Comparison of error metrics in iterative error analysis algorithm for endmember extraction from hyperspectral data

Abstract

This study represents the effect of methods for estimating error in iterative error analysis (IEA) algorithm. Three different methods are presented for estimating error in each iteration: the L2-norm, which is used in the original IEA, the L1-norm and the spectral angle. For comparing the effect of applying those error metrics and evaluating the performance of each algorithm, two hyperspectral datasets, simulated and real hyperspectral images, were used. The results of endmember extraction with those algorithms were compared to spectral library by spectral distance and the 2-D plane projection of datasets. The results with the simulated image indicated that the spectral angle based IEA algorithm performed better than other two IEAs, the original and the L1-norm based algorithm. The spectral angle based IEA selected correct locations of endmember pixels while other two algorithms worked poorly. In addition, the spectral angle IEA produced stable results with various signal-to-noise ratio (SNR). In particular, the algorithm with the spectral angle showed a robustness when the data was highly affected by changes in pixel brightness. The 2-D projection illustrated illumination insensitivity of the spectral angle based IEA algorithm. The experiment with the real hyperspectral data displayed similar results to those of the simulated image. Even though big difference was not detected, the spectral angle based IEA produced slightly better results of endmember spectra. The 2-D projection plane of extracted endmembers also showed that the spectral angle based algorithm produced reliable results when the image contains topographically complex regions. The result of this study suggest that the IEA algorithms with different error metrics produce different results and the algorithm based on the spectral angle error is a reliable approach to extract endmembers from the image of topographically complex region.