Applicability of Different Fractional Order Differential Forms in the Hyperspectral Inversion of Saline Soil Conductivity
ZHOU Feng-xi1, 2, TENG Xiang-shuai1, HAO Jun-ming1, 3, WANG Li-ye1
1. School of Civil Engineering, Lanzhou University of Technology, Lanzhou 730050, China
2. Western Engineering Research Center of Disaster Mitigation in Civil Engineering of Ministry of Education, Lanzhou University of Technology, Lanzhou 730050, China
3. Gansu Emergency Surveying and Mapping Engineering Research Center, Lanzhou University of Technology, Lanzhou 730050, China
Abstract：In recent years, some scholars have applied the fractional order differential theory to the hyperspectral inversion of the conductivity of saline soils and achieved more significant results. However, the Grünwald-Letnikov fractional-order differential definition form has been used in most of the existing studies. The application of the Riemann-Liouville and Caputo fractional-order differential definition form has been less studied. The applicability of the Riemann-Liouville and Caputo fractional-order differential definition form to the hyperspectral inversion of saline soil conductivity is still unclear. In this study, based on the measured soil conductivity and hyperspectral data, we consider the common Grünwald-Letnikov, Riemann-Liouville, and Caputo fractional-order differential definitions and realize the Grünwald-Letnikov, Riemann-Liouville and Caputo fractional-order differential processing functions through software programming. The differences in the hyperspectral data of the soil samples in different fractional-order differential definitions are compared and analyzed after the same-order differential processing, and the characteristics of the changes with the increase of the order. The results show that the spectral reflectance curves of soil samples under different fractional-order differential definitions show significant differences after the same-order differential treatment; in the range of 0.1~1 order, the number of highly variable bands of Grünwald-Letnikov, Riemann-Liouville, and Caputo after fractional-order differential treatment shows an increasing tendency as the number of differential orders increases; When the differential order tends to 1, the differential value of spectral reflectance gradually decreases and approaches 0, and the fluctuation range gradually decreases, while the variability of the spectral data is enhanced with the decrease of the fluctuation range; Grunwald-Letnikov fractional differential processing increased the correlation coefficients by 9.5% and 6.7% at the 0.6 and 0.7 orders; after Riemann-Liouville and Caputo fractional differential processing, the correlation coefficients increased by about 1% at the 0.8~0.9 orders and 0.7~0.9 orders respectively. This study provides a new research idea for hyperspectral data preprocessing and a better reference for applying fractional differential theory to soil salinization remote sensing inversion.
Key words：Saline soil; Electrical conductivity; Spectral reflectance; Fractional order differential
周凤玺，滕祥帅，郝君明，王立业. 不同分数阶微分形式在盐渍土电导率高光谱反演中的适用性研究[J]. 光谱学与光谱分析, 2025, 45(01): 272-281.
ZHOU Feng-xi, TENG Xiang-shuai, HAO Jun-ming, WANG Li-ye. Applicability of Different Fractional Order Differential Forms in the Hyperspectral Inversion of Saline Soil Conductivity. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2025, 45(01): 272-281.
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