On the Influence of Whitening Transformations on Hyperspectral Data

Abstract

The whitening transformation transforms a random matrix into a whitened matrix with expectation 0 and covariance matrix I. By removing the first and second order statistical structures, higher order structures can be looked at for better classification. This is why Stage Gate 11 B.V. has employed whitening in the preprocessing of their hyperspectral data. The aim of this work is to gain insight into the whitening transformation and how it influences hyperspectral data.
To gain this insight, synthetic data was created and used to make synthetic scans. The signal-to-noise ratio of a target spectrum was calculated, and Monte Carlo simulations were used to reveal hidden patterns in the data. In case of a high contrast scenario, multi-area whitening was employed and the cosine similarity between the target spectrum and its signature was determined. It was observed that the shape and intensity of the whitened target spectrum differs, depending on if pixels were used as observations or wavelengths. However, both are subject to the ‘bleeding’ effect. Further, it was found that if the number of pixels in the scan is greater than the number of spectral bands (548), then the signal-to-noise ratio becomes better as the number of whitened pixels in the scan increases. In case of a high contrast scenario, multi-area whitening guarantees the uniformity of the spectra, resulting in a higher
cosine similarity between the target spectrum and its signature. But as multi-area whitening uses a smaller
number of pixels in the scan, it cannot be concluded if multi-area whitening is better than global whitening, as it is not known how the increase in cosine similarity and the decrease in signal-to-noise ratio relate to the classification process. Finally, it is concluded that when working with real and unknown data, using pixels as
observations is much more feasible.