# Compressed SAR Interferometry in the Big Data Era

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## Abstract

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## 1. Introduction

## 2. PSDS InSAR: Combination of PS and DS Targets

## 3. ComSAR: Compressed PSDS InSAR Algorithm

## 4. Simulation Performances

## 5. Experiments with Real Data

#### 5.1. Study Site

#### 5.2. Processing SAR Data

#### 5.3. Performance Evaluation

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Appendix on TomoSAR

## References

- Torres, R.; Snoeij, P.; Geudtner, D.; Bibby, D.; Davidson, M.; Attema, E.; Potin, P.; Rommen, B.; Floury, N.; Brown, M.; et al. GMES Sentinel-1 mission. Remote Sens. Environ.
**2012**, 120, 9–24. [Google Scholar] [CrossRef] - Rosen, P.A.; Kim, Y.; Kumar, R.; Misra, T.; Bhan, R.; Sagi, V.R. Global persistent SAR sampling with the NASA-ISRO SAR (NISAR) mission. In Proceedings of the 2017 IEEE Radar Conference (RadarConf), Seattle, WA, USA, 8–12 May 2017; pp. 0410–0414. [Google Scholar] [CrossRef]
- Pierdicca, N.; Davidson, M.; Chini, M.; Dierking, W.; Djavidnia, S.; Haarpaintner, J.; Hajduch, G.; Laurin, G.V.; Lavalle, M.; López-Martínez, C.; et al. The Copernicus L-band SAR mission ROSE-L (Radar Observing System for Europe) (Conference Presentation). In Active and Passive Microwave Remote Sensing for Environmental Monitoring III; Bovenga, F., Notarnicola, C., Pierdicca, N., Santi, E., Eds.; International Society for Optics and Photonics: Bellingham, WA, USA, 2019; Volume 11154. [Google Scholar] [CrossRef]
- Ulaby, F.T.; Long, D.G. Microwave Radar and Radiometric Remote Sensing; The University of Michigan Press: Ann Arbor, MI, USA, 2014. [Google Scholar]
- Ho Tong Minh, D.; Hanssen, R.; Rocca, F. Radar Interferometry: 20 Years of Development in Time Series Techniques and Future Perspectives. Remote Sens.
**2020**, 12, 1364. [Google Scholar] [CrossRef] - Hanssen, R.F. Radar Interferometry: Data Interpretation and Error Analysis; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2001. [Google Scholar]
- Ferretti, A.; Fumagalli, A.; Novali, F.; Prati, C.; Rocca, F.; Rucci, A. A New Algorithm for Processing Interferometric Data-Stacks: SqueeSAR. Geosci. Remote Sens. IEEE Trans.
**2011**, 49, 3460–3470. [Google Scholar] [CrossRef] - Berardino, P.; Fornaro, G.; Lanari, R.; Sansosti, E. A New Algorithm for Surface Deformation Monitoring Based on Small Baseline Differential SAR Interferograms. Geosci. Remote Sens. IEEE Trans.
**2002**, 40, 2375–2383. [Google Scholar] [CrossRef] [Green Version] - Schmidt, D.A.; Bürgmann, R. Time-dependent land uplift and subsidence in the Santa Clara valley, California, from a large interferometric synthetic aperture radar data set. J. Geophys. Res. Solid Earth
**2003**, 108. [Google Scholar] [CrossRef] [Green Version] - Lanari, R.; Mora, O.; Manunta, M.; Mallorqui, J.J.; Berardino, P.; Sansosti, E. A small-baseline approach for investigating deformations on full-resolution differential SAR interferograms. IEEE Trans. Geosci. Remote Sens.
**2004**, 42, 1377–1386. [Google Scholar] [CrossRef] - Doin, M.P.; Lodge, F.; Guillaso, S.; Jolivet, R.; Lasserre, C.; Ducret, G.; Grandin, R.; Pathier, E.; Pinel, V. Presentation of the Small Baseline NSBAS Processing Chain on a Case Example: The Etna Deformation Monitoring from 2003 to 2010 Using Envisat Data; Fringe Workshop: Frascati, Italy, 2011. [Google Scholar]
- Yunjun, Z.; Fattahi, H.; Amelung, F. Small baseline InSAR time series analysis: Unwrapping error correction and noise reduction. Comput. Geosci.
