Influence of Fractional Differential on Correlation Coefficient between EC<sub>1:5</sub> and Reflectance Spectra of Saline Soil

Xia, Nan; Tiyip, Tashpolat; Kelimu, Ardak; Nurmemet, Ilyas; Ding, Jianli; Zhang, Fei; Dong, Zhang

doi:10.1155/2017/1236329

Cited by 14 publications

(12 citation statements)

References 48 publications

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“…This is mainly because in these applications, the fractional-order model has more accurate results than the original integer differential model. FD mainly has three forms of expressions [8,9]: Riemann-Liouville (R-L), Grünwald- Journal of Sensors Letnikov (G-L), and Caputo. Of which, the generally G-L FD can be defined as…”

Section: Comparison Of Fractional Differential and Integermentioning

confidence: 99%

“…Also, this novel pretreatment method for saline soils could prevent the loss of important information caused by only considering the traditional integer order. Xia et al [9] took the 43 saline soil samples of Ebinur Lake in Xinjiang, China, as data sources, and analyzed the correlation between original spectral reflectance and electrical conductivity. Results showed that fractional derivate could improve the CC for some single bands, such as 505 nm, 2239 nm, and 2443 nm.…”

Section: Introductionmentioning

confidence: 99%

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Application of Fractional Differential Calculation in Pretreatment of Saline Soil Hyperspectral Reflectance Data

et al. 2018

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Pretreatment of spectrum data is a necessary and effective method for improving the accuracy of hyperspectral model building. Traditional differential calculation pretreatment only considers the integer-order differential, such as the 1st order and 2nd order, and overlooks important spectrum information located at fractional order. Since fractional differential (FD) has rarely been applied to spectrum field measurement, there are few reports on the spectrum features of saline soils under different degrees of human interference. We used FD to analyze field spectrum data of saline soil collected from Xinjiang’s Fukang City. Order interval of 0.2 was adopted to divide 0–2 orders into 11-order differentials. MATLAB programming was used to convert the raw spectral reflectance and its four common types of mathematics and to conduct FD calculation. Spectrum data for area A (no human interference area) and area B (human interference area) was separately processed. From the statistical analysis of soil salinization characteristics, the salinization degree and type for area B were more diverse and complicated than area A. MATLAB simulation results showed that FD calculation could depict the minute differences between different FD order spectra under different human interference areas. The overall differential value trend appeared to move towards 0 reflectance value. After differential processing, the trend of bands that passed the 0.05 significance test of correlation coefficient (CC) showed an increase first then decrease later. The maximum CC absolute value for five spectrum transformations all appeared in the fractional order. FD calculation could significantly increase the correlation between spectral reflectance and soil salt content both for full-band and single-band spectra. Results of this study can serve as a reference for the application of FD in field hyperspectral monitoring of soil salinization for different human interference areas.

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Section: Comparison Of Fractional Differential and Integermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of Fractional Differential Calculation in Pretreatment of Saline Soil Hyperspectral Reflectance Data

et al. 2018

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“…In addition to the pretreatment of hyperspectral signals for saline soil between spectral reflectance and salt content, fractional derivatives can also be used to pretreat other types of soil hyperspectral signals between spectral reflectance and nutrient content. For example, Xia et al [32] used fractional derivative to preprocess the spectrum collected in Ebinur Lake of Xinjiang, China, and the correlation coefficient between electricity conductivity and soil reflectance spectra was analyzed. Results show that fractional derivative details the varying trends of soil reflectance spectra among 0-order to 2-order.…”

Section: Discussionmentioning

confidence: 99%

Impact of Fractional Calculus on Correlation Coefficient between Available Potassium and Spectrum Data in Ground Hyperspectral and Landsat 8 Image

