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Tytuł artykułu

Quaternions and octonions in signal processing - fundamentals and some new results

Autorzy
Identyfikatory
Warianty tytułu
PL
Kwaterniony i oktoniony w przetwarzaniu sygnałów - podstawy teoretyczne i wybrane zastosowania
Języki publikacji
EN
Abstrakty
EN
The paper shows relations between Cayley-Dickson hypercomplex algebras and the theory of 2D and 3D signals. Basics concerning properties of quaternions and octonions and chosen applications are described. The latest results of research in the domain of complex and hypercomplex multidimensional analytic signals are presented.
PL
Pokazano związki pomiędzy hiper zespolonymi algebrami Cayleya-Dicksona a teorią sygnałów 2- i 3-wymiarowych. Przypomniano podstawowe własności kwaternionów i oktonionów oraz opisano ich przykładowe zastosowania. Przedstawiono uzyskane ostatnio wyniki w dziedzinie zespolonych i hiper zespolonych analitycznych sygnałów wielowymiarowych.
Rocznik
Tom
Strony
618--622
Opis fizyczny
Bibliogr. 47 poz., rys., tab
Twórcy
autor
  • Instytut Radioelektroniki, Wydział Elektroniki i Technik Informacyjnych Politechniki Warszawskiej
Bibliografia
  • [1] Hahn S., Snopek K.: The Unified Theory of Complex and Hypercomplex Analytic Signals, Buli. Polish Ac. Sci. Tech. Sci., 59, 2, 2011
  • [2] Snopek K.: Studies on Complex and Hypercomplex Multidimensional Analytic Signals, Prace Naukowe Elektronika (Warsaw University of Technology), 190,2013
  • [3] Błaszczyk Ł., Snopek K.: Symmetry properties of the Octonion Fourier Transform, London Mathematical Society, 2015
  • [4] Snopek K., Zienkowicz N.: Ouatemion polar representation in analysis of brightness of cotour images, Institute of Radioelectronics, Warsaw, Polanod, 2014
  • [5] Rządkowski W., Snopek K.: A new quatemion color image watermarking algorithm, 8th IEEE International Conference on Intelligent Data Acguisition and Advanced Computing Systems: technology and Applications, 24-26 September 2015, Warsaw, Poland, 2015
  • [6] Conway J., Guy R.: Cayley Numbers, The Book of Numbers, New York, SpringerVertag, 1996
  • [7] Conway J., Smith D., On Ouatemions and Octonions: Their Geometry, Arithmetic and Symmetry, A.K. Peters Ltd., 2003
  • [8] Hamilton R.: On quatemions, Proc. Royal Irish Academy, 3,1847
  • [9] Bulow I, Sommer G.: The Hypercpmplex Signal - A Novel Extensions of the Analytic Signal to the Multidimensional Case, IEEE Trans. Signal Processing, 49,11,2001
  • [10] Hahn S.: Multidimensional Complex Signals with Single-Orthant Spectra, Proc. IEEE, 80, 8,1992
  • [11] Hahn S.: Hilbert Transforms in Signal Processing, Artech House Inc., 1996
  • [12] Hahn S.: Complex Signals with Single-Orthant Spectra as Boundary Distributions of Multidimensional Analytic Functions, Buli. Polish Ac, Sci. Tech. Sci., 51, 2, 2003
  • [13] Snopek K.: New Hypercomplex Analytic Signals and Fourier Transforms in Cayley-Dickson Algebras, Electr. Tel. Ouarterly, 55, 3, 2009
  • [14] Snopek K.: The New Insight into the Theory of 2-0 Complex and Ouaternion Analytic Signals, Intl. J. Electr. Telecomm., 57, 3, 2011
  • [15] Snopek K.: The n-D Analytic Signals and Fourier Spectra in Complex and Hypercomplex Domains, 34th Int. Conf. on Telecommunications and Signal Processing, Budapest, 2011, August 18-20
  • [16] Snopek K.: The Study of Properties of n-D Analytic Signals in Complex and Hypercomplex Domains, Radioengineering, 21,2,2012
  • [17] Sangwine S.: Fourier transforms of colour images using quatemion or hypercomplex number, Electron. Lett., 32,21,1996
  • [18] Sangwine S., Eli T: Colour image filtersbased on hypercomplex convolution, IEEE Proc. Vision, Image and Signal Processing, 49,21,2000
  • [19] Sangwine S., Evans C., Eli T: Colour-sensitive edge detection using hypercomplex filters, 10th European Signal Processing Conference EUSIPCO, Tampere, Finland, 2000
