Characterization of hyperspectral images prior to unmixing, based on eigendecompositions and sum-to-one condition

When performing blind unmixing of hyperspectral images, the mixing model properties determine which unmixing methods are adequate and how their parameters should be set. One should therefore derive these properties before unmixing, directly from the observed mixed data. We show how to deduce such properties from the eigenvalues of the correlation and covariance matrices of observed hyperspectral images, separately considered as spectral and spatial functions. This analysis is shown to apply both to linear mixtures (i.e. linear combinations of standard spectra, here called “monospectra”) and linear-quadratic mixtures (linear combinations of monospectra and “bispectra”, i.e. products of two monospectra). Our methods first determine if the sum of all coefficients is the same for all pixels. Moreover, we show how to estimate the total number of monospectra and bispectra, if any, mixed in observations. Performance is validated for synthetic mixtures of real pure spectra.