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高光谱盲解混是解决混合像元问题的重要技术。其中，非负矩阵分解（Nonnegative matrix factorization，NMF）凭借其明确的物理意义，为无监督线性光谱解混的发展奠定了基础。由于传统NMF采用欧氏距离度量原始矩阵与重构矩阵之间的误差，不能有效挖掘各维度特征间关系，影响解混精度。为充分利用高光谱图像中丰富的相关特征，本文在Earth Mover’s Distance（EMD）的基础上引入熵正则约束，由Sinkhorn距离代替欧氏距离，建模不同维度特征之间的关系。进一步地，为刻画数据的流形结构，将图正则项作为丰度的约束条件，提出了一种基于Sinkhorn距离和图正则约束的非负矩阵解混算法（SDGNMF）。论文采用乘性迭代规则对提出的解混模型进行求解，在模拟数据集、Urban数据集以及Jasper数据集上进行实验，实验结果验证了所提出算法的有效性。
Objective Hyperspectral remote sensing technology, as a new type of earth observation technology, provides rich spectral information of features and is capable of identifying and finely classifying feature targets. Limited by the spatial resolution, a single pixel in hyperspectral images contains multiple features making the mixed pixels widespread, which becomes the main problem that the accuracy of pixel-level applications is difficult to improve. Nonnegative matrix factorization (NMF), with its clear physical meaning, lays the foundation for the development of unsupervised linear spectral unmixing. For all that, traditional NMF often uses Euclidean distance as a similarity measure method. On the one hand, hyperspectral data are manifold distribution, simple linear measurement between two points cannot accurately represent the distance between data, which makes the sample internal features weakly correlated, resulting in the NMF algorithm having an inaccurate prediction of the high-dimensional spatial inaccurate prediction of the translational noise in high-dimensional space. On the other hand, the objective function constructed based on this method ignores the correlation characteristics in the image space, which inhibits the performance of the algorithm performance. Method Considering the correlation between data manifolds and features, this paper proposes a non-negative matrix factorization unmixing algorithm based on Sinkhorn distance and graph regularization constraint (SDGNMF). On the basis of fully exploiting the advantages of EMD, the algorithm imposes entropy regularization constraint on EMD, improves EMD to sinkhorn distance, and takes it as the standard of measuring error, which effectively reduces the computational complexity. In addition, EMD with entropy regularization constraint, that is, the representation of the model by sinkhorn distance, can better model the relationship between different dimensional features, and make full use of the correlation of features. In particular, based on the sinkhorn distance, this paper introduces the graph regularity constraint to further characterize the manifold structure of data. Compared with the unmixing model constructed by Euclidean distance, SDGNMF is relatively insensitive to the noise in hyperspectral data and can better extract the internal structural information of the data, thus improving the unmixing accuracy. Result The experiment was carried out on simulated datasets and real datasets. Experiments prove that the algorithm proposed in this paper has achieved excellent subspace learning results and has good robustness. Compared with several other algorithms, SDGNMF has the advantage of being able to retain the similar structure after iteration, and the correlation between the endmember features is fully considered, thus the similar substances distributed in adjacent regions can be separated. Therefore, SDGNMF can better display the details of local abundance and obtain a more realistic and perfect abundance map. Conclusion In general, the unmixing model proposed in this paper can overcome noise, and consider the correlation of features and data manifold structure at the same time. Experiments show that the algorithm proposed in this paper can effectively improve the unmixing accuracy of most hyperspectral remote sensing data, especially those with high feature correlation. However, the algorithm proposed in this paper still faces the problem of high computational complexity. In addition, the algorithm only considers the prior knowledge of abundance. Therefore, future work will focus on solving these problems.