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In this paper, we address the problem of recovering a hyperspectral texture descriptor. We do this by viewing the wavelength-indexed bands corresponding to the texture in the image as those arising from a stochastic process whose statistics can be captured making use of the relationships between moment generating functions and Fourier kernels. In this manner, we can interpret the probability distribution of the hyper-spectral texture as a heavy-tailed one which can be rendered invariant to affine geometric transformations on the texture plane making use of the spectral power of its Fourier cosine transform. We do this by recovering the affine geometric distortion matrices corresponding to the probability density function for the texture under study. This treatment permits the development of a robust descriptor which has a high information compaction property and can capture the space and wavelength correlation for the spectra in the hyperspectral images. We illustrate the utility of our descriptor for purposes of recognition and provide results on real-world datasets. We also compare our results to those yielded by a number of alternatives.