{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:49:04Z","timestamp":1760240944465,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2019,10,23]],"date-time":"2019-10-23T00:00:00Z","timestamp":1571788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Persistent scatterer interferometry (PSI) is commonly applied to monitor surface displacements with millimetric precision. However, this technique still has trouble estimating non-linear displacements because the algorithm is designed for the slow and linear displacements. Additionally, there is a variety of non-linear displacement types, and finding an appropriate displacement model for PSI is still assumed to be a fairly large task. In this paper, the conventional PSI technique is extended using a non