光谱解混是高光谱技术中的关键部分, 对地物成分的定量分析至关重要。 线性光谱解混方法在计算端元丰度时, 大多需要涉及矩阵求逆或方阵行列式的计算, 导致软件实现的计算复杂度高, 且硬件实现困难。 同时, 当端元数量增加时, 算法的计算量也会随之呈指数级快速增长。 论文基于传统的正交子空间投影方法, 利用正交原理, 提出了一种新的光谱解混方法——正交向量投影。 该方法首先利用Gram-Schmidt过程计算每个端元的最终正交向量分量, 并将其作为代表端元的投影向量。 然后对于任意的待解混光谱向量, 直接将其投影到该正交向量上。 最后, 计算得到投影分量的长度与正交向量的长度比, 即为该正交向量所代表端元的无约束丰度。 该过程避免了正交子空间投影和最小方差方法中计算复杂、 实现困难的矩阵求逆运算, 更便于并行计算的设计和硬件实现。 通过理论的推导分析, 证明了该算法与正交子空间投影和最小方差方法是完全一致的。 另外, 由于算法避免了矩阵相乘和求逆运算, 简化了解混过程, 通过对不同算法复杂度的具体分析, 也证明该算法相对其他算法可以对端元数量降低一个量级。 最后, 在模拟数据和实际图像上分别进行实验测试, 结果的分析和比较, 也说明了算法的有效性。

Spectrum unmixing is an important part of hyperspectral technologies, which is essential for material quantity analysis in hyperspectral imagery. Most linear unmixing algorithms require computations of matrix multiplication and matrix inversion or matrix determination. These are difficult for programming, especially hard for realization on hardware. At the same time, the computation costs of the algorithms increase significantly as the number of endmembers grows. Here, based on the traditional algorithm Orthogonal Subspace Projection, a new method called Orthogonal Vector Projection is prompted using orthogonal principle. It simplifies this process by avoiding matrix multiplication and inversion. It firstly computes the final orthogonal vector via Gram-Schmidt process for each endmember spectrum. And then, these orthogonal vectors are used as projection vector for the pixel signature. The unconstrained abundance can be obtained directly by projecting the signature to the projection vectors, and computing the ratio of projected vector length and orthogonal vector length. Compared to the Orthogonal Subspace Projection and Least Squares Error algorithms, this method does not need matrix inversion, which is much computation costing and hard to implement on hardware. It just completes the orthogonalization process by repeated vector operations, easy for application on both parallel computation and hardware. The reasonability of the algorithm is proved by its relationship with Orthogonal Subspace Projection and Least Squares Error algorithms. And its computational complexity is also compared with the other two algorithms’, which is the lowest one. At last, the experimental results on synthetic image and real image are also provided, giving another evidence for effectiveness of the method.