融入结构信息的稀疏低秩丰度估计在光谱解混中的应用
投稿时间:2017-08-13  修订日期:2017-11-14  点此下载全文
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作者单位E-mail
袁静 清华大学 yuanjing20110824@sina.com.cn 
章毓晋 清华大学  
杨德贺 中国地震局地壳应力研究所 ydhmmm@163.com 
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目)
中文摘要:丰度估计(AE)是从高光谱图像中识别地物的关键预处理技术。鉴于线性混合模型的可解释性以及数学上的可操作性,基于约束线性回归理论的丰度矩阵估计的方法备受关注。目前,这些方法存在的缺陷是其拟合过程中仅仅考虑到估计数据与真实数据之间的拟合误差,忽略了估计数据的结构与真实数据的结构之间的相似性信息。基于此,提出了融合结构信息的线性回归模型,并应用于稀疏低秩的丰度矩阵估计领域。首先,通过增加结构信息改进传统的线性回归模型,并经数学理论证明了增加结构信息的线性回归模型较传统模型更加有效。其次,应用该方法改进稀疏低秩丰度估计的数学模型。最后,采用交替乘子法(ADMM)技术求解新模型。实验结果表明,多结构信息的稀疏低秩丰度估计算法能够有效地提高仿真数据和实际高光谱数据的丰度估计的估计精度,改善其抗噪性能。
中文关键词:解混  稀疏低秩  结构信息  丰度矩阵  ADMM
 
Sparse and Low-Rank Abundance Estimation with Structural Information
Abstract:Abundance estimation(AE) plays an essential role in the hyperspectral image processing and analysis. Owing to the simplicity and mathematical tractability, various methods based on the constrained linear regression are usually developed to estimate abundance matrix. The obvious limitation of these approaches is that the fitness between the estimated data and ground-truth data does not include the structural information, e.g. row difference, column difference and so on. In this paper, a novel linear regression algorithm is proposed by jointly adding the multi-structured information to the traditional linear regression model. And it is employed to modify sparse and low-rank abundance estimation model to improve estimated accuracy and robustness. Firstly, a new linear regression model is established by taking into account the structural information. Then, mathematical proof of the new linear regression method is presented. Afterwards, it is applied to modify the sparse low-rank abundance estimation model. Finally, Alternating Direction Method of Multipliers(ADMM) technique is adopted to solve the new model. The experimental results demonstrate that the proposed algorithms can capture structural information and improve the estimated performance on the simulated dataset and the real hyperspectral remote sensing images.
keywords:unmixing,sparse and low rank, structural information,abundance matrix,ADMM
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