Abstract：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.
[1] Bioucas-Dias J M, Plaza A, Dobigeon N, et al. Selected Topics in Applied Earth Observations and Remote Sensing，2012, 5(2): 354. [2] Chang C I. Hyperspectral Data Processing: Signal Processing Algorithm Design and Analysis. Wiley, N. J., 2013. [3] Song M P，Chang C I. IEEE Transactions on Geoscience and Remote Sensing, 2015, 53(6): 3055. [4] Honeine P，Richard C. IEEE Transactions on Geoscience and Remote Sensing，2012, 50(6): 2185. [5] Ren H，Chang C I. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4): 1232. [6] Song M P, Li H, Chang C I. Gram-Schmidt Orthogonal Vector Projection for Hyperspectral Unmixing: IEEE International Geoscience and Remote Sensing Symposium, Canada, 2014. [7] GENG Xiu-rui, TONG Qing-xi, ZHENG Lan-fen(耿修瑞，童庆禧，郑兰芬). Progress in Natural Science(自然科学进展), 2005, 15(4): 509. [8] Settle J J. IEEE Transactions on Geoscience and Remote Sensing, 1996, 34(4): 1045. [9] Du Q, Younan N H，King R L. Applied Optics, 2008, 47(28): F77.
