# Soil Organic Matter Prediction Model with Satellite Hyperspectral Image Based on Optimized Denoising Method

^{1}

^{2}

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## Abstract

**:**

^{2}, 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 (R

^{2}= 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.

## 1. Introduction

^{2}= 0.79, the residual predictive deviation (RPD) is 2.21) was more accurate than a model based on the reflectance (R

^{2}= 0.77, RPD = 2.01). The above study generally utilized the difference, ratio and normalization spectral indexes, meaning that the spectral index is not fully developed. To better develop and utilize spectral information, we extracted more spectral indexes to improve the SOM prediction accuracy.

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, with an average elevation of 249.2 m. The eastern part of the study area is located in the Xiaoxing’an Mountains, and the western part is located in the hinterland of the Songnen Plain. The elevation gradually decreases from the middle to the eastern and western sides. The annual average temperature is approximately 2.9 °C, and the annual average precipitation is approximately 480 mm. Figure 1c is the Second National Soil Survey map, which is the great group level according to the Genetic Soil Classification of China. The map was obtained from http://vdb3.soil.csdb.cn/, accessed on 1 June 2020. The map was produced in the 1980s, and it was produced by the government by digging out and analyzing the soil profile. The scale of the map is 1:1,000,000. The study area includes Phaeozems, Chernozems and Cambisols, according to the World Reference Base for Soil Resources (Figure 1c). Phaeozems and Chernozems have higher SOM contents and good water-holding capacities. Different from Phaeozems, the surface layer of Chernozems has a calcic horizon. Cambisols primarily occur in relatively low-lying areas dispersed among the other soil classes. The study area is called the black soil region by local people because the surface of soil appears black, and the topsoil of the region is covered with black or dark humus. The soil in the black soil region is clayey soil; thus, the difference in soil pH and texture is small, with little influence on the prediction results.

#### 2.2. Data Acquisition and Treatment

#### 2.2.1. Soil Sample Collection and Treatment

#### 2.2.2. GF-5 Hyperspectral Data Acquisition and Treatment

#### 2.3. Fractional-Order Derivatives (FOD)

#### 2.4. Denoising Methods

#### 2.4.1. Singular Value Decomposition (SVD)

_{m}) of the spectral reflectance signal, H

_{m}is a matrix of m*n, and the decomposition function of H

_{m}can be described as follows

^{*}is the conjugate transpose of V, and Σ is a m*n positive semidefinite matrix. When there is noise in the signal, H

_{m}is a nonsingular matrix. The following relation occurs among the singular values after decomposition

#### 2.4.2. Fourier Transform (FT)

#### 2.4.3. Discrete Wavelet Transform (DWT)

#### 2.5. Optimal Band Combination Algorithm

#### 2.6. Recursive Feature Elimination (RFE)

#### 2.7. Random Forest (RF)

- (1)
- Samples are randomly selected from the calibration set, and then each sample is used to build a decision tree;
- (2)
- Each split node in the decision tree is randomly selected from n inputs, such that the variable space can be completely divided;
- (3)
- The final result of the RF model is the average value of the predicted results of all decision trees.

#### 2.8. Model Calibration and Validation

^{2}), the root mean square error (RMSE) and the ratio of performance to interquartile range (RPIQ). In general, a well-performing model should have a high R

^{2}and RPIQ and low RMSE. The calculation formulas of the above parameters are as follows

_{i}is the laboratory-measured SOM content of sample i, ${\widehat{y}}_{i}$ is the predicted SOM content of soil sample i, $\overline{y}$ is the average SOM content of the whole-soil sample, IQ is the interquartile range (IQ = Q3 − Q1) of the observed values, Q1 is the first quartile and Q3 is the third quartile.

## 3. Results

#### 3.1. Description of Soil Samples

^{−1}, with a mean value of 40.81 g kg

^{−1}, an SD of 6.55 g kg

^{−1}, and a CV of 16.10%. Compared with the CV of the whole dataset, the CV of the calibration dataset is higher and that of the validation dataset is lower.

