Unsupervised Sparsity-based Unmixing of Hyperspectral Imaging Data Using an Online Sparse Coding Dictionary

Due to the low spatial resolution of the hyperspectral cameras, the acquired spectral pixels are mixtures of present materials in the scene called endmembers. All spectral pixels are assumed to be mixtures of these endmembers with different amounts called abundances. Unmixing of the spectral pixels is a very important task for the analysis of these hyperspectral data cubes. Unsupervised unmixing aims to estimate the endmembers signatures and their abundances in each pixel without any prior knowledge about the given cube. Sparsity is one of the recent approaches used in the unmixing techniques. Solving the basis pursuit problem could be used as a sparsity-based approach to solving this unmixing problem where the endmembers are assumed to be sparse in a domain known as a dictionary. The choice of an appropriate dictionary is important for obtaining sparser representations of the given spectral pixels for better unmixing results. Two main approaches of dictionaries for sparse representation; analytic dictionaries approach and learned custom dictionaries approach. The contribution of this paper is the use of the recent online sparse coding dictionary as a learned custom dictionary for more fitting of the spectral pixels in solving the basis pursuit unmixing problem. While using the online sparse coding algorithm is more computational than any predefined transform family, but it has the advantage of no need for choosing a suitable family for the given spectral pixels. The online dictionary learning was successfully used in solving the basis pursuit unmixing problem to unmix both real AVIRIS data cube obtained from AVIRIS-NASA website and a synthetic cube made up from few materials selected from the given ASTER spectral library.