Improved iterative error analysis for endmember extraction from hyperspectral imagery

Abstract

Automated image endmember extraction from hyperspectral imagery is a challenge and a critical step in spectral mixture analysis (SMA). Over the past years, great efforts were made and a large number of algorithms have been proposed to address this issue. Iterative error analysis (IEA) is one of the well-known existing endmember extraction methods. IEA identifies pixel spectra as a number of image endmembers by an iterative process. In each of the iterations, a fully constrained (abundance nonnegativity and abundance sum-to-one constraints) spectral unmixing based on previously identified endmembers is performed to model all image pixels. The pixel spectrum with the largest residual error is then selected as a new image endmember. This paper proposes an updated version of IEA by making improvements on three aspects of the method. First, fully constrained spectral unmixing is replaced by a weakly constrained (abundance nonnegativity and abundance sum-less-or-equal-to-one constraints) alternative. This is necessary due to the fact that only a subset of endmembers exhibit in a hyperspectral image have been extracted up to an intermediate iteration and the abundance sum-to-one constraint is invalid at the moment. Second, the search strategy for achieving an optimal set of image endmembers is changed from sequential forward selection (SFS) to sequential forward floating selection (SFFS) to reduce the so-called "nesting effect" in resultant set of endmembers. Third, a pixel spectrum is identified as a new image endmember depending on both its spectral extremity in the feature hyperspace of a dataset and its capacity to characterize other mixed pixels. This is achieved by evaluating a set of extracted endmembers using a criterion function, which is consisted of the mean and standard deviation of residual error image. Preliminary comparison between the image endmembers extracted using improved and original IEA are conducted based on an airborne visible infrared imaging spectrometer (AVIRIS) dataset acquired over Cuprite mining district, Nevada, USA.