Robust Affine Set Fitting and Fast Simplex Volume Max-Min for Hyperspectral Endmember Extraction

Hyperspectral endmember extraction is to estimate endmember signatures (or material spectra) from the hyperspectral data of an area for analyzing the materials and their composition therein. The presence of noise and outliers in the data poses a serious problem in endmember extraction. In this paper, we handle the noise- and outlier-contaminated data by a two-step approach. We first propose a robust-affine-set-fitting algorithm for joint dimension reduction and outlier removal. The idea is to find a contamination-free data-representative affine set from the corrupted data, while keeping the effects of outliers minimum, in the least squares error sense. Then, we devise two computationally efficient algorithms for extracting endmembers from the outlier-removed data. The two algorithms are established from a simplex volume max-min formulation which is recently proposed to cope with noisy scenarios. A robust algorithm, called worst case alternating volume maximization (WAVMAX), has been previously developed for the simplex volume max-min formulation but is computationally expensive to use. The two new algorithms employ a different kind of decoupled max-min partial optimizations, wherein the design emphasis is on low-complexity implementations. Some computer simulations and real data experiments demonstrate the efficacy, the computational efficiency, and the applicability of the proposed algorithms, in comparison with the WAVMAX algorithm and some benchmark endmember extraction algorithms.