**2019**, 133, 104331. [Google Scholar] [CrossRef] [Green Version] - Ferreti, A.; Prati, C.; Rocca, F. Nonlinear subsidence rate estimation using permanent scatterers in differential SAR interferometry. IEEE Trans. Geosci. Remote Sens.
**2000**, 38, 2202–2212. [Google Scholar] [CrossRef] [Green Version] - Ferretti, A.; Prati, C.; Rocca, F. Permanent scatterers in SAR interferometry. IEEE Trans. Geosci. Remote Sens.
**2001**, 39, 8–20. [Google Scholar] [CrossRef] - Hooper, A.; Zebker, H.; Segall, P.; Kampes, B. A new method for measuring deformation on volcanoes and other natural terrains using InSAR persistent scatterers. Geophys. Res. Lett.
**2004**, 31. [Google Scholar] [CrossRef] - Hooper, A. A multi-temporal InSAR method incorporating both persistent scatterer and small baseline approaches. Geophys. Res. Lett.
**2008**, 35, 1–5. [Google Scholar] [CrossRef] [Green Version] - De Zan, F.; Monti Guarnieri, A. TOPSAR: Terrain Observation by Progressive Scans. IEEE Trans. Geosci. Remote Sens.
**2006**, 44, 2352–2360. [Google Scholar] [CrossRef] - Hajnsek, I.; Shimada, M.; Eineder, M.; Papathanassiou, K.; Motohka, T.; Watanabe, M.; Ohki, M.; De Zan, F.; Lopez-Dekker, P.; Krieger, G.; et al. Tandem-L: Science Requirements and Mission Concept. In Proceedings of the 10th European Conference on Synthetic Aperture Radar, Berlin, Germany, 3–5 June 2014; pp. 1–4. [Google Scholar]
- Casu, F.; Elefante, S.; Imperatore, P.; Zinno, I.; Manunta, M.; De Luca, C.; Lanari, R. SBAS-DInSAR Parallel Processing for Deformation Time-Series Computation. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2014**, 7, 3285–3296. [Google Scholar] [CrossRef] - Ansari, H.; De Zan, F.; Bamler, R. Sequential Estimator: Toward Efficient InSAR Time Series Analysis. IEEE Trans. Geosci. Remote Sens.
**2017**, 55, 5637–5652. [Google Scholar] [CrossRef] [Green Version] - Ho Tong Minh, D.; Ngo, Y.N. ComSAR: A new algorithm for processing Big Data SAR Interferometry. In Proceedings of the 2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, Brussels, Belgium, 11–16 July 2021; pp. 820–823. [Google Scholar] [CrossRef]
- Zebker, H.A.; Villasenor, J. Decorrelation in interferometric radar echoes. Geosci. Remote Sens. IEEE Trans.
**1992**, 30, 950–959. [Google Scholar] [CrossRef] [Green Version] - Samiei-Esfahany, S.; Martins, J.E.; van Leijen, F.; Hanssen, R.F. Phase Estimation for Distributed Scatterers in InSAR Stacks Using Integer Least Squares Estimation. IEEE Trans. Geosci. Remote Sens.
**2016**, 54, 5671–5687. [Google Scholar] [CrossRef] [Green Version] - De Zan, F.; Zonno, M.; López-Dekker, P. Phase Inconsistencies and Multiple Scattering in SAR Interferometry. IEEE Trans. Geosci. Remote Sens.
**2015**, 53, 6608–6616. [Google Scholar] [CrossRef] [Green Version] - Ansari, H.; De Zan, F.; Parizzi, A. Study of Systematic Bias in Measuring Surface Deformation with SAR Interferometry. IEEE Trans. Geosci. Remote Sens.
**2021**, 59, 1285–1301. [Google Scholar] [CrossRef] - Guarnieri, A.M.; Tebaldini, S. On the Exploitation of Target Statistics for SAR Interferometry Applications. Geosci. Remote Sens. IEEE Trans.
**2008**, 46, 3436–3443. [Google Scholar] [CrossRef] - Ansari, H.; De Zan, F.; Bamler, R. Efficient Phase Estimation for Interferogram Stacks. IEEE Trans. Geosci. Remote Sens.
**2018**, 56, 4109–4125. [Google Scholar] [CrossRef] - Goel, K.; Adam, N. A Distributed Scatterer Interferometry Approach for Precision Monitoring of Known Surface Deformation Phenomena. IEEE Trans. Geosci. Remote Sens.
**2014**, 52, 5454–5468. [Google Scholar] [CrossRef] - Ho Tong Minh, D.; Van Trung, L.; Toan, T.L. Mapping Ground Subsidence Phenomena in Ho Chi Minh City through the Radar Interferometry Technique Using ALOS PALSAR Data. Remote Sens.
**2015**, 7, 8543–8562. [Google Scholar] [CrossRef] [Green Version] - Ho Tong Minh, D.; Tran, Q.C.; Pham, Q.N.; Dang, T.T.; Nguyen, D.A.; El-Moussawi, I.; Le Toan, T. Measuring Ground Subsidence in Ha Noi Through the Radar Interferometry Technique Using TerraSAR-X and Cosmos SkyMed Data. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2019**, 12, 3874–3884. [Google Scholar] [CrossRef] - Cao, N.; Lee, H.; Jung, H.C. A Phase-Decomposition-Based PSInSAR Processing Method. IEEE Trans. Geosci. Remote Sens.
**2016**, 54, 1074–1090. [Google Scholar] [CrossRef] - Cohen-Waeber, J.; Bürgmann, R.; Chaussard, E.; Giannico, C.; Ferretti, A. Spatiotemporal Patterns of Precipitation-Modulated Landslide Deformation from Independent Component Analysis of InSAR Time Series. Geophys. Res. Lett.
**2018**, 45, 1878–1887. Available online: https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2017GL075950 (accessed on 4 January 2022). [CrossRef] - Engelbrecht, J.; Inggs, M.R. Coherence Optimization and Its Limitations for Deformation Monitoring in Dynamic Agricultural Environments. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens.
**2016**, 9, 5647–5654. [Google Scholar] [CrossRef] - Zan, F.D. Progressive InSAR Phase Estimation. 2020. Available online: https://arxiv.org/pdf/2010.02533.pdf (accessed on 4 January 2022).
- Jolliffe, I.T. Principal Component Analysis; Springer Series in Statistics; Springer: New York, NY, USA, 2002. [Google Scholar]
