关键词: 非负矩阵分解, 高光谱线性解混, 空间相关, 马尔可夫随机场, 交替迭代, 空间能量

Abstract: Aiming at the problems of initialization and "local minima" of Non-negative Matrix Factorization (NMF) in hyperspectral unmixing, a spatial correlation constrained NMF linear unmixing algorithm based on Markov Random Field (MRF) (MRF-NMF) was proposed. Firstly, the number of endmembers was estimated by Hyperspectral Signal identification by minimum error (HySime) method, the endmember matrix and abundance matrix were initialized by Vertex Component Analysis (VCA) and Fully Constrained Least Squares (FCLS). Secondly, the energy function of depicting the spatial distribution characteristics of ground objects was established by using MRF to depict the spatial correlation distribution features of ground objects. Finally, the spatial correlation constraint function based on MRF and the NMF standard objective function were used for unmixing in the form of alternating iteration, and the endmember information and abundance decomposition results of hyperspectral data were obtained. The theoretical analysis and experimental results of real data show that, with hyperspectral data of low spatial correlation, compared with the three reference algorithms of Minimum Volume Constrained NMF(MVC-NMF), Piecewise Smoothness NMF with Sparseness Constraints (PSNMFSC) and NMF with Alternating Projected Subgradients (APS-NMF), the endmember decomposition precision of MRF-NMF increases by 7.82%, 12.4% and 10.1%, and the abundance decomposition precision of MRF-NMF increases by 8.34%, 12.6% and 9.87%. The proposed MRF-NMF can make up for NMF's deficiency in depicting spatial correlation features, and reduce the spatial energy distribution error of ground objects.

Key words: Non-negative Matrix Factorization (NMF), hyperspectral linear unmixing, spatial correlation, Markov Random Field (MRF), alternative iteration, spatial energy