  • [20] Sangwine S.: Colour in image processing, Electronic and CommunicationEng.J., 12, 5, 2000
  • [21] Pei S.-C., Ding J.-J., Chang J.: Color pattern recognition by quaternion correlation, IEEE Int. Conf. Image Process., Thessaloniki, Greece, 2010
  • [22] Witten B., Shragge J.: Ouatemion-based Signal Processing, Stanford Exploration Project, New Orleans Meeting, 2006
  • [23] Gao C.,Zhou J.,Lang F., Pu Q., Liu C.: Novel Approach to Edge Detection of Color Image Based on Quatemion Fractional Directional Differentation, Advances in Auation and Robotics, 1,2012
  • [24] Tpok C., Mandic D.: The Ouatemion LMS Algorithm for Adaptive Filtering of HypercompleK Processes, IEEE Trans. Signal Processing, 57,4,2009
  • [25] Dubey V: Quatemion Fourier Transform for Colour Images, Int. J. Computer Science and Information Technologies, 5,3,2014
  • [26] Lengyel E.: Mathematics for 30 Programming and Computer Graphics, Charles River Media 2001
  • [27] Farrell J.: Mathematics for Game Developpers, Premier Press Inc., 2004
  • [28] Andreis D., Canuto E.: Orbit dynamics and kinematics with fuli quaternions, American Control Conference, Boston, Massachusetts, 2004
  • [29] Chanyal B., Bisht R, Negi O.: Generalized Octonion Electrodynamics Int. J. Theor. Physics, 49, 2010
  • [30] Kapłan A.: Quatemions and Octonions in Mechanics, Revista de la Union Mathematica Argentina, 49,2, 2008
  • [31] Eli T, le Bihan N. i Sangwine S.: Quatemion Fourier Transforms for Signal and Image Processing, Wiley - ISTE, 2014
  • [32] Brackx F., Delanghe R., Sommen F.: Clifford Analysis, Boston: Pitman 1982
  • [33] Pei S.-C., Ding J.-J., Chang J.-H^Efficiernt lmplementation of Quaternion Fourier Transform, Comolution, and Correlation by 2-D Complex FFT IEEE Trans. Signal Processing, 49, 11, 2001
  • [34] Bulow T.: Hypercomplex spectral signal representation for the processing ananalysis of images, Kieł, 1999.
  • [35] Eli T, Sangwine S.: Hypercomplex Fourier Transforms for Color Images IEEE Trans. Image Processing, 16,1, 2007 [36] Khalil M.: Applying Ouatemion Fourier Transforms for Enhancing Color Images, Int. J. of Image, Graphics and Signal Processing, MECS, 4,2 2012
  • [37] Femandez-Maloigne, C. (Ed.): Advanced Color Image Processing an Analysis, New York: Springer Science+Bussiness Media, 2013
  • [38] Bas R, le Bihan N., Chassery J.: Color Image Watermarking Using Quaternion Fourier Transform, ICASSP, Hong Kong, 2003
  • [39] Tsui T., Zhang X.-P i Androustos D.: Quatemion Image Watermarkin, using the Spatio-Chromatic Fourier Coefficients Analysis, 14th Annual ACM Int. Conf. on Multimedia MM'2006, Santa Bamara, California, US 2006
  • [40] Ma, X., Y Xu, X. Yang: Color image watermarking using local quaternion Fourier spectra analysis, IEEE Int. Conf. Multimedia and Expo, Hannower 2008
  • [41] Li C., Li B., Xiao L, Hu Y, Tian L: A Watermarking Method Based on Hypercomplex Fourier Transform and Visual Attention, J. information & Computational Science, 9,15, 2012
  • [42] Jing S., Jing- Y yu: Quatemion Frequency Watermarking Algorithm for Color Images, Int. Conf. Multimedia Technology, Ningbo, 2010
  • [43] X. W., Wang C., Yang H., Niu R: A robust blind color image watermaking in quatemion Fourier transform domain, J. Systems and Softwai 86, 2, 2013
  • [44] Assefa D., Mansinha L., Tiampo K., Rasmussen H., Abdella K.: Local quaternion Fourier transform and color texture analysis, Signal Processing, 60, 6, 2010
  • [45] Bahri M.: Discrete Quaternion Fourier Transform and Properties, Int. J. Math Analysis, 7, 25, 2013.
  • [46] Eli T.: Hypercomplex spectral transformation, University of Minessota 1992
  • [47] Eli T.A., Sangwine J.: Decomposition of 2D hypercomplex Fourier transforms into pair of complex Fourier transforms, Proc. EUSIPCO 2000
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-06efa89b-eda4-445f-8d89-8bc95ee8b472
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