# Multi-Temporal Speckle Filtering of Polarimetric P-Band SAR Data over Dense Tropical Forests: Study Case in French Guiana for the BIOMASS Mission

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## Abstract

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## 1. Introduction

## 2. Data Selection

## 3. Multi Temporal and Multi Channel Speckle Filter

#### 3.1. Intensity-Based Multi-Temporal Filtering Techniques

#### 3.2. Extension to SLC Data

#### 3.2.1. General Form

#### 3.2.2. Application to Polarimetric SAR Data

## 4. Results

#### 4.1. Implementation

#### 4.2. Preservation of the Average

#### 4.3. Analysis in Terms of Speckle Reduction

#### 4.3.1. The Equivalent Number of Looks (ENL)

#### 4.3.2. Estimation of the Polarimetric Orientation Angle (${\widehat{\psi}}_{N}^{az}$)

## 5. Discussion

**C**matrices. From the methods proposed in [13], it is possible to estimate the gain in ${L}_{eq}$ obtained after using a MCMT filter. Figure 10 (right side) shows the theoretical ${L}_{eq}$ obtained after filtering for 3 correlation levels 0.3, 0.5 and 0.7 as a function of time. The solid lines are for MCMT filtering which takes into account the decorrelation of the data. The dashed lines are for the MCMT filtering proposed in this paper. The results of Figure 10 (right side) allow to conclude that the MCMT filtering is slightly under optimal in terms of gain in ${L}_{eq}$ although, it remains very efficient.

## 6. Conclusions and Further Prospects

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MCMT | Multi Channel and Multi Temporal |

POA | Polarization Orientation Angle |

AGB | Above Ground Biomass |

DEM | Digital Elevation Model |

SRTM | Shuttle Radar Topography Mission |

ENL | Equivalent Number of Looks |

RMSE | Root Mean Squared Error |

SLC | Single Look Complex |

## References

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**Figure 2.**Results of REF and MCMT filtering of an image ${T}_{33}=4\langle {S}_{HV}^{\ast}\rangle $ from the data from the Paracou test site acquired during the TropiSAR airborne campaign. The two maps on the left have an output resolution of 5 m, the two maps on the right have an output resolution of 50 m.

**Figure 3.**Estimation of ${t}^{0}$ as a fonction of forest biomass obtained for the P-band PolSAR data from the Paracou test site acquired with a bandwidth of 125 MHz with a resolution after filtering equivalent to 5 m. On the left, 15 ROIs of 6.25 ha are considered as well as 1 ROI of 25 ha. On the right, 84 ROIs of 1 ha are considered.

**Figure 4.**Estimation of ${t}_{MCMT}^{0}$ as a function of ${t}_{REF}^{0}$ obtained for the P-band PolSAR data from the Paracou test site acquired with a bandwidth of 125 MHz with a resolution after filtering equivalent to 5 m. On the left, 15 ROIs of 6.25 ha are considered as well as 1 ROI of 25 ha. On the right, 84 ROIs of 1 ha are considered.

**Figure 5.**Impact of the multilook pixel size on the equivalent number of looks ${L}_{eq}$ (

**left**) and on the ratio $\rho ={L}_{eq}^{MCMT}/{L}_{eq}^{REF}$ (

**right**) for the 4 ROIs shown in Figure 2.

**Figure 6.**Azimuthal slopes estimation from Paracou test site. Image on the left side corresponds to azimuthal slopes ${\psi}_{N}^{Az}$ extracted from the SRTM DEM. The four images, arranged in two lines on the right side, corresponds to azimuthal slopes ${\widehat{\psi}}_{N}^{az}$, estimated from filtered coherency matrices ${\widehat{\mathbf{T}}}_{REF}$ and ${\widehat{\mathbf{T}}}_{MCMT}$ with a spatial resolution at the output of the filter corresponding to 25 m and 50 m. The red box corresponds to the area of interest selected for Figure 7 and Figure 8.

