Application of MRF's spatial correlation model in NMF-based linear unmixing

doi:10.11772/j.issn.1001-9081.2017.12.3563

Abstract

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

摘要： 针对基于非负矩阵分解（NMF）的高光谱解混存在的初始化与"局部极小"等问题，提出一种基于马尔可夫随机场（MRF）的空间相关约束NMF线性解混算法（MRF-NMF）。首先，通过基于最小误差的高光谱信号识别（HySime）法估算端元数量，同时利用顶点成分分析（VCA）和全约束最小二乘法（FCLS）初始化端元矩阵与丰度矩阵；其次，利用MRF模型建立描述地物空间分布规律的能量函数，以此描述地物分布的空间相关特征；最后，将基于MRF的空间相关约束函数与NMF标准目标函数以交替迭代的形式参与解混，得出高光谱数据的端元信息与丰度分解结果。理论分析和真实数据实验结果表明，在高光谱数据空间相关程度较低的情况下，相比最小体积约束的NMF （MVC-NMF）、分段平滑和稀疏约束的NMF （PSNMFSC）和交互投影子梯度非负矩阵分解（APS-NMF）三种参考算法，所提算法的端元分解精度仍分别提高了7.82%、12.4%和10.1%，其丰度分解精度仍分别提高了8.34%、12.6%和9.87%。MRF-NMF能够弥补NMF对于空间相关特征描述能力的不足，减小解混结果中地物的空间能量分布误差。

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

CLC Number:

TP751.1

YUAN Bo. Application of MRF's spatial correlation model in NMF-based linear unmixing[J]. Journal of Computer Applications, 2017, 37(12): 3563-3568.

袁博. 马尔可夫随机场的空间相关模型在非负矩阵分解线性解混中的应用[J]. 计算机应用, 2017, 37(12): 3563-3568.

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