Efficient sparse unmixing analysis for hyperspectral imagery based on random projection

Hyperspectral imagery including rich spectral information could be applied to detect and identify objects at a distance. In this paper, we concentrate on the surface material identification of interested objects within the domain of space object identification (SOI) and geological survey. One of the approaches is the unmixing analysis that identifies the components (called endmembers) in each pixel and estimates their corresponding fractional abundances, and then, we could obtain the space distributions of substances. To solve this problem, we present an approach in a semi-supervised fashion, by assuming that the measured spectrum is expressed in the form of linear combination of a number of pure spectral signatures in a spectral library and the fractional abundances are their weights. Thus, the abundances are sparse and we propose a sparse regression model to realize the sparse unmixing analysis. We apply random projection technique to accelerate the sparse unmixing process and use split Bregman iteration to optimize the objective function. Our algorithm is tested and compared with other classic algorithms by using simulated hyperspectral images and a real-world image.