Abstract
Many concepts that are used in multi-dimensional signal processing are derived from one-dimensional signal processing. As a consequence, they are only suited to multi-dimensional signals which are intrinsically one-dimensional. We claim that this restriction is due to the restricted algebraic frame used in signal processing, especially to the use of the complex numbers in the frequency domain. We propose a generalization of the two-dimensional Fourier transform which yields a quaternionic signal representation. We call this transform quaternionic Fourier transform (QFT). Based on the QFT, we generalize the conceptions of the analytic signal, Gabor filters, instantaneous and local phase to two dimensions in a novel way which is intrinsically two-dimensional. Experimental results are presented.
This work was supported by the Studienstiftung des deutschen Volkes (Th.B.) and by the DFG (So-320-2-1) (G.S.).
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References
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© 1997 Springer-Verlag Berlin Heidelberg
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Billow, T., Sommer, G. (1997). Multi-dimensional signal processing using an algebraically extended signal representation. In: Sommer, G., Koenderink, J.J. (eds) Algebraic Frames for the Perception-Action Cycle. AFPAC 1997. Lecture Notes in Computer Science, vol 1315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017865
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DOI: https://doi.org/10.1007/BFb0017865
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