Hyperspectral fluorescence data fusion using quaternion and octonion phase

While common hyperspectral images comprise two spatial and one spectral dimension, hyperspectral fluorescence images can have the excitation wavelength as an additional fourth dimension. We consider hyperspectral fluorescence spectra of minerals for which the emitted fluorescence spectra vary with the irradiated excitation wavelength. In comparison with reflectance spectra, the fluorescence spectra at a fixed excitation wavelength exhibit far less characteristic details and are rather flat. Using these spectra for object classification leads to low classification rates. For this reason, the data contained in the fourth dimension (excitation wavelength) is fused to obtain more characteristic spectra. In this contribution, we will use quaternions and octonions for the fusion: By considering their phase, the information contained in the fourth dimension is compressed and a three-dimensional image containing “pseudo spectra” in the original spectral dimension is derived. Doing so results in more discriminative spectra that allow for a more robust classification. We will demonstrate the benefit of the proposed method applied to a hyperspectral fluorescence dataset of mineral samples. While the classification rates using only hyperspectral fluorescence images of one wavelength are low, using the pseudo spectra derived from the fusion results in an object classification rate of 85 to 90 %.