Gan

Yuan

et al. 2019

Mathematics

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As the level of potassium can interfere with the normal circulation process of biosphere materials, the available potassium is an important index to measure the ability of soil to supply potassium to crops. There are rarely studies on the inversion of available potassium content using ground hyperspectral remote sensing and Landsat 8 multispectral satellite data. Pretreatment of saline soil field hyperspectral data based on fractional differential has rarely been reported, and the corresponding relationship between spectrum and available potassium content has not yet been reported. Because traditional integer-order differential preprocessing methods ignore important spectral information at fractional-order, it is easy to reduce the accuracy of inversion model. This paper explores spectral preprocessing effect based on Grünwald-Letnikov fractional differential (order interval is 0.2) between zero-order and second-order. Field spectra of saline soil were collected in Fukang City of Xinjiang. The maximum absolute of correlation coefficient between ground hyperspectral reflectance and available potassium content for five mathematical transformations appears in the fractional-order. We also studied the tendency of correlation coefficient under different fractional-order based on seven bands corresponding to the Landsat 8 image. We found that fractional derivative can significantly improve the correlation, and the maximum absolute of correlation coefficient under five spectral transformations is in Band 2, which is 0.715766 for the band at 467 nm. This study deeply mined the potential information of spectra and made up for the gap of fractional differential for field hyperspectral data, providing a new perspective for field hyperspectral technology to monitor the content of soil available potassium.Mathematics 2019, 7, 488 2 of 15 of convenience, speed, and high precision [8][9][10]. Visible, near-infrared and mid-infrared spectroscopy technologies have been widely applied in soil science.In recent years, domestic and foreign scholars have conducted extensive research on soil salinity, moisture, organic matter, and total nitrogen in different types of ecosystems, such as wetlands, forests, grasslands, and farmlands in arid and semi-arid regions [11][12][13][14][15]. There is less research on available potassium content [16]. Liu et al. [17] adopted visible/short-wave near-infrared spectroscopy to measure soil available nitrogen and available potassium. They introduced first-order differential algorithm for spectral pretreatment, and their simulation showed that the model built by least squares support vector machine (LS-SVM) combined with 1-order differential has higher precision. However, the hyperspectral inversion models established for available potassium are mainly constructed based on 1-order or 2-order derivative for spectral reflectance, reciprocal, and logarithm. However, related research points out that traditional integer-order differential transformation ignores the gradual fractional differential informat...

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“…Wang et al [27] studied the application of fractional-order derivative in the hyperspectral detection of chromium content in desert soil and revealed that 1.8-order derivative model was much better than others. Xia et al [28] studied the soil salinization in Ebinur Lake and proposed a new method to analyze the correlation coefficient between EC 1:5 and spectrum using fractional differential. Results showed that fractional differential mined more hidden details of the spectra.…”

Section: Introductionmentioning

confidence: 99%

Study on the Effect of Fractional Derivative on the Hyperspectral Data of Soil Organic Matter Content in Arid Region

Xiong

Tian

2019

Journal of Spectroscopy

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Discussion on the application of fractional derivative algorithm in monitoring organic matter content in field soil is scarce. This study is aimed at improving the accuracy of soil organic matter (SOM) content estimation in arid region, and the undesirable model precision caused by the missing information associated with the larger discrepancy between conventional integer-order, i.e., first order and second order, derivative, and raw spectral data. We utilized fractional derivative (of zeroth order to second order in 0.2-order interval) processing on the field spectral reflectance (R) of the salinized soil sample from Fukang, Xinjiang, and its square root-transformed (R), log-transformed (lgR), inverse-transformed (1/R), and inverse log-transformed (1/lgR) values. The correlation coefficient of each fractional derivative of transformed value with SOM content was calculated. The simulation showed the derivative reflectance value approximates zero. When increasing from zeroth order to first order, the derivative curve gradually aligns to the first-order curve, and the destination alignment was also seen while increasing from first order to second order. The significance test of 0.05 showed initial increase and later decay of bands in the five spectral transformations as the order increases. For specific bands, the derivative algorithm clearly justifies the correlation between soil spectra and organic matter content, and all of the absolute highest correlation coefficient values were obtained at fractional orders. When compared with integer-order derivative, fractional derivative is significantly better in improving correlation, showing overall superiority. The result supports the application of fractional derivative in the hyperspectral remote monitor of SOM in arid zone, which may in turn realize the timely and accurate SOM monitor in arid zone, and provides the basis for ecological restoration.

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Influence of Fractional Differential on Correlation Coefficient between EC_1:5 and Reflectance Spectra of Saline Soil

Cited by 14 publications

References 48 publications

Application of Fractional Differential Calculation in Pretreatment of Saline Soil Hyperspectral Reflectance Data

Application of Fractional Differential Calculation in Pretreatment of Saline Soil Hyperspectral Reflectance Data

Impact of Fractional Calculus on Correlation Coefficient between Available Potassium and Spectrum Data in Ground Hyperspectral and Landsat 8 Image

Study on the Effect of Fractional Derivative on the Hyperspectral Data of Soil Organic Matter Content in Arid Region

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Influence of Fractional Differential on Correlation Coefficient between EC1:5 and Reflectance Spectra of Saline Soil

Cited by 14 publications

References 48 publications

Application of Fractional Differential Calculation in Pretreatment of Saline Soil Hyperspectral Reflectance Data

Application of Fractional Differential Calculation in Pretreatment of Saline Soil Hyperspectral Reflectance Data

Impact of Fractional Calculus on Correlation Coefficient between Available Potassium and Spectrum Data in Ground Hyperspectral and Landsat 8 Image

Study on the Effect of Fractional Derivative on the Hyperspectral Data of Soil Organic Matter Content in Arid Region

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Influence of Fractional Differential on Correlation Coefficient between EC_1:5 and Reflectance Spectra of Saline Soil