# Using TSX/TDX Pursuit Monostatic SAR Stacks for PS-InSAR Analysis in Urban Areas

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Standard PS-InSAR

_{non-linear}, and noise term $\Delta {\varphi}_{noise}$ are considered as residual phase $\epsilon $, as we can see in:

^{k}and β

^{k}are the coefficients of mean velocity Δv

_{x-y}and the residual topographic phase Δh

_{x-y}; Δv

_{x-y}and Δh

_{x-y}are unknowns, and they have to be determined under maximized temporal coherence γ.

_{x-y}and the residual topographic phase Δh

_{x-y}in Equation (4), periodogram spectral analysis [29] is applied in the standard PS-InSAR technique. The method can transform the residual phase into a frequency domain in space {Δh, Δv}, and search for the location of single PS points that could maximize the temporal coherence γ. This method is based on the original wrapped interferograms, and the performance of this method depends on the temporal and spatial distribution of baselines; with an increased number and a more even distribution of the temporal baseline, the performance could be improved.

_{x-y}and the residual topographic phase Δh

_{x-y}. After estimation of the topographic error and deformation for each point along the network based on a previously selected sparse PSC network, their topography and deformation can be derived, starting from a selected reference point. The remaining phase residuals caused by atmospheric effects and are subsequently used to estimate the atmospheric phase screen (APS) of each interferogram. The atmospheric components in differential phases can be extracted through low-pass filtering in the spatial domain, and high-pass filtering in the temporal domain [30]. On this basis, the APS of each interferogram can be obtained by interpolation, using various methods, for instance, kriging. After removing the APS, the deformation and topographic error for every PSC in the stack are estimated relative to the previously selected reference point.

- Preliminary processing: image import; master selection; co-registration; resampling; reflectivity map generation; amplitude stability index generation;
- Preliminary geocoding: ground control point (GCP) selection; external DEM input; projection of external DEM and synthetic amplitude in SAR coordinates; Mask for PSCs;
- APS estimation: interferometric formation using star graph; select a subset of PSCs according to a certain threshold; triangulation of sparse PSC network and generation of differential phase; deformation and topographic estimation based on given search space; selection of reference point; inversion of initial APS;
- Sparse estimation: interferometric formation using star graph; selection of all PSCs based on a certain threshold; Input of initial APS, differential phase and reference points; deformation and topographic estimations based on the given search space for the PSCs.

#### 2.2. A PS-InSAR Solution for Mono-Static Pursuit Datasets

- Preliminary processing: image import; master selection; co-registration; resampling; reflectivity map generation; amplitude stability index generation;
- Preliminary geocoding: GCP selection; external DEM input; projection of external DEM and synthetic amplitude in SAR coordinates; Mask for PSCs;
- First APS estimation: interferometric formation using only 10 s PM pairs; selection of a subset of PSCs according to a certain threshold; triangulation of sparse PSC network and generation of the differential phase; topographic estimation only based on a given search space; selection of the reference point; inversion of the initial APS;
- First sparse estimation: interferometric formation using only 10 s PM pairs; selection of all PSCs based on a certain threshold; input of initial APS, differential phase, and reference point; topographic estimation only based on the given search space for PSCs;
- Second APS estimation: interferometric formation using a star graph; selection of a subset of PSCs according to a certain threshold; triangulation of sparse PSC networks and generation of a differential phase; deformation estimation based on residual phase components derived in the first round within a given search space; selection of the reference point; inversion of the initial APS;
- Second Sparse estimation: interferometric formation using star graph; selection of all PSCs based on a certain threshold; Input of initial APS, differential phase and reference point; deformation estimation based on the residual phase component derived in first round within a given search space for PSCs;

## 3. Experiment Results

#### 3.1. Study Area and Dataset Information

#### 3.2. Experimental Results

#### 3.2.1. Processing Results from the Standard Method

#### 3.2.2. Processing Results from Our Proposed Method

## 4. Discussion

#### 4.1. Temporal Coherence

#### 4.2. Topography Estimation

#### 4.2.1. PS Point Numbers

#### 4.2.2. Persistent Scatterer Density

#### 4.3. Deformation Estimation

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Interferometric formation of the proposed method for height estimation from TerraSAR-X (TSX) and TanDEM-X (TDX) image pairs.

