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Open AccessArticle

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

1
Faculty of Land Resource Engineering, Kunming University of Science and Technology, Kunming 650093, China
2
College of Information Engineering, Qujing Normal University, Qujing 655011, China
3
College of Applied Arts and Science, Beijing Union University, Beijing 100083, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(6), 488; https://doi.org/10.3390/math7060488
Received: 1 May 2019 / Revised: 21 May 2019 / Accepted: 22 May 2019 / Published: 28 May 2019
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. View Full-Text
Keywords: field spectrum; fractional calculus; desert soil; available potassium; correlation analysis field spectrum; fractional calculus; desert soil; available potassium; correlation analysis
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Fu, C.; Gan, S.; Yuan, X.; Xiong, H.; Tian, A. Impact of Fractional Calculus on Correlation Coefficient between Available Potassium and Spectrum Data in Ground Hyperspectral and Landsat 8 Image. Mathematics 2019, 7, 488.

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