分数阶微分算法对盐渍土高光谱数据的影响研究

以艾比湖流域为研究区域，典型盐渍土为研究对象，引入分数阶微分，以0.2 为微分阶数间隔，将0~2 细分为11 阶微分，对原始光谱反射率及其常用的均方根、倒数等数学变换进行微分计算，结合实验室实测的土壤含盐量，从相关系数、标准差及信息熵三个角度探讨分数阶微分算法对土壤高光谱数据的影响。结果表明：随着微分阶数的增加，相关系数通过0.01显著性检验的波段数量总体上呈逐渐减少的趋势，且1 lg R 提升相关性的效果优于其他三种数学变换；高光谱数据总体分布变得相对集中，样本差异性逐渐降低；信息熵逐渐减小，信息无序度变小，有效信息量增加。分数阶微分能够细化相关系数、标准差及信息熵的变化趋势，丰富高光谱数据的预处理方法，可从光谱维的角度深层挖掘光谱信息，为深度利用高光谱数据提供崭新的视角，同时也可为特征波段选择、地表参数反演等高光谱数据的应用提供参考依据。

Abstract

The Ebinur Lake Basin is selected as the studied area, and typical saline soil is chosen as the research object. By introducing fractional differential algorithm, setting 0.2 as the order interval and dividing 0~2 into 11 orders, the differentials of the raw spectral reflectance and its four mathematical transformations are calculated. Combining with the soil salt content measured in laboratory, the effect of fractional differential algorithm on soil hyperspectral data is explored from the perspective of correlation coefficient, standard deviation and information entropy, respectively. The results show that with the increase of the differential order, the number of bands whose correlation coefficient passes the 0.01 level of the significance test follows a decreasing trend and the 1 lg R transformation has better capacity to enhance the correlation coefficient than the other three mathematical transformations; the overall distribution of hyperspectral data becomes relatively concentrated and the difference among soil samples is gradually reduced; the total information entropy decreases, the disorder degree of the information becomes smaller and the amount of valid information increases. Fractional differential can detail the varying trend of correlation coefficient, standard deviation and information entropy, enrich the methods of hyperspectral data pre-processing, delve into spectral information based on the spectral dimension, provide a new perspective on the deep exploitation of hyperspectral data, and offer a reference for various applications of hyperspectral data, such as characteristic band selection and quantitative inversion of land surface parameters.

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