Abstract: The 2D Quaternionic Fourier Transform (QFT), applied to a real 2D image, produces an invertible quaternionic spectrum. If we conserve uniquely the first quadrant of this spectrum, it is possible, after inverse transformation, to obtain, not the original image, but a 2D quaternion image, which generalize in 2D the classical notion of 1D analytical image. From this quaternion image, we compute the corresponding correlation product, then, by applying the direct QFT, we obtain the 4D Wigner-Ville distribution of this analytical signal. With reference to the shift variables ?1 , ?2 used for the computation of the correlation product, we obtain a local quaternion Wigner-Ville distribution spectrum.

Yang LIU and Robert GOUTTE, “Quaternionic Wigner-Ville distribution of analytical signal in hyperspectral imagery” International Journal of Advanced Computer Science and Applications(IJACSA), 4(10), 2013. http://dx.doi.org/10.14569/IJACSA.2013.041015

@article{LIU2013,
title = {Quaternionic Wigner-Ville distribution of analytical signal in hyperspectral imagery},
journal = {International Journal of Advanced Computer Science and Applications},
doi = {10.14569/IJACSA.2013.041015},
url = {http://dx.doi.org/10.14569/IJACSA.2013.041015},
year = {2013},
publisher = {The Science and Information Organization},
volume = {4},
number = {10},
author = {Yang LIU and Robert GOUTTE}
}