L1-Endmembers: A Robust Endmember Detection and Spectral Unmixing Algorithm

A hyperspectral endmember detection and spectral unmixing algorithm based on an l(1) norm factorization of the input hyperspectral data is developed and compared to a method based on l(2) norm factorization. Both algorithms, the L1-Endmembers algorithm based on the l(1) norm and the SPICE algorithm based on the l(2) norm, simultaneously and autonomously estimate endmember spectra, abundance values and the number of endmembers needed for a hyperspectral image. The l(1) norm factorization of the hyperspectral data is approximated through the use of the Huber M-estimator. Results showing the stability of the L1-Endmembers algorithm in terms of the number of endmembers estimated with noise and outliers are presented. Results indicate that the proposed algorithm is more consistent in estimating the correct number of endmembers over SPICE. However, when both algorithms determine the correct number of endmembers, SPICE results provide a better estimate of endmembers and a lower variance of endmember estimates over many runs with random initialization.