to mathematical concepts, imaging applications, and matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers. Morerecently,hypercomplexspectraltransformations and color images processing techniques have been introduced by. 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. However, floating point math is far from being perfectly precise, and errors accumulate the more operations you do. Efficient implementation of quaternion fourier transform. A signal processing based on quaternion for three axes. At present, many proposals include quaternion, octonion and lie algebra solutions. Qft is a central component of processing color images and com.
This expansion presents the notable advantage of transforming the original four. Quaternion singular value decomposition qsvd is imposed on quaternion matrix to conduct dimension reduction of color vector data and to obtain color texture segmentation using kmeans technique. Adaptive filtering using complex data and quaternions. The last and longest of his books, elements of quaternions, was 800 pages long. We investigate the problem of quaternion beamforming based on widely linear processing. Pathological signal quantitative analysis using quaternion.
Image disparity estimation is a hypercomplex, phasebased technique, using quaternions, that can nd differences between subtlety varying images. Quaternions can be used as an alternative to model the fundamental patterns of electroencephalographic eeg signals in the time domain. A novel perceptual hashing for color images using a full. Processing is an electronic sketchbook for developing ideas. Instantaneous frequency and amplitude of orthocomplex. Quaternionmusic for vectorsensor array processing gipsa lab. Ieee transactions on signal processing 1 quaternionmusic for vectorsensor array processing abstract this paper considers the problem of direction of arrival doa and polarization parameters estimation in the case of multiple polarized sources impinging on a. Detection of continuoustime quaternion signals in additive. Report by international journal of communication networks and information security ijcnis. Frequency domain quaternion adaptive filters signal processing.
First, a quaternion model of linear symmetric array with twocomponent electromagnetic em vector sensors is presented. This expansion presents the notable advantage of transforming the original fourdimensional. According to the development of the real fractional differential and its applications in the modern signal processing, the authors extend it to quaternion body and put forward a new concept. The potential advantages of multidimensional signal processing are. First, a complex quaternion leastmean squares cqlms algorithm is proposed and its performance is analyzed. 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. Based on arrays quaternion model, we propose the general expression of a quaternion semiwidely linear qswl beamformer. 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. It is based on the work of authors in this field of study and presents mathematical concepts. Decomposition of 2d hypercomplex fourier transforms into pairs of complex fourier transforms.
We then study the problem of vectorsensor array signals, and introduce a subspace method for wave separation on such arrays. 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. Applications signal processing and wavelet math are good partners, opening the door to hypercomplex analysis 1 hypercomplex analysis is used to power many wavelet applications. 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.
Quaternion valued signal processing, neural networks, and machine learning. Quaternionbased adaptive output feedback attitude control of spacecraft using chebyshev neural networks ieee transactions on neural networks, vol. 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. Yang, an image quality assessment metric based on quaternion wavelet transform, in. In this chapter, the problem of quaternion beamformer based on linear and widely linear hypercomplex processing is investigated in scenarios, where there exist one signal and one interference that are uncorrelated.
Adaptive beamforming based on complex quaternion processes. Quaternionbased polarimetric array manifold interpolation. Read quaternion fourier transforms for signal and image processing by todd a. The suggested solutions are based on an extension of the karhunenloeve expansion to the quaternion domain which provides uncorrelated scalar realvalued random coefficients. Quaternion based edge detection and pattern matching are then implemented on segmentation results to locate glands. A novel quaternionvalued leastmean kurtosis qlmk adaptive filtering algorithm is proposed for three and fourdimensional processes by using the recent generalised hamiltonreal ghr calculus.
Edge detection of colour image based on quaternion fractional. Computers and internet cryptography methods data security signal processing. Quaternionbased sparse tight frame for multicomponent signal. Quaternion fourier transforms for signal and image. Proceedings of the 20 ieee international conference on multimedia and expo workshops icmew 20, held in san jose, california. For this reason, quaternions are used in computer graphics, computer vision, robotics, control theory, signal processing, attitude control, physics. The development of the quaternion wavelet transform signal. Widely linear modeling, quaternion lms qlms, quaternion widely linear lms wlqlms, adaptive prediction, wind forecasting.
