Modified Independent Component Analysis for Initializing Non-negative Matrix Factorization : An approach to Hyperspectral Image Unmixing

Abstract

Hyperspectral unmixing consists of identifying, from mixed pixel spectra, a set of pure constituent spectra (endmembers) in a scene and a set of abundance fractions for each pixel. Most linear blind source separation (BSS) techniques are based on Independent Component Analysis (ICA) or Non-Negative Matrix Factorization (NMF). Using only one of these techniques does not resolve the unmixing problem because of, respectively, the statistical dependence between the abundance fractions of the different constituents and the non-uniqueness of the NMF results. To overcome this issue, we propose an unsupervised unmixing approach called ModifICA-NMF (which stands for modified version of ICA followed by NMF). Consider the ideal case of a hyperspectral image combining (M-1) statistically independent source images, and an Mth image depending on them due to the sum-to-one constraint. Our modified ICA first estimates these (M-1) sources and associated mixing coefficients, then derives the remaining source and coefficients, while it also removes the BSS scale indeterminacy. In real conditions, the above (M-1) sources may be somewhat dependent. Our modified ICA method then only yields approximate data. These are then used as the initial values of an NMF method, which refines them. Our tests show that this joint modifICA-NMF approach significantly outperforms the considered classical methods.