#### 3.2. Selected Optimal FOD

^{2}= 0.71, RMSE = 3.93 g kg

^{−1}, RPIQ = 1.07). Therefore, in this paper, the optimal FOD is 0.6-order, and a further analysis is made on the basis of 0.6-order FOD.

#### 3.3. Spectral Characteristics of Different Denoising Methods

#### 3.4. Optimal Band Combination Algorithm

#### 3.5. Selection of the Input Variables

#### 3.6. Prediction Accuracy and Spatial Distribution of SOM

^{2}= 0.62, RMSE = 4.20 g kg

^{−1}and RPIQ = 0.59), the SOM prediction accuracy can be improved by using different denoising methods. OR-SVD is less effective in improving the SOM prediction accuracy. OR-FT and OR-DWT can greatly improve the SOM prediction accuracy. The prediction accuracy of OR-DWT is the highest (R

^{2}= 0.77, RMSE = 3.57 g kg

^{−1}, RPIQ = 1.59). With the 0.6-order reflectance, the SOM prediction accuracy can be further improved under different denoising methods. The highest prediction accuracy is achieved by 0.6-order-DWT (R

^{2}= 0.84, RMSE = 3.36 g kg

^{−1}, RPIQ = 1.71). Compared with those of OR, the R

^{2}and RPIQ of 0.6-order-DWT are 22% and 1.12 higher, and the RMSE is 0.84 g kg

^{−1}lower.

## 4. Discussion

#### 4.1. Advantages of the Fractional-Order Derivative Method

#### 4.2. Comparation on the Performances of Different Denoising Methods

#### 4.3. Discrepancies between Spectral Indexes of Laboratory-Measured and Satellite Hyperspectral Data

^{**}(Table 3). With the 0.6-order-DWT, the selected bands with the highest correlation appear at 400–600 and 2100 nm; the correlation is approximately −0.66

^{**}(Table 3). Compared with the sensitive bands between the laboratory-measured hyperspectral data and SOM content (600–800, 1200 nm) [74], the sensitive bands between the satellite hyperspectral data and SOM content occur in the range of visible light, especially after the FOD processing.

#### 4.4. Advantages of Recursive Feature Elimination

^{2}= 0.57, RMSE = 4.33 g kg

^{−1}, RPIQ = 0.30), that of the selected input variables after RFE is better (R

^{2}= 0.62, RMSE = 4.20 g kg

^{−1}, RPIQ = 0.59) (Figure 2 and Figure 5). The method has the following advantages. First, the model can reduce the redundant information in hyperspectral data and effectively improve the computational efficiency of the model. Second, the algorithm directly discriminates the optimal set of input variables through the prediction accuracy. Compared with the method of selecting the input variables according to the correlation, the model established in this paper can simplify the analysis process of SOM prediction, be more easily transformed for subsequent practical applications and be applied to remote sensing satellites for regional-scale SOM prediction. Finally, compared with the principal component analysis commonly used in previous research [5,78], RFE can retain the physical meaning of input, which is helpful for better understanding the relationship between the input and changes in SOM content [79].

#### 4.5. The Uncertainty Analysis

## 5. Conclusions

^{2}= 0.71, RMSE = 3.93 g kg

^{−1}, RPIQ = 1.07), because the 0.6-order spectral curve still retains some of the obvious absorption peak and absorption valley of original reflectance, and the curve is relatively smooth. (2) The correlation coefficients between the five extracted spectral indexes and SOM content passed the significance test at the 0.01 level. Compared with the SOM-sensitive bands of laboratory-measured hyperspectral data, the selected bands of different spectral indexes occured more in the range of visible light. (3) The selected input variables after the RFE algorithm were mainly spectral indexes. RFE can simplify the analysis process of SOM prediction and is more easily applied to remote-sensing satellites for regional-scale SOM prediction. (4) Both denoising methods can improve the SOM content prediction accuracy; the accuracies of the different denoising methods were ranked DWT > FT > SVD, and the highest prediction accuracy was achieved by 0.6-order-DWT (R