- Brigitte, L.R.; Rouanet, H. Geometric Data Analysis, From Correspondence Analysis to Structured Data Analysis; Kluwer: Dordrecht, The Netherlands, 2004. [Google Scholar]
- De Zan, F.; Parizzi, A.; Prats-Iraola, P.; López-Dekker, P. A SAR Interferometric Model for Soil Moisture. IEEE Trans. Geosci. Remote Sens.
**2014**, 52, 418–425. [Google Scholar] [CrossRef] [Green Version] - Raucoules, D.; Maisons, C.; Carnec, C.; Le Mouelic, S.; King, C.; Hosford, S. Monitoring of slow ground deformation by ERS radar interferometry on the Vauvert salt mine (France): Comparison with ground-based measurement. Remote Sens. Environ.
**2003**, 88, 468–478. [Google Scholar] [CrossRef] - Furst, S.L.; Doucet, S.; Vernant, P.; Champollion, C.; Carme, J.L. Monitoring surface deformation of deep salt mining in Vauvert (France), combining InSAR and leveling data for multi-source inversion. Solid Earth
**2021**, 12, 15–34. [Google Scholar] [CrossRef] - Prats-Iraola, P.; Scheiber, R.; Marotti, L.; Wollstadt, S.; Reigber, A. TOPS Interferometry With TerraSAR-X. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 3179–3188. [Google Scholar] [CrossRef] [Green Version] - Scheiber, R.; Moreira, A. Coregistration of interferometric SAR images using spectral diversity. IEEE Trans. Geosci. Remote Sens.
**2000**, 38, 2179–2191. [Google Scholar] [CrossRef] - ESA. Sentinel Application Platform v8.0; 2021. Available online: http://step.esa.int (accessed on 4 January 2022).
- Delgado Blasco, J.M.; Foumelis, M.; Stewart, C.; Hooper, A. Measuring Urban Subsidence in the Rome Metropolitan Area (Italy) with Sentinel-1 SNAP-StaMPS Persistent Scatterer Interferometry. Remote Sens.
**2019**, 11, 129. [Google Scholar] [CrossRef] [Green Version] - Neuhäuser, M. An exact two-sample test based on the baumgartner-weiss-schindler statistic and a modification of lepage’s test. Commun. Stat.-Theory Methods
**2000**, 29, 67–78. [Google Scholar] [CrossRef] - Jiang, M.; Ding, X.; Hanssen, R.F.; Malhotra, R.; Chang, L. Fast Statistically Homogeneous Pixel Selection for Covariance Matrix Estimation for Multitemporal InSAR. IEEE Trans. Geosci. Remote Sens.
**2015**, 53, 1213–1224. [Google Scholar] [CrossRef] - De Zan, F.; Lopez-Dekker, P. SAR Image Stacking for the Exploitation of Long-Term Coherent Targets. IEEE Geosci. Remote Sens. Lett.
**2011**, 8, 502–506. [Google Scholar] [CrossRef] [Green Version] - Ho Tong Minh, D.; Ngo, Y.N. TomoSAR platform supports for Sentinel-1 TOPS persistent scatterers interferometry. In Proceedings of the 2017 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Fort Worth, TX, USA, 23–28 July 2017; pp. 1680–1683. [Google Scholar] [CrossRef]
- Ho Tong Minh, D.; Tebaldini, S.; Rocca, F.; Koleck, T.; Borderies, P.; Albinet, C.; Villard, L.; Hamadi, A.; Le Toan, T. Ground-Based Array for Tomographic Imaging of the Tropical Forest in P-Band. Geosci. Remote Sens. IEEE Trans.
**2013**, 51, 4460–4472. [Google Scholar] [CrossRef] - Ho Tong Minh, D.; Tebaldini, S.; Rocca, F.; Le Toan, T.; Borderies, P.; Koleck, T.; Albinet, C.; Hamadi, A.; Villard, L. Vertical Structure of P-Band Temporal Decorrelation at the Paracou Forest: Results From TropiScat. Geosci. Remote Sens. Lett. IEEE
**2014**, 11, 1438–1442. [Google Scholar] [CrossRef] [Green Version] - El Moussawi, I.; Ho Tong Minh, D.; Baghdadi, N.; Abdallah, C.; Jomaah, J.; Strauss, O.; Lavalle, M.; Ngo, Y.-. N Monitoring Tropical Forest Structure Using SAR Tomography at L- and P-Band. Remote Sens.
**2019**, 11, 1934. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**ComSAR: Compressed PSDS InSAR algorithm. The algorithm divides the massive data into many mini-stacks and then compresses them.