After the signal expression based on quaternion is given, a transformation of measurement signal into a series of periodic function and its inverse is led. Quaternion fourier transforms for signal and image processing. Quaternion fourier transforms for signal and image processing presents stateoftheart together with the most recent research results, in the use of quaternion fourier transforms qft for the processing of color images and complex valued signals. Quaternionbased encryptiondecryption of audio signal using digital image as a variable key. To manipulate three axes sensors signals simultaneously, a signal processing using quaternion form is presented. In signal processing, it is only in the last decade that quaternionbased algorithms were proposed1. Three dimensional signal processing based on quaternion abstract.
The quaternion gradient plays an important role in quaternion signal processing, and has undergone several modifications. Quaternion filtering based on quaternion involutions and its. Quaternionbased signal processing ben witten and jeff shragge, stanford university summary and multiplication as hypercomlex numbers are primarily used for pattern recognition, offer many useful applications to geophysics. Quaternionbased edge detection and pattern matching are then implemented on. Three dimensional signal processing based on quaternion. The book s attention to mathematical concepts quaternion fourier transforms for signal and image processing focus series. Based on updates to signal and image processing technology made in the last two decades, this text examines the most rec. Quaternions and octonions in signal processing fundamentals. Kuosmanen, editors, proceedings of eusipco 2000, tenth european signal processing conference, volume ii, pages 10611064, tampere, finland, 58 sept. Since a lot of signal processing is based on linear algebra the noncommutativity has to be considered. Report by ksii transactions on internet and information systems. Computers and internet engineering research hashing functions methods image processing quaternions mathematics research transformations mathematics.
Efficient implementation of quaternion fourier transform, convolution. Quaternionbased robust attitude estimation using an adaptive unscented kalman filter. Based on updates to signal and image processing technology made in the last. We have developed a quaternionbased sparse tight frame qstf with the help of quaternion matrix and tight frame analyses, which can be used to process the vectorvalued multicomponent data by following a vectorial processing workflow. Buy quaternion fourier transforms for signal and image processing focus series.
Pdf quaternions and octonions in signal processing. The concepts of quaternion fourier transform qft, quaternion convolution qcv, and quaternion correlation, which are based on quaternion algebra, have b. Ieee transactions on signal processing 1 quaternion music for vectorsensor array processing abstract this paper considers the problem of direction of arrival doa and polarization parameters estimation in the case of multiple polarized sources impinging on a vectorsensor array. Quaternionbased polarimetric array manifold interpolation signal. A concept manipulating multiple signals from three axes sensors flexibly is presented. In this chapter, the problem of quaternion beamformer based on linear and. 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. Adoption of quaternions requires a shift from real or complex signal processing to quaternionbased signal processing. In signal processing, it is only in the last decade that quaternion based. Recently, however, quaternions have been applied to signal processing, most notably pattern recogni tion.
Pdf quaternionbased signal processing jeffrey shragge. We introduce the concept of quaternionic signal and give some primary tools to characterize it. Qft is a central component of processing color images and complex valued signals. Averaging quaternions journal of guidance, control, and. First, we introduce brief information about the quaternion algebra and a quaternion model of linear symmetric array with twocomponent electromagnetic em vectorsensors is. We provide an overview of complexdata and quaternionbased nonlinear.
Thus, we will adopt a notation first presented in 20 and later analyzed in 21. Throughout this work two distinct matrix products are used. Together, digital signal processing groups started developing multidimensional algorithms in the hypercomplex domains. We present a new approach for vectorsensor signal modelling and processing, based on the use of quaternion algebra. As already pointed out by guyrt, the way you do accumulation is not good. Quaternionbased adaptive attitude tracking controller. The generalized sidelobe canceller based on quaternion widely. Image disparity estimation is a hypercomplex, phase based technique, using quaternions, that can nd differences between subtlety varying images. Recently, three methods for obtaining the quaternion gradient have been proposed based on generalized hr calculus, the quaternion product, and quaternion involutions, respectively. Quaternionbased signal processing stanford university.
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