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目前大多数高光谱图像波段选择方法仅考虑波段信息冗余问题，忽略了所选波段的噪声水平，致使选取的代表性波段子集中可能含有噪声水平较高的波段。为解决这一问题，本文提出一种噪声鲁棒的高光谱图像波段自适应分区与子空间搜索方法。首先，基于皮尔逊相关系数构造高光谱图像波段相关性矩阵；然后，将高光谱图像光谱波段等分为若干子空间，通过构造与皮尔逊相关系数相适应的子空间划分最优目标函数，自适应地调整子空间的分割点；最后，综合考虑波段的信息熵和噪声水平，在子空间波段选择时将噪声水平以惩罚项的形式反映在优化问题的目标函数中。在Indian Pines、Washington DC和Salinas三个数据集上进行了实验，采用波段平均相关性、分类精度两种指标对不同方法的波段选择结果进行评价，并分析各种波段选择方法的噪声鲁棒性。实验结果表明，本文方法能够挑选出信息量大且噪声水平低的代表性波段。与其它波段选择方法相比，本文方法所选择的代表性波段平均相关性弱，分类精度高，在包含噪声波段的高光谱图像中效果尤为显著。
Objective: Most of the proposed hyperspectral image band selection methods only consider the problem of band information redundancy and ignore the noise level of the selected bands. Therefore, the representative band subset may contain high-noise bands, which is not conducive to subsequent semantic segmentation, image classification, and other applications. In response to this problem, this paper proposes a noise-robust band selection method based on Pearson correlation coefficient, Information Entropy and Noise Level, referred to as PIENL. Method: In the proposed PIENL method, the Pearson correlation coefficient is first used to calculate the correlation between the bands, and the band correlation matrix is constructed. Then, the spectral bands of the hyperspectral image are divided into several subspaces of the same size, and an optimal subspace division objective function adapted to the Pearson correlation coefficient is constructed to adjust the division points of subspace. Finally, a new band information measurement criterion is proposed, which observes band information entropy and noise level at the same time and uses noise level as a penalty item in the objective function of the optimization problem. According to this criterion, the spectral band with high information entropy and low noise level in each subspace is selected as the representative band. Result: Experiments were conducted on three public hyperspectral datasets of Indian Pines, Salinas and Washington DC. Different band selection methods are evaluated using the average correlation degree of bands, classification accuracy and the noise robustness. The experimental results show that compared with other advanced band selection methods, this proposed PIENL method demonstrated outstanding band selection performance in terms of class separability, average correlation of representative bands, and noise robustness. Conclusion: The PIENL method has strong robustness to noise, and has achieved significant results on hyperspectral datasets containing noise bands. Through this study, we can conclude that: (1) Compared with Euclidean distance, the similarity measurement method based on the Pearson correlation coefficient is more suitable for measuring the spectral difference between the noisy hyperspectral image bands; (2) Eliminating the influence of noise level on the band information entropy helps to select representative bands with high image quality; (3) Compared with other band selection methods, the representative bands selected by the proposed PIENL method have weaker correlation and better class separability. The result is particularly significant in hyperspectral images with a lot of noise.