**Figure 7.**Zoom corresponding to the red rectangle in Figure 6. Image on the left side corresponds to azimuthal slopes ${\psi}_{N}^{Az}$ extracted from the SRTM DEM. The four images, arranged in two lines on the right side, corresponds to azimuthal slopes ${\widehat{\psi}}_{N}^{az}$, estimated from filtered coherency matrices ${\widehat{\mathbf{T}}}_{REF}$ and ${\widehat{\mathbf{T}}}_{MCMT}$ with a spatial resolution at the output of the filter corresponding to 25 m and 50 m.

**Figure 8.**In the left block, 2D histograms of ${\psi}_{N}^{az}$ versus ${\widehat{\psi}}_{N}^{az}$ computed for the red box area of the Figure 6. In the right block, 2D histogram of the left block with local slope filtering. On the first line, results obtained with a resolution of 25 m at the filter output, on the second line, results obtained with a resolution of 50 m at the filter output.

**Figure 9.**Flowchart representing the overall process for filtering P-band PolSAR time series and estimating properties and performances indicators developed in this paper.

**Figure 10.**On the left: semi-empirical model of the repeat-pass correlation between the duration given along the x-axis, with upper and lower bounds corresponding to 3-day correlations of 0.87 and 0.37 respectively. On the right: theoretical ${L}_{eq}$ resulting from the filtering of 7 Biomass like polarimetric acquisitions as a function of the 3-day temporal correlation which determines the other temporal baseline (up to 18 days) through the semi-empirical decorrelation model (on the left). The various colors are for different stationary correlation between HH and VV, ranging from $0.7$ to $0.3$, and the dot and plain lines are for the optimal or non-optimal versions of the MCMT filter respectively.

**Table 1.**Parameters of regression models estimated for ${t}^{0}=f\left(AGB\right)$ shown in Figure 3 and associated statistics (Pearson Coefficient (${r}_{p}$), Root Mean Squared Error (RMSE), ${\chi}^{2}$ parameter).

16 ROIs | a | b | ${r}_{p}$ | RMSE | ${\chi}^{2}$ |

REF | 5.79 | −25.51 | 0.78 | 21.84 | 5.13 |

MCMT | 5.97 | −26.0 | 0.76 | 19.37 | 5.33 |

84 ROIs | a | b | ${r}_{p}$ | RMSE | ${\chi}^{2}$ |

REF | 5.65 | −25.12 | 0.54 | 33.63 | 27.14 |

MCMT | 5.84 | −25.62 | 0.54 | 33.84 | 32.53 |

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**MDPI and ACS Style**

Gelas, C.; Villard, L.; Ferro-Famil, L.; Polidori, L.; Koleck, T.; Daniel, S.
Multi-Temporal Speckle Filtering of Polarimetric P-Band SAR Data over Dense Tropical Forests: Study Case in French Guiana for the BIOMASS Mission. *Remote Sens.* **2021**, *13*, 142.
https://doi.org/10.3390/rs13010142

**AMA Style**

Gelas C, Villard L, Ferro-Famil L, Polidori L, Koleck T, Daniel S.
Multi-Temporal Speckle Filtering of Polarimetric P-Band SAR Data over Dense Tropical Forests: Study Case in French Guiana for the BIOMASS Mission. *Remote Sensing*. 2021; 13(1):142.
https://doi.org/10.3390/rs13010142

**Chicago/Turabian Style**

Gelas, Colette, Ludovic Villard, Laurent Ferro-Famil, Laurent Polidori, Thierry Koleck, and Sandrine Daniel.
2021. "Multi-Temporal Speckle Filtering of Polarimetric P-Band SAR Data over Dense Tropical Forests: Study Case in French Guiana for the BIOMASS Mission" *Remote Sensing* 13, no. 1: 142.
https://doi.org/10.3390/rs13010142