Adoption of quaternions requires a shift from real or complex signal processing to quaternionbased signal processing. 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. Recently, three methods for obtaining the quaternion gradient have been proposed based on generalized hr calculus, the quaternion product, and. 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. 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. 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. Quaternionbased polarimetric array manifold interpolation.
Efficient implementation of quaternion fourier transform. The suggested solutions are based on an extension of the karhunenloeve expansion to the quaternion domain which provides uncorrelated scalar realvalued random coefficients. Different kinds of quaternion signal detection problems in continuoustime by using a widely linear processing are dealt with. This expansion presents the notable advantage of transforming the original four. Morerecently,hypercomplexspectraltransformations and color images processing techniques have been introduced by. Throughout this work two distinct matrix products are used. First, we introduce brief information about the quaternion algebra and a quaternion model of linear symmetric array with twocomponent electromagnetic em vectorsensors is. Quaternionbased signal processing stanford university. Many books discuss about quaternions and their properties.
The book s attention to mathematical concepts quaternion fourier transforms for signal and image processing focus series. Quaternion fourier transforms for signal and image. The last and longest of his books, elements of quaternions, was 800 pages long. Image disparity estimation is a hypercomplex, phasebased technique, using quaternions, that can nd differences between subtlety varying images. 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. Proceedings of the 20 ieee international conference on multimedia and expo workshops icmew 20, held in san jose, california. Quaternionbased adaptive output feedback attitude control of spacecraft using chebyshev neural networks ieee transactions on neural networks, vol.
The cqlms algorithm is suitable for adaptive beamforming of vectorsensor array. Mandic, the quaternion lms algorithm for adaptive filtering of hypercomplex processes, ieee trans. Processing is an electronic sketchbook for developing ideas. 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. Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results. In signal processing, it is only in the last decade that quaternion based. Computers and internet cryptography methods data security signal processing. Quaternionbased polarimetric array manifold interpolation signal. During the recent years, signal processing research started investigating hypercomplex numbers and their usefulness in the modeling of systems. 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. Quaternions can be used as an alternative to model the fundamental patterns of electroencephalographic eeg signals in the time domain.
In signal processing, it is only in the last decade that quaternionbased algorithms were proposed1. 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. Beamformer based on quaternion processes intechopen. Quaternions and octonions in signal processing fundamentals. Detection of continuoustime quaternion signals in additive.
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. Quaternionbased edge detection and pattern matching are then implemented on. Decomposition of 2d hypercomplex fourier transforms into pairs of complex fourier transforms. Since the introduction of the quaternion fourier transform there has been a concern that perhaps a quaternionvalued signal or image requires a transform based on a higher algebra, just as the fourier. Adaptive filtering using complex data and quaternions. Singular value decomposition of quaternion matrices.
A concept manipulating multiple signals from three axes sensors flexibly is presented. Read quaternion fourier transforms for signal and image processing by todd a. Frequency domain quaternion adaptive filters signal processing. Based on updates to signal and image processing technology made in the last.
Quaternionbased encryptiondecryption of audio signal using. Widely linear modeling, quaternion lms qlms, quaternion widely linear lms wlqlms, adaptive prediction, wind forecasting. The potential advantages of multidimensional signal processing are. Recently, three methods for obtaining the quaternion gradient have been proposed based on generalized hr calculus, the quaternion product, and quaternion involutions, respectively. 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. Quaternionmusic for vectorsensor array processing gipsa lab. Report by ksii transactions on internet and information systems. Averaging quaternions journal of guidance, control, and. At present, many proposals include quaternion, octonion and lie algebra solutions. Quaternion based edge detection and pattern matching are then implemented on segmentation results to locate glands. This expansion presents the notable advantage of transforming the original fourdimensional. 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. A novel perceptual hashing for color images using a full.
For this reason, quaternions are used in computer graphics, computer vision, robotics, control theory, signal processing, attitude control, physics. It is based on the work of authors in this field of study and presents mathematical concepts. Quaternionbased encryptiondecryption of audio signal using digital image as a variable key. The development of the quaternion wavelet transform signal. 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.
In this chapter, the problem of quaternion beamformer based on linear and. Quaternionbased sparse tight frame for multicomponent signal. 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. Qft is a central component of processing color images and com. 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. To manipulate three axes sensors signals simultaneously, a signal processing using quaternion form is presented. Quaternion filtering based on quaternion involutions and its. We present a new approach for vectorsensor signal modelling and processing, based on the use of quaternion algebra. The book s attention to mathematical concepts, imaging applications, and matlab compatibility render it an irreplaceable. The quaternion gradient plays an important role in quaternion signal processing, and has undergone several modifications. 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. As already pointed out by guyrt, the way you do accumulation is not good.
Together, digital signal processing groups started developing multidimensional algorithms in the hypercomplex domains. Buy quaternion fourier transforms for signal and image processing focus series. 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. Report by international journal of communication networks and information security ijcnis. First, a quaternion model of linear symmetric array with twocomponent electromagnetic em vector sensors is presented. First, a complex quaternion leastmean squares cqlms algorithm is proposed and its performance is analyzed.
Qft is a central component of processing color images and complex valued signals. Thus, we will adopt a notation first presented in 20 and later analyzed in 21. Quaternionbased adaptive attitude tracking controller. 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. 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. Adaptive beamforming based on complex quaternion processes. 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. Three dimensional signal processing based on quaternion abstract. Image disparity estimation is a hypercomplex, phase based technique, using quaternions, that can nd differences between subtlety varying images. Quaternionic rankreduction methods for vectorfield seismic data. The concepts of quaternion fourier transform qft, quaternion convolution qcv, and quaternion correlation, which are based on quaternion algebra, have b. A novel perceptual hashing for color images using a full quaternion representation. A signal processing based on quaternion for three axes.
Quaternion fourier transforms for signal and image processing. Pdf quaternionbased signal processing jeffrey shragge. The generalized sidelobe canceller based on quaternion widely. The book s attention to mathematical concepts, imaging applications, and matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers. Sensors free fulltext quaternionbased signal analysis. Quaternion valued signal processing, neural networks, and machine learning.
Quaternionbased robust attitude estimation using an adaptive unscented kalman filter. Quaternions and octonions in signal processing fundamentals and some new results. Efficient implementation of quaternion fourier transform, convolution. Yang, an image quality assessment metric based on quaternion wavelet transform, in.
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. We introduce the concept of quaternionic signal and give some primary tools to characterize it. Based on updates to signal and image processing technology made in the last two decades, this text examines the most rec. May 23, 2012 quaternion based adaptive output feedback attitude control of spacecraft using chebyshev neural networks ieee transactions on neural networks, vol.
Computers and internet engineering research hashing functions methods image processing quaternions mathematics research transformations mathematics. 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. Edge detection of colour image based on quaternion fractional. 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. 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. Instantaneous frequency and amplitude of orthocomplex. 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.
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