Piece-wise convex spatial-spectral unmixing of hyperspectral imagery using possibilistic and fuzzy clustering

Imaging spectroscopy refers to methods for identifying materials in a scene using cameras that digitize light into hundreds of spectral bands. Each pixel in these images consists of vectors representing the amount of light reflected in the different spectral bands from the physical location corresponding to the pixel. Images of this type are called hyperspectral images. Hyperspectral image analysis differs from traditional image analysis in that, in addition to the spatial information inherent in an image, there is abundant spectral information at the pixel or sub-pixel level that can be used to identify materials in the scene. Spectral unmixing techniques attempt to identify the material spectra in a scene down to the sub-pixel level. In this paper, a piece-wise convex hyperspectral unmixing algorithm using both spatial and spectral image information is presented. The proposed method incorporates possibilistic and fuzzy clustering methods. The typicality and membership estimates from those methods can be combined with traditional material proportion estimates to produce more meaningful proportion estimates than obtained with previous spectral unmixing algorithms. An analysis of the utility of using all three estimates produce a better estimate is given using real hyperspectral imagery.