# High-Spatial-Resolution NDVI Reconstruction with GA-ANN

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Dataset Preprocessing

#### 2.1. Study Area

#### 2.2. Dataset and Data Preprocessing

## 3. Methodology

#### 3.1. NDVI Calculation

#### 3.2. Reconstructing NDVI Model Based on GA-ANN Algorithm

#### 3.3. The Other Existing Reconstruction Models

_{1}; (2) estimate the temporal change of each class in the coarse-resolution image from t

_{1}to t

_{2}; (3) predict the fine-resolution image at t

_{2}using the class-level temporal change and calculate the residuals at each coarse pixel; (4) predict the fine-resolution image from the coarse image at t

_{2}with a TPS interpolator; (5) distribute residuals based on the TPS prediction; and (6) obtain the final prediction of the fine-resolution image using information in the neighborhood [37]. This method needs one pair of MODIS and Landsat images to be prepared with a matching time and position, a classification map of the Landsat image, and one MODIS image at the predicted time.

#### 3.4. Accuracy Assessment

^{2}), the correlation coefficient (R), the peak signal-to-noise ratio (PSNR), the structural similarity index measure (SSIM), and other indexes are usually used to describe whether two sets of data are correlated or similar [41,42,43]. Among them, the SSIM is used to measure the similarity of two images. It ranges from 0 to 1, and the larger the image, the more similar it is. The PSNR is a metric for evaluating image quality. Its unit is dB, and the larger its value, the less image distortion there is. R

^{2}is generally used to assess the degree of agreement between the predicted value and the actual value. R is used to describe the degree of linear correlation between two variables; if $\mathrm{R}>0$, there is a positive correlation; if $\mathrm{R}=0$, there is no correlation; and if $\mathrm{R}<0$, there is a negative correlation.

## 4. Results

#### 4.1. Performance of Reconstructed NDVI Model

#### 4.1.1. The Self-Validation of Reconstructed NDVI Model

#### 4.1.2. Evaluation of Reconstructed NDVI Model

#### 4.1.3. Verification with Sentinel Data

#### 4.2. Comparison with Existing Methods

## 5. Analysis and Discussion

#### 5.1. Spatiotemporal Analysis of the High-Spatial-Resolution NDVI Product

#### 5.2. Uncertainty of Reconstructed NDVI Model Based on GA-ANN Algorithm

#### 5.2.1. Influence of Selection of Random Points

#### 5.2.2. Influence of Data Resampling

#### 5.2.3. Influence of Land Use Data and Different Sensors and Bands Used by MODIS, Landsat, and Sentinel

#### 5.3. Advantages of the Reconstructed NDVI Model Based on GA-ANN

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Flowchart for reconstructing the NDVI (“polluted by clouds” refers to areas covered by clouds and cloud shadows; “missing” refers to areas not covered by Landsat imagery).

**Figure 3.**The RMSE and R of different hidden layers of the reconstructed NDVI model based on GA-ANN.

**Figure 6.**Validation of random point and true-color image distribution and comparison of the mean NDVI statistical analysis for the method in this paper and Sentinel. (

**a**) Validation of random point and true-color image distribution. (

**b**) Change in the mean value of NDVI. (

**c**) Comparison of this paper's method with Sentinel NDVI for different vegetation types.

**Figure 8.**The NDVIs of ESTARFM, FSDAF, and the methods used in this study from a visual point of view.

**Figure 11.**The MAE, RMSE, and R with different numbers of random points and hidden layers (3 to 9 are hidden layers).

**Figure 12.**RMSE and R for two resampling methods (Landsat resampled to 250 m; MODIS resampled to 30 m).

**Table 1.**The satellite data used in this study and the spatial and temporal resolution of the reconstructed NDVI.

Data | Spatial Resolution | Temporal Resolution | Band | Time Range |
---|---|---|---|---|

MOD13Q1 | 250 m | 16 d | NDVI | 2018-01-01–2020.12.31 |

Landsat 8 L2 | 30 m | 16 d | SR_B4 (RED) SR_B5 (NIR) | 2018-01-01–2020.12.31 |

Sentinel-2 L2 | 10 m | 5 d | B4 (RED) B8 (NIR) | |

Reconstructed NDVI | 30 m | 16 d |

Landsat 8 L2 | Sentinel-2 L2 | ||||
---|---|---|---|---|---|

Band | Bandwidth (nm) | NDVI Formula | Band | Bandwidth (nm) | NDVI Formula |

4 | 636–673 | $\mathrm{NDVI}=\frac{B5-B4}{B5+B4}$ | 4 | 664.5 nm (S2A)/665 nm (S2B) | $\mathrm{NDVI}=\frac{B8-B4}{B8+B4}$ |

