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In order to improve the signal-to-noise ratio of the hyperspectral sensors and exploit the potential of satellite hyperspectral data for predicting soil properties, we took MingShui County as the study area, which the study area is approximately 1481 km2, and we selected Gaofen-5 (GF-5) satellite hyperspectral image of the study area to explore an applicable and accurate denoising method that can effectively improve the prediction accuracy of soil organic matter (SOM) content. First, fractional-order derivative (FOD) processing is performed on the original reflectance (OR) to evaluate the optimal FOD. Second, singular value decomposition (SVD), Fourier transform (FT) and discrete wavelet transform (DWT) are used to denoise the OR and optimal FOD reflectance. Third, the spectral indexes of the reflectance under different denoising methods are extracted by optimal band combination algorithm, and the input variables of different denoising methods are selected by the recursive feature elimination (RFE) algorithm. Finally, the SOM content is predicted by a random forest prediction model. The results reveal that 0.6-order reflectance describes more useful details in satellite hyperspectral data. Five spectral indexes extracted from the reflectance under different denoising methods have a strong correlation with the SOM content, which is helpful for realizing high-accuracy SOM predictions. All three denoising methods can reduce the noise in hyperspectral data, and the accuracies of the different denoising methods are ranked DWT > FT > SVD, where 0.6-order-DWT has the highest accuracy (R2 = 0.84, RMSE = 3.36 g kg−1, and RPIQ = 1.71). This paper is relatively novel, in that GF-5 satellite hyperspectral data based on different denoising methods are used to predict SOM, and the results provide a highly robust and novel method for mapping the spatial distribution of SOM content at the regional scale.

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