# Dimension Reduction of Multi-Spectral Satellite Image Time Series to Improve Deforestation Monitoring

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## Abstract

**:**

## 1. Introduction

## 2. Study Area

## 3. Methods

#### 3.1. PCA

#### 3.2. Forming SRI

#### 3.3. Monitoring Deforestation Using SRI

- The model is estimated on a stable historical period where the parameters are assumed to be stable.
- A fluctuation process is initialized and captures deviations from the model. Under the null hypothesis, the fluctuation process converges to a Gaussian stochastic process.
- For each incoming observation, the fluctuation process is updated. If the fluctuation process exceeds the threshold for the limiting Gaussian process, there is evidence that the structure of the time series has changed.

#### 3.4. Seasonality Assessment

#### 3.5. Comparison of Different Indices

## 4. Accuracy Assessment

## 5. Results

#### Comparison of Seasonality in SRI and NDMI

## 6. Discussion

#### 6.1. Indices Comparison

#### 6.2. Applying PCA to the Whole Time Series

#### 6.3. Advantages, Limitations and Future Studies

## 7. Conclusions

## Supplementary Materials

## Author Contributions

## Conflicts of Interest

## Abbreviations

IR | Near and shortwave Infrared |

NDVI | Normalized Difference Vegetation Index |

NDMI | Normalized Difference Moisture Index |

SRI | Seasonality Reduced Index |

TCT | Tasseled Cap Transformation |

NBI | Natural Burn Index |

TW | TCT Wetness |

TG | TCT Greenness |

TB | TCT Brightness |

PCA | Principle Component Analysis |

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**Figure 1.**Map of the study area and validation points, using Landsat ETM+ image Bands 3, 4 and 5 in red, blue and green channels, respectively, to composite the images. (

**a**) Brazilian site; the composite image is for 22 July 2011; green circles indicate validation points; (

**b**) Bolivian site; the composite image is for 7 August 2011; green circles indicate validation points; (

**c**) locations of the two study sites.

**Figure 2.**The PC loadings for all the testing time series containing no deforestation events at each site. The PC loadings with a band relationship that is indicated in PC3 of (

**a**) and PC2 of (

**b**) are selected based on (Equation (2)).

**Figure 3.**Diagram illustrating the proposed multispectral time series change monitoring method. PCA: Principal Component Analysis, MEFP: Monitor of Empirical Fluctuation Process.

**Figure 4.**Flowchart of our experiment comparing SRI and conventional vegetation indices. MOSUM, Moving Cumulative Sum.

**Figure 5.**Number of available Landsat TM and ETM + images of each year from 1984–2014 of the Bolivian and Brazilian study area.

**Figure 6.**Boxplot of ${R}^{2}$ of fitting first order harmonic terms to each SRI and NDMI of the testing dataset locations in the Bolivian study site (100 points).

**Figure 7.**Time series of NDMI, NDVI, TCT and SRI at two sample locations of the Bolivian site. The red dashed line indicates real deforestation time; the blue dotted line indicates the time of MEFP detected deforestation. (

**a**) Time series at location (18.341${}^{\circ}$ S, 62.541${}^{\circ}$ W); (

**b**) time series at location (18.364${}^{\circ}$ S, 62.584${}^{\circ}$ W).

**Figure 8.**Time series of NDMI, NDVI, TCT and SRI at two sample locations of the Brazilian site. The red dashed line indicates real deforestation time; the blue dotted line indicates the time of MEFP detected deforestation. (

**a**) Time series at location (10.345${}^{\circ}$ S, 63.862${}^{\circ}$ W); (

**b**) time series at location (10.686${}^{\circ}$ S, 63.595${}^{\circ}$ W).

**Table 1.**Figure Of Merit (FOM, %), Producer’s Accuracy (PA, %), User’s Accuracy (UA, %), Overall Accuracy (OA, %) and Temporal Delay (TD, observation) at the Bolivian site. A mean model is used in the MEFP for the method introduced here (SRI), and a first-order harmonic model is used for the other indices.

FOM | PA | UA | OA | TD | |
---|---|---|---|---|---|

SRI | 39.4 | 87.5 | 41.8 | 88.6 | 6 |

NDMI | 19.9 | 81.3 | 20.8 | 73.8 | 19 |

NDVI | 21.5 | 54.6 | 26.2 | 83 | 24 |

TB | 15.8 | 18.4 | 52.8 | 91.1 | 41 |

TG | 21.5 | 79.6 | 22.7 | 74.9 | 17 |

TW | 22 | 99 | 22 | 70.3 | 5 |

**Table 2.**FOM (%), PA (%), UA (%), OA (%) and (observation) at the Brazilian site. A mean model is used in the MEFP for the method introduced here (SRI), and a first-order harmonic model is used for the other indices.

FOM | PA | UA | OA | TD | |
---|---|---|---|---|---|

SRI | 17.7 | 64.6 | 19.6 | 47.4 | 11 |

NDMI | 22.4 | 62.5 | 25.9 | 59.6 | 17 |

NDVI | 18.4 | 44.3 | 23.9 | 63.2 | 16 |

TB | 9.5 | 13.9 | 23 | 65.5 | 27 |

TG | 21.1 | 54.9 | 25.6 | 55.5 | 24 |

TW | 20.3 | 87.1 | 20.9 | 38.1 | 30 |

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## Share and Cite

**MDPI and ACS Style**

Lu, M.; Hamunyela, E.; Verbesselt, J.; Pebesma, E. Dimension Reduction of Multi-Spectral Satellite Image Time Series to Improve Deforestation Monitoring. *Remote Sens.* **2017**, *9*, 1025.
https://doi.org/10.3390/rs9101025

**AMA Style**

Lu M, Hamunyela E, Verbesselt J, Pebesma E. Dimension Reduction of Multi-Spectral Satellite Image Time Series to Improve Deforestation Monitoring. *Remote Sensing*. 2017; 9(10):1025.
https://doi.org/10.3390/rs9101025

**Chicago/Turabian Style**

Lu, Meng, Eliakim Hamunyela, Jan Verbesselt, and Edzer Pebesma. 2017. "Dimension Reduction of Multi-Spectral Satellite Image Time Series to Improve Deforestation Monitoring" *Remote Sensing* 9, no. 10: 1025.
https://doi.org/10.3390/rs9101025