基于稀疏和正交约束非负矩阵分解的高光谱解混

针对基于非负矩阵分解(NMF)的高光谱解混存在的容易陷入局部极小值和受初始值影响较大的问题,提出一种稀疏和正交约束相结合的NMF的线性解混算法SONMF。首先,从传统的基于NMF的高光谱线性解混方法出发,分析高光谱数据本身的理化特性;然后,结合丰度的稀疏性和端元的独立性两个方面,将稀疏非负矩阵分解(SNMF)和正交非负矩阵分解(ONMF)两种方法结合应用到高光谱解混当中。模拟数据和真实数据实验表明,相比顶点成分分析法(VCA)、SNMF和ONMF这三种参考解混算法,所提算法提高了线性解混的性能;其中,评价指标光谱角距离(SAD)降低了0.012~0.145。SONMF能够结合两种约束条件的优势,弥补传统基于NMF线性解混方法对高光谱数据表达的不足,取得较好的效果。

Hyperspectral unmixing based on sparse and orthogonal constrained non-negative matrix factorization

Aiming at the problem that hyperspectral unmixing based on Non-negative Matrix Factorization (NMF) is easy to fall into local minimum and greatly affected by initial value, a linear unmixing algorithm based on Sparse and Orthogonal constrained Non-negative Matrix Factorization (SONMF) was proposed. Firstly, based on the traditional NMF hyperspectral linear unmixing method, the physical and chemical properties of the hyperspectral data was analyzed. Then the sparsity of the abundance and the independence of the endmember were combined together, two methods of Sparse Non-negative Matrix Factorization (SNMF) and Orthogonal Non-negative Matrix Factorization (ONMF) were combined and applied into hyperspectral unmixing. The experiments on simulation data and real data show that, compared with the three reference unmixing algorithms of Vertex Component Analysis (VCA), SNMF and ONMF, the proposed algorithm has improved the performance of linear unmixing, in which the Spectral Angle Distance (SAD) is reduced by 0.012 to 0.145. SONMF can combine the advantages of the two constraints to make up for the lack the expression of hyperspectral data by traditional NMF based linear unmixing methods, and achieve good results.