**Figure 3.**Flow charts of the standard processing chain (

**left**) and the proposed processing method (

**right**) for PS-InSAR.

**Figure 5.**Temporal coherence map of the selected persistent scatterer candidates in the standard processing result: (

**A**) The whole study area; (

**B**) Subset of the map in test region A; (

**C**) Subset of the map in test region B.

**Figure 6.**Residual height map for pursuit monostatic (PM) data in Guangzhou using the standard PS-InSAR method.

**Figure 7.**3D demonstration of the highly temporal coherent persistent scatterers in test region A using standard PS-InSAR processing.

**Figure 8.**Linear deformation map generated from standard processing results using PS points with a temporal coherence bigger than 0.85.

**Figure 9.**3D-view of the estimated linear deformation trends visualized with Google Earth for the standard processing method.

**Figure 10.**Temporal coherence map of the selected PSC in the standard processing result: (

**A**) The whole study area (

**B**) Subset of the map in test region A (

**C**) Subset of the map in test region B.

**Figure 11.**Residual height map for pursuit mono-static data in Guangzhou, using a proposed processing chain.

**Figure 13.**Linear deformation map generated from the proposed processing results, using PS points with a temporal coherence of larger than 0.85.

**Figure 14.**3D view of the estimated linear deformation trends visualized with Google Earth for the proposed method.

**Figure 15.**Histogram of PS points for temporal coherence in both standard and proposed processing results.

**Figure 17.**Statistics result of the two methods in sub-region 1: (

**A**) variance of the standard processing method (

**B**) mean height of the standard processing method (

**C**) variance of the proposed processing method (

**D**) mean height of the proposed processing method (

**E**) Histogram of the variance difference to the standard processing method (

**F**) Histogram of the mean height difference to the standard processing method.

**Figure 18.**Statistical result of the two methods in sub-region 2: (

**A**) variance of the standard processing method (

**B**) mean height of the standard processing method (

**C**) variance of the proposed processing method (

**D**) mean height of the proposed processing method (

**E**) Histogram of the variance difference to the standard processing method (

**F**) Histogram of the mean height difference to the standard processing method.

**Figure 19.**Linear regression results between thermal deformation and PS height: (

**A**) the proposed processing result in sub-region 1, (

**B**) the standard processing result in sub-region 1, (

**C**) the proposed processing result in sub-region 2, (

**D**) the standard processing result in sub-region 2.

Operation Mode | Pursuit Mono-Static | |
---|---|---|

Image Mode | Staring Spotlight (ST) | |

Look Angle | 43.4° | |

Polarization | VV | |

Direction | Ascending | |

Resolution | 0.24 m (azimuth) | |

0.80 m (ground range) | ||

Azimuth Extent | 3 km | |

Range Extent | 5.5 km | |

External Information | Acquisition Time | Temperature (°C) |

20141211 | 14.5 | |

20141222 | 9.1 | |

20150102 | 11.6 | |

20150113 | 11.2 | |

20150204 | 12.4 | |

20150215 | 16.7 | |

20150226 | 22.0 |

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## Share and Cite

**MDPI and ACS Style**

Wang, Z.; Balz, T.; Zhang, L.; Perissin, D.; Liao, M.
Using TSX/TDX Pursuit Monostatic SAR Stacks for PS-InSAR Analysis in Urban Areas. *Remote Sens.* **2019**, *11*, 26.
https://doi.org/10.3390/rs11010026

**AMA Style**

Wang Z, Balz T, Zhang L, Perissin D, Liao M.
Using TSX/TDX Pursuit Monostatic SAR Stacks for PS-InSAR Analysis in Urban Areas. *Remote Sensing*. 2019; 11(1):26.
https://doi.org/10.3390/rs11010026

**Chicago/Turabian Style**

Wang, Ziyun, Timo Balz, Lu Zhang, Daniele Perissin, and Mingsheng Liao.
2019. "Using TSX/TDX Pursuit Monostatic SAR Stacks for PS-InSAR Analysis in Urban Areas" *Remote Sensing* 11, no. 1: 26.
https://doi.org/10.3390/rs11010026