光谱解混是高光谱数据分析的重要技术之一.全约束(即非负性约束和归一化约束)最小二乘线性光谱混合模型(FCLS-LSMM)具有模型简单和物理意义明确等优点而得以广泛使用.然而, FCLS-LSMM的传统优化求解方法的迭代过程非常复杂.近年提出的几何方法为降低LSMM的求解复杂度提供了新思路, 但是所获得的结果并非真正意义上的全约束最小二乘解.为此, 建立了一种完全符合FCLS要求的LSMM几何求解方法, 具有复杂度低和可以获得理论最优解等优点.实验表明了所提出方法的有效性.

Spectral unmixing is one of the important techniques for hyperspectral data analysis. Full constrained (i.e., non-negative and sum to one constrained) least squares linear spectral mixture modeling (FCLS-LSMM) is widely used for its conciseness and clarity of physical meaning. Unfortunately, the traditional iterative processing for solving FCLS-LSMM is of heavy computational burden. The recently developed geometric analysis method of LSMM provided a new way for decreasing the complexity of LSMM. The unmixing results, however, are not in line with the FCLS requirements. In this case, a new geometric unmixing method is constructed to completely meet the FCLS requirements. The method is of very low complexity and has the capability to obtain the theoretically optimal solution. Experiments show the effectiveness of the proposed method.