基于分数阶微分预处理高光谱数据的荒漠土壤有机碳含量估算

对光谱数据进行预处理是提升高光谱建模精度十分必要和有效的途径。为了研究分数阶微分预处理方法在高光谱数据估算荒漠土壤有机碳含量中的应用，该研究以艾比湖流域为研究靶区，利用2015年5月采集的103个表层土壤样本的实测有机碳数据和室内测定的高光谱数据，以0.2阶为步长对原始光谱反射率及对应的倒数变换、对数变换、对数倒数变换、均方根变换的0-2阶微分进行分数阶运算预处理并研究其与土壤有机碳含量相关性，基于通过0.01显著性检验的特征波段对土壤有机碳含量进行偏最小二乘回归建模并进行精度分析。结果表明：1）分数阶微分预处理可以细化土壤有机碳及其光谱反射率相关性的变化趋势；2）各阶微分预处理后的相关系数通过显著性检验波段的数量均呈现先增后减的趋势，但波段数量最多的对应阶数并不统一；3）对数变换的1.6阶微分所建立的模型为最优模型，该模型的RMSEC=2.433 g/kg，R2c=0.786，RMSEP=2.263 g/kg，R2p=0.825，RPD=2.392。说明了分数阶预处理过后的模型精度和稳健性较整数阶微分有了大幅提升，并且运用在高光谱反演土壤有机碳含量上是可行的。

Estimation of desert soil organic carbon content based on hyperspectral data preprocessing with fractional differential

Abstract: Soil organic carbon (SOC) is a crucial soil property which has attracted wide attention in the field of global change. This is especially true in the arid and semi-arid regions. In recent years, it is a hot topic to estimate SOC content by hyperspectral remote sensing technology, however, it is hard to estimate SOC content in desert area precisely when it is less than 2%. Existing work, including related research history and current status, has mostly focused on integer differential, which yet might influence the effective information detection and cause the loss of spectral information to some extent. Therefore, this study aimed to bring fractional order differential algorithm into the preprocessing of hyperspectral data. With 103 surface soil samples collected from the Ebinur Lake basin in Xinjiang Uighur Autonomous Region, China, the SOC contents and reflectance spectra were measured in the laboratory. After removing the marginal bands (350-400 and 2401-2500 nm) and smoothed by Savitzky-Golay filter, the raw hyperspectral reflectance (R) data were transformed by 4 mathematical methods, i.e., the reciprocal, logarithm, logarithm-reciprocal and root mean square method, respectively. Secondly, their 0-2 order differentials (taking 0.2-order as step) were calculated by Grünwald-Letnikov fractional differential equation. And then, we computed the correlation coefficients between each fractional order differential value of R, its 4 mathematical transformation forms and SOC content. After choosing the feature bands whose correlation coefficient passed the significance test at 0.01 level, 103 samples were divided into 2 parts: 69 for model calibration and 34 for validation. Subsequently, partial least squares regression (PLSR) was employed to build the hyperspectral estimation models of SOC content. And then, root mean square error of calibration (RMSEC), determination coefficient of calibration (R2c), root mean square error of prediction (RMSEP), determination coefficient of predicting (R2p) and relative prediction deviation (RPD) were used for accuracy assessment. The results showed that: 1) Fractional order differential algorithm could refine the correlation coefficient curves between the SOC content and the raw hyperspectral reflectance in the wavelength ranges of 450-600, 640-700 and 1400-1500 nm, and also reduce the information loss to some extent; 2) With the order increasing, the number of bands whose correlation coefficient passed the significance test at 0.01 level firstly increased and then decreased, but the number of bands did not reach the maximum at the same order, and some differences occurred; 3) Comparing the predictive effects of 55 SOC estimating models calibrated by PLSR, the model based on 1.6-order differential of logarithm transform was much better than others, and had better performance in predicting SOC content in the study area (RMSEC=2.433 g/kg, R2c=0.786, RMSEP=2.263 g/kg, R2p=0.825, RPD=2.392). And indeed, the models based on fractional order differentials were more robust and accurate than the conventional integer differential ones. Over all, it is a fairly satisfactory preprocessing method of hyperspectral data in the quantitative study on soil nutrients by means of remote sensing. In order to achieve more universal and stable inversion model, the next step is to enlarge the sampling area and the number of soil samples as much as possible to improve and perfect the soil hyperspectral database.