5 | 851–879 | 8 | 835.1 nm (S2A)/833 nm (S2B) |

Model Parameter | Type/Value | Model Parameter | Type/Value |
---|---|---|---|

Population size | 10 | Elite count | 9 |

Population type | Double vector | Migration direction | Forward |

Population initial range | 16 × 2 double | Migration interval | 11 |

Selection mechanism | Roulette wheel | Time limit | Infinite |

Basis of chromosome selection | Fitness function | Stall generation limit | Infinite |

Crossover type | Double | Maximum number of generations | 50 |

Crossover probability | 0.4 | Termination criteria | 0.00001 |

Mutation type | Gaussian | Display | Iteration |

Mutation probability | 0.2 |

Site | RMSE | MAE | PSNR | SSIM |
---|---|---|---|---|

Sample plot 1 | 0.0199 | 0.0331 | 15.9963 | 0.7838 |

Sample plot 2 | 0.0241 | 0.0518 | 15.6056 | 0.7024 |

Sample plot 3 | 0.0131 | 0.0198 | 20.4122 | 0.8679 |

Sample plot 4 | 0.0066 | 0.0392 | 16.1757 | 0.7632 |

Sites | ESTARFM | FSDAF | GA-ANN | |||
---|---|---|---|---|---|---|

RMSE | MAE | RMSE | MAE | RMSE | MAE | |

Sample plot 1 | 0.0153 | 0.0243 | 0.0437 | 0.0457 | 0.0199 | 0.0331 |

Sample plot 2 | 0.2317 | 0.2319 | 0.2301 | 0.2305 | 0.0241 | 0.0518 |

Sample plot 3 | 0.0140 | 0.0213 | 0.0120 | 0.0332 | 0.0131 | 0.0198 |

Sample plot 4 | 0.0346 | 0.0577 | 0.0478 | 0.0610 | 0.0066 | 0.0392 |

Hidden Layer | Random Points | ||||||||
---|---|---|---|---|---|---|---|---|---|

500 | 1000 | 2000 | |||||||

MAE | RMSE | R | MAE | RMSE | R | MAE | RMSE | R | |

3 | 0.0282 | 0.0526 | 0.8931 | 0.0557 | 0.0509 | 0.8966 | 0.1050 | 0.0502 | 0.8908 |

4 | 0.0281 | 0.0522 | 0.8947 | 0.0557 | 0.0508 | 0.8969 | 0.1051 | 0.0502 | 0.8907 |

5 | 0.0281 | 0.0524 | 0.8941 | 0.0557 | 0.0508 | 0.8971 | 0.1050 | 0.0502 | 0.8906 |

6 | 0.0281 | 0.0523 | 0.8942 | 0.0557 | 0.0508 | 0.8969 | 0.1051 | 0.0502 | 0.8907 |

7 | 0.0281 | 0.0523 | 0.8944 | 0.0557 | 0.0509 | 0.8968 | 0.1054 | 0.0505 | 0.8892 |

8 | 0.0281 | 0.0523 | 0.8945 | 0.0557 | 0.0509 | 0.8967 | 0.1050 | 0.0502 | 0.8907 |

9 | 0.0281 | 0.0523 | 0.8943 | 0.0560 | 0.0508 | 0.8969 | 0.1050 | 0.0502 | 0.8904 |

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## Share and Cite

**MDPI and ACS Style**

Zhao, Y.; Hou, P.; Jiang, J.; Zhao, J.; Chen, Y.; Zhai, J.
High-Spatial-Resolution NDVI Reconstruction with GA-ANN. *Sensors* **2023**, *23*, 2040.
https://doi.org/10.3390/s23042040

**AMA Style**

Zhao Y, Hou P, Jiang J, Zhao J, Chen Y, Zhai J.
High-Spatial-Resolution NDVI Reconstruction with GA-ANN. *Sensors*. 2023; 23(4):2040.
https://doi.org/10.3390/s23042040

**Chicago/Turabian Style**

Zhao, Yanhong, Peng Hou, Jinbao Jiang, Jiajun Zhao, Yan Chen, and Jun Zhai.
2023. "High-Spatial-Resolution NDVI Reconstruction with GA-ANN" *Sensors* 23, no. 4: 2040.
https://doi.org/10.3390/s23042040