# Satellite Image Time Series Decomposition Based on EEMD

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## Abstract

**:**

## 1. Introduction

## 2. Proposed Framework

#### 2.1. Ensemble Empirical Mode Decomposition

_{1}(t) as shown in Figure 2.

_{1}(t) is subtracted from x(t) to approximate an IMF, as:

_{1}(t) as a new time series, and step 1 and step 2 are repeated until the following stop criterion is satisfied.

_{1}from the rest of the data:

_{1}, we can extract the second highest frequency IMF c

_{2}and residue r

_{2}by the sifting process described above. Similarly, all the IMFs c

_{i}can be repeatedly extracted from high to low frequency, level by level:

_{i}becomes a monotonic function and there are no more IMFs that can be extracted, the process stops. Finally, the time series is decomposed as:

_{m}(t) is added to the original time series x(t):

_{m}(t) is decomposed by EMD:

**Figure 2.**For the above random time series (blue line), the upper and lower envelopes (dot-dashed lines) and the mean curve (green line) are provided.

**Figure 3.**For the above random time series, an illustration of the decomposed components using Ensemble Empirical Mode Decomposition (EEMD) is provided. The original time series (blue line) is decomposed into six Intrinsic Mode Functions (IMFs) (red line) and a residue (green line).

#### 2.2. EEMD for SITS

**Figure 4.**Statistical significance test between the energy density and the averaged period. Note that the green dots from left to right show the energy density as a function of the averaged period.

#### 2.2.1. Seasonal Component Extraction

#### 2.2.2. Trend Component Extraction

#### 2.2.3. Trend Component for Change Detection

_{i}(t) represents the i-th IMF and G

_{i}represents the IMF wave energy, which is the aggregation of the mean deviations of the series elements. Clearly, the energy increases proportionally to the wave intensity. For the residue r(t) of a nonzero-mean series, the energy G

^{r}can be further defined as:

## 3. Experiment and Discussion

**Field Study:**The study area is located in the Yinan River Forest in the northeast of Heilongjiang Province, China. A disastrous fire occurred in this area on 27 April 2009 and was not put out until 2 May 2009. Figure 5 shows a false-color-composite image of Landsat TM shot on 23 May 2009 of the burned area. In this experiment, SITS were generated from MODIS 250 m 16-day composite gridded vegetation index products (MOD13Q1) from 1 January 2001 to 31 December 2009. We converted the original data to a projection of WGS 84/UTM zone 52N.

**Experiment Setup:**We first validated our decomposition model by a 16-day composition NDVI time series of forest type. SITS were collected from a normal region (denoted as yellow block 1 in Figure 5), which was used to illustrate and discuss the time series decomposition procedure. Second, the decomposition mode was validated by a 16-day composition GEMI time series with disturbance. In this experiment, SITS were from a burned area (yellow block 2 in Figure 5), which was used to detect the fire disturbance, and we also analyze a method of selecting IMFs to generate the trend component.

#### 3.1. 16-Day Composite NDVI Time Series of Forest Type

#### 3.1.1. Seasonal-Trend Decomposition

**Figure 7.**NDVI mean time series decomposed using EEMD. The time series (blue line) is decomposed into 7 IMFs (red line) and a residue (green line).

**Figure 8.**Statistical significance test between the energy density and the averaged period. Note that the green dots from left to right indicate the energy density as a function of the averaged period.

#### 3.1.2. Validation of the Seasonal Component

#### 3.2. Sixteen-Day Composition GEMI Time Series with Disturbance

**Table 1.**Energy of the residue and IMFs illustrated in Figure 14.

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | Residue | |
---|---|---|---|---|---|---|---|---|

Energy | 0.878 | 2.606 | 6.860 | 1.522 | 0.370 | 0.002 | 0.212 | 0.760 |

**Figure 17.**The results of change point detection of Breaks for Additive Season and Trend (BFAST) algorithm.

**Figure 20.**Detection map of the proposed method. (

**a**) Landsat TM image shot on 23 May 2009. (

**b**) Burned area detection map.

## 4. Conclusions

- (1)
- Further algorithm improvement should consider the sensitivity of change point detection of the seasonal or trending component.
- (2)
- Further research is necessary to incrementally update an event database when new observations are available and to enhance the prediction algorithm to achieve real-time change detection (see Schnebele, et al. [35]).

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Kong, Y.-l.; Meng, Y.; Li, W.; Yue, A.-z.; Yuan, Y.
Satellite Image Time Series Decomposition Based on EEMD. *Remote Sens.* **2015**, *7*, 15583-15604.
https://doi.org/10.3390/rs71115583

**AMA Style**

Kong Y-l, Meng Y, Li W, Yue A-z, Yuan Y.
Satellite Image Time Series Decomposition Based on EEMD. *Remote Sensing*. 2015; 7(11):15583-15604.
https://doi.org/10.3390/rs71115583

**Chicago/Turabian Style**

Kong, Yun-long, Yu Meng, Wei Li, An-zhi Yue, and Yuan Yuan.
2015. "Satellite Image Time Series Decomposition Based on EEMD" *Remote Sensing* 7, no. 11: 15583-15604.
https://doi.org/10.3390/rs71115583