线性混合模型（linear mixture model，LMM）在端元提取中起着至关重要的作用。在LMM假设下，理想的端元提取效果需要重建误差最小。但是在实际的高光谱数据集中噪声是不可避免的，单纯追求重建误差最小化可能会导致最终结果偏离真实端元。为平衡重建误差与噪声的影响，使用几何优化模型计算重建误差，通过约束重建误差来最小化单形体体积，提出新的误差约束优化模型EIC-OSV （error invariant constrained-optimal simplex volume）。模拟数据及真实数据下的实验表明，EIC-OSV可以提高现有端元提取方法的准确性。
The linear mixture model (LMM) plays a crucial role in endmember extraction. In general, under the assumption of LMM, the endmembers in an image can be obtained by minimizing the model reconstruction error. However, due to the existence of noise, the endmembers corresponding to the minimum model reconstruction error often deviate from the real ones. In order to balance the effects of reconstruction error and noise, the geometric optimization model is adopted to evaluate the reconstruction error in this paper and the reconstruction error is used as the constraint to further minimize the volume of the simplex. The presented method is called the error invariant constrained-optimal simplex volume method (EIC-OSV). The experiments with simulated and real hyperspectral data demonstrate that EIC-OSV can improve the overall accuracy of the popular endmember extraction methods.
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