Does Independent Component Analysis Play a~Role in Unmixing Hyperspectral Data?

Independent Component Analysis (ICA) have recently been proposed as a tool to unmix hyperspectral data. ICA is founded on two assumptions: i) The observed data vector is a linear mixture of the sources (abundance fractions); ii) sources are independent. Concerning hyperspectral data, the first assumption is valid whenever the constituent substances are surface distributed. The second assumption, however, is violated, since the sum of abundance fractions associated to each pixel is constant due to physical constraints in the data acquisition process. Thus, sources cannot be independent. This paper gives evidence that ICA, at least in its canonical form, is not suited to unmix hyperspectral data. We arrive to this conclusion by minimizing the mutual information of simulated hyperspectral mixtures. The hyperspectral data model includes signature variability, abundance perturbation, sensor Point Spread Function (PSF), abundance constraint and electronic noise. Mutual information computation is based on fitting mixtures of Gaussians to the observed data.