^{2}= 0.84, RMSE = 3.36 g kg

^{−1}, RPIQ = 1.71).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Overview of the study area: (

**a**) northern Songnen Plain map; (

**b**) GF-5 hyperspectral image; (

**c**) soil sampling location and soil classes; (

**d**,

**e**) photographs of the soil surface of cultivated land after plowing; (

**f**) sampling with the five-point method.

**Figure 2.**With increasing from 0 to 2 with a 0.2 step length, prediction accuracy of the laboratory-measured versus predicted SOM contents from the validation dataset in the RF prediction model with the full spectrum as input variables.

**Figure 3.**Spectral reflectance curves under different denoising methods. Note: OR represents the original reflectance. OR-SVD, OR-FT, OR-DWT and 0.6-order represents the reflectance after singular value decomposition, fourier transform, discrete wavelet transform and 0.6-order derivatives processing, respectively. 0.6-order-SVD, 0.6-order-FT and 0.6-order-DWT represents the 0.6-order reflectance after singular value decomposition, fourier transform and discrete wavelet transform processing, respectively.

**Figure 4.**Established optimal spectral indexes under different denoising methods. Note: OR-DI represents the difference index of the OR, OR-SVD-DI represents the difference index of the reflectance after SVD processing, 0.6-order-SVD-DI represents the difference index of the 0.6-order reflectance after SVD, etc.

**Figure 5.**Scatter plots of the laboratory-measured versus predicted SOM contents from the validaTable 1. line, and the red solid lines represent the regression line.

**Figure 7.**Varying spectral curves of the whole dataset under different FODs (0 to 2, increment of 0.2). The red curve represents the average spectral curve of the whole dataset.

Spectral Index and Formula | Literature |
---|---|

$DI({R}_{i},{R}_{j})={R}_{i}-{R}_{j}$ | [35] |

$RI({R}_{i},{R}_{j})=\frac{{R}_{i}}{{R}_{j}}$ | [35] |

$NDI({R}_{i},{R}_{j})=\frac{{R}_{i}-{R}_{j}}{{R}_{i}+{R}_{j}}$ | [35] |

$RDVI({R}_{i},{R}_{j})=\frac{{R}_{i}-{R}_{j}}{\sqrt{{R}_{i}+{R}_{j}}}$ | [54,55] |

$MSR({R}_{i},{R}_{j})=\frac{{R}_{i}}{{R}_{j}}-1/\sqrt{\frac{{R}_{i}}{{R}_{j}}+1}$ | [56,57] |

_{i}and R

_{j}represent the bands selected from 430–900, 1050–1350, 1451–1771 and 1982–2450 nm. The spectral indexes are constructed from the OR and FODs, respectively. The process of constructing the spectral indexes is implemented in MATLAB R2016b.

**Table 2.**Statistical descriptions of the SOM contents on the whole, calibration and validation datasets.

Set | N | Max (g kg ^{−1}) | Min (g kg ^{−1}) | Mean (g kg ^{−1}) | SD (g kg ^{−1}) | CV (%) |
---|---|---|---|---|---|---|

Whole dataset | 166 | 56.30 | 26.10 | 40.81 | 6.55 | 16.10 |

Calibration dataset | 111 | 56.30 | 26.10 | 40.90 | 6.76 | 16.53 |

Validation dataset | 55 | 55.80 | 26.20 | 40.64 | 6.11 | 15.03 |

Denoising Method | DI | RI | NDI | RDVI | MSR | |||||
---|---|---|---|---|---|---|---|---|---|---|

Bands | R | Bands | R | Bands | R | Bands | R | Bands | R | |

OR | R_{805}, R_{775} | 0.55 ** | R_{2412}, R_{741} | −0.57 ** | R_{822}, R_{771} | −0.55 ** | R_{565}, R_{557} | −0.61 ** | R_{2412}, R_{527} | −0.57 ** |

