Wyniki 1-1 spośród 1 dla zapytania: authorDesc:"Kajetana M. Snopek"

Quaternions and octonions in signal processing - fundamentals and some new results DOI:10.15199/59.2015.6.6

  In the last years, the theory of hypercomplex algebras has considerably proliferated into the domain of multidimensional signals. Many scientific papers and books concerning quaternions and their applications have been printed in the last decade, e.g. [1], [2]. The Cayley-Dickson algebra of octonions is also frequently exploited by scientists, especially in the field of theoretical physics. The Signals and Systems Division (Institute of Radioelectronics, Warsaw University of Technology) is currently involved in research concerning further development of theory and applications of different hypercomplex algebras in signal processing. In this paper, some latest, earlier published in [3], results concerning symmetry properties of the Octonion Fourier transform are highlighted. Also, some new applications of our team in color image analysis [4] and watermarking [5] are described. This paper is devoted to quaternions and octonions and their applications in 2D and 3D signal processing. Presents briefly definitions and properties of Cayley-Dickson algebras of quaternions and octonions. Next definitions of quaternion and octonion multidimensional signals are introduced with emphasis on analytic signals being the subject of the monograph [2]. Then, some applications of quaternions in color image processing are described. The Quaternion (QFT) and Octonion (OFT) Fourier transformations (FTs) are recalled and their relations to 2D and 3D complex FTs are shown. This part is devoted to chosen applications of QFT in color image analysis, including watermarking techniques. Summary describes shortly future plans of research in the domain of hypercomplex algebras in relation to signal theory. Ba sic s of Cayley -Dick son alge bra s of quaternion s and octonion s The Cayley -Dickson construction The Cayley-Dickson construction [6], [7] is a tool to define Cayley-Dickson algebras - the family of hypercomplex algebras of order 2N over the real [...]

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