Geometrical constrained independent component analysis for hyperspectral unmixing

One of the limitations of the hyperspectral remote sensing application is the existence of mixed pixels in image data. Spectral decomposition, which separates the mixed pixels into a set of endmember spectra and abundance fractions, is the most effective way to solve the mixed pixel problem. Due to the independence of source signals, independent component analysis (ICA) has been developed for hyperspectral unmixing by adding auxiliary constraints. Abundance sum-to-one and nonnegative constraints are two obvious features for hyperspectral data. In this paper, by processing these two constraints sequentially from the geometrical point of view to restrain the sum-to-one constraint thoroughly at each iteration, geometrical constrained ICA (GCICA) is proposed based on treating the abundance distribution as the independent signal. To validate the proposed algorithm, the synthetic data, and real image data are used for unmixing, respectively. Synthetic data are generated based on spectra from the ENVI (Environment for Visualizing Images) software spectral library. The real images are used with three hyperspectral datasets, AVIRIS (Airborne Visible Infrared Imaging Spectrometer) Cuprite dataset, AVIRIS Indiana Pine dataset and HYDICE (Hyperspectral Digital Imagery Collection Experiment) dataset. Results, in comparison with previously proposed algorithms, show that the proposed method has better performance for the decomposition of hyperspectral data in abundance and endmember spectral extraction, thus providing a new and effective method for spectral unmixing and signal separation without prior information.