OR-SVD | R_{531}, R_{514} | 0.59 * | R_{2311}, R_{548} | −0.61 ** | R_{544}, R_{540} | 0.61 ** | R_{2252}, R_{1114} | 0.60 ** | R_{2311}, R_{548} | −0.61 ** |

OR-FT | R_{771}, R_{651} | 0.59 ** | R_{2412}, R_{527} | −0.62 ** | R_{450}, R_{441} | 0.61 ** | R_{1350}, R_{651} | −0.62 ** | R_{2412}, R_{488} | −0.61 ** |

OR-DWT | R_{882}, R_{771} | 0.58 ** | R_{2226}, R_{766} | −0.61 ** | R_{818}, R_{771} | −0.58 ** | R_{2066}, R_{1131} | 0.62 ** | R_{2218}, R_{762} | −0.61 ** |

0.6-order | R_{1072}, R_{822} | 0.59 ** | R_{1468}, R_{433} | −0.63 ** | R_{1468}, R_{1433} | −0.62 ** | R_{570}, R_{753} | −0.70 ** | R_{1468}, R_{433} | −0.64 ** |

0.6-order-SVD | R_{2024}, R_{1072} | −0.60 ** | R_{514}, R_{454} | −0.62 ** | R_{493}, R_{454} | −0.63 ** | R_{2201}, R_{843} | 0.64 ** | R_{514}, R_{454} | 0.67 ** |

0.6-order-FT | R_{1603}, R_{886} | −0.64 ** | R_{1721}, R_{685} | −0.65 ** | R_{1721}, R_{445} | −0.62 ** | R_{578}, R_{749} | −0.77 ** | R_{1721}, R_{685} | −0.65 ** |

0.6-order-DWT | R_{2176}, R_{890} | −0.64 ** | R_{2066}, R_{441} | −0.65 ** | R_{2074}, R_{433} | −0.62 ** | R_{574}, R_{835} | −0.77 ** | R_{2066}, R_{441} | −0.64 ** |

_{805}represents the band at 805 nm, * represents significant value at the 0.01 < p < 0.05 level, and ** represents significant value at the p < 0.01 level.

Denoising Method | Input Variables |
---|---|

OR | R_{1485}, R_{1511}, RI, NDI, RDVI, MSR |

OR-SVD | R_{1485}, R_{1536}, RI, NDI, MSR |

OR-FT | DI, RI, NDI, RDVI, MSR |

OR-DWT | RI, NDI, RDVI, MSR |

0.6-order | R_{488}, R_{531}, RI, NDI, MSR |

0.6-order-SVD | R_{598}, DI, NDI, RDVI, MSR |

0.6-order-FT | DI, RI, NDI, RDVI, MSR |

0.6-order-DWT | DI, RI, NDI, RDVI |

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## Share and Cite

**MDPI and ACS Style**

Meng, X.; Bao, Y.; Ye, Q.; Liu, H.; Zhang, X.; Tang, H.; Zhang, X.
Soil Organic Matter Prediction Model with Satellite Hyperspectral Image Based on Optimized Denoising Method. *Remote Sens.* **2021**, *13*, 2273.
https://doi.org/10.3390/rs13122273

**AMA Style**

Meng X, Bao Y, Ye Q, Liu H, Zhang X, Tang H, Zhang X.
Soil Organic Matter Prediction Model with Satellite Hyperspectral Image Based on Optimized Denoising Method. *Remote Sensing*. 2021; 13(12):2273.
https://doi.org/10.3390/rs13122273

**Chicago/Turabian Style**

Meng, Xiangtian, Yilin Bao, Qiang Ye, Huanjun Liu, Xinle Zhang, Haitao Tang, and Xiaohan Zhang.
2021. "Soil Organic Matter Prediction Model with Satellite Hyperspectral Image Based on Optimized Denoising Method" *Remote Sensing* 13, no. 12: 2273.
https://doi.org/10.3390/rs13122273