Abstract
Spectral unmixing is a popular tool for remotely sensed hyperspectral data interpretation and classification. It aims at identifying the spectra of all endmembers in the scene to find the fractional abundances of pure spectral signatures in each mixed pixel collected by an imaging spectrometer. Complete spectral unmixing exploits the theory that the reflectance spectrum of any pixel is the result of linear combinations of the spectra of all endmembers inside that pixel and simply solves a set of l linear equations for each pixel, where l is the number of bands in the image. But often the estimation of all the endmember signatures may be difficult due to the unavailability of pure spectral signatures in the original data, or inadequacy of spatial resolution. For such cases, partial unmixing can be used where only the user chosen targets need to be mapped and the unmixing equations are partially solved. Like complete unmixing, a pixel value in the output image of partial unmixing is proportional to the fraction of the pixel that contains the target material. In this paper, we study the partial spectral unmixing problem under the light of recent theoretical results published in those areas. Our experimental results, which are conducted using real hyperspectral data sets collected by the NASA Jet Propulsion Laboratory's Airborne Visible Infrared Imaging Spectrometer (AVIRIS) and spectral libraries publicly available; indicate the potential of partial unmixing techniques in the task of accurately characterizing the mixed pixels using the library spectra. Furthermore, we provide a comparison of complete spectral unmixing and partial spectral unmixing for the oil spill detection in the sea.