应用Sinkhorn距离和图正则约束的高效解混算法

杨露露; 李春芝; 陈晓华; 王丽

doi:10.11834/jrs.20221126

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应用Sinkhorn距离和图正则约束的高效解混算法
Efficient unmixing algorithm using Sinkhorn distance and graph regularization constraints
2023年27卷第11期页码：2603-2616
纸质出版日期： 2023-11-07 ，
DOI： 10.11834/jrs.20221126

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杨露露，李春芝，陈晓华，王丽.2023.应用Sinkhorn距离和图正则约束的高效解混算法.遥感学报，27（11）： 2603-2616

Yang L L，Li C Z，Chen X H and Wang L. 2023. Efficient unmixing algorithm using Sinkhorn distance and graph regularization constraints. National Remote Sensing Bulletin， 27（11）：2603-2616
杨露露，李春芝，陈晓华，王丽.2023.应用Sinkhorn距离和图正则约束的高效解混算法.遥感学报，27（11）： 2603-2616 DOI： 10.11834/jrs.20221126.

Yang L L，Li C Z，Chen X H and Wang L. 2023. Efficient unmixing algorithm using Sinkhorn distance and graph regularization constraints. National Remote Sensing Bulletin， 27（11）：2603-2616 DOI： 10.11834/jrs.20221126.

摘要

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。由于传统非负矩阵分解采用欧氏距离度量原始矩阵与重构矩阵之间的误差，因而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，本研究在地球移动距离的基础上引入熵正则约束，用Sinkhorn距离代替欧氏距离，建模不同维度特征之间的关系。同时，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。本研究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。

Abstract

Hyperspectral remote sensing technology

as a new type of earth observation technology

provides rich spectral information of features and can identify and finely classify feature targets. A single pixel in hyperspectral images contains multiple features as limited by the spatial resolution. As a result

the mixed pixels become widespread. Ultimately

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. Thus

traditional NMF often uses Euclidean distance as a similarity measure method. On the one hand

hyperspectral data have manifold distribution. Thus

simple linear measurement between two points cannot accurately represent the distance between data. This problem makes the sample internal features weakly correlated

which results 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.

Method Considering the correlation between data manifolds and features

this study proposes a nonnegative 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 fully utilize the correlation of features. In particular

this study introduces the graph regularity constraint based on the Sinkhorn distance 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

which improves the unmixing accuracy.

Result An experiment was conducted on simulated and real datasets. Experimental results prove that the proposed algorithm proposed has achieved excellent subspace learning results and has good robustness. Compared with several other algorithms

SDGNMF can retain the similar structure after iteration. The correlation between the endmember features is also fully considered in SDGNMF. 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 proposed unmixing model can overcome noise and consider the correlation of features and data manifold structure simultaneously. Experimental results show that the proposed algorithm can effectively improve the unmixing accuracy of most hyperspectral remote sensing data

especially those with high feature correlation. However

the proposed algorithm has high computational complexity. In addition

the algorithm only considers the prior knowledge of abundance. Therefore

future work will focus on solving these problems.

关键词

高光谱解混非负矩阵分解Sinkhorn距离熵正则图正则

Keywords

hyperspectral unmixingnonnegative matrix factorization (NMF)Sinkhorn distanceentropy regularizationgraph regularization

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