**Figure 2.**Comparison scenarios on phase linking performances for DS targets. The RMSE of phase estimation is used as a performance indicator; (

**b**) is the zoom version at a different scale of (

**a**) to appreciate the visualization.

**Figure 3.**View of the Vauvert located in Southern France. (

**a**) Optical Google Earth images; (

**b**) amplitude image (377 pixel in azimuth and 1612 pixel in range) from the Sentinel-1 of the test site. The whole area is approximately 5 km × 5 km, and its center is located at 4.29E longitude, 43.68N latitude.

**Figure 4.**Internal results from PSDS-based processing. (

**a**) the phase linking coherence corresponding to the SHP map; (

**b**) the number of SHP identified using a 9 × 35 window.

**Figure 6.**Velocity histogram. The total pixels are 5100, 42,517, and 58,216 points for PSI, PSDS, and ComSAR, respectively.

**Figure 7.**Velocities with coordination associated. (

**a**) reference velocity in mm/year; (

**b**) estimated velocity using ComSAR. A circle-shaped subsidence zone is visible with a 5 km diameter and subsidence up to 20 mm/year.

**Figure 8.**The cross-plot 1:1 velocity comparison. (

**a**) estimated velocity using PSI; (

**b**) estimated velocity using PSDS; (

**c**) estimated velocity using ComSAR.

Parametes | PSI | PSDS | ComSAR |
---|---|---|---|

Total image | 89 | 89 | 17 |

Total point | 5100 | 42,517 | 58,216 |

Density (point/km${}^{2}$) | 204 | 1700 | 2328 |

Duration (minute) | 8 | 168 | 25 |

Coefficient R${}^{2}$ | 0.81 | 0.86 | 0.94 |

RMSE (mm/year) | 2.9 | 2.5 | 2.3 |

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**MDPI and ACS Style**

Ho Tong Minh, D.; Ngo, Y.-N.
Compressed SAR Interferometry in the Big Data Era. *Remote Sens.* **2022**, *14*, 390.
https://doi.org/10.3390/rs14020390

**AMA Style**

Ho Tong Minh D, Ngo Y-N.
Compressed SAR Interferometry in the Big Data Era. *Remote Sensing*. 2022; 14(2):390.
https://doi.org/10.3390/rs14020390

**Chicago/Turabian Style**

Ho Tong Minh, Dinh, and Yen-Nhi Ngo.
2022. "Compressed SAR Interferometry in the Big Data Era" *Remote Sensing* 14, no. 2: 390.
https://doi.org/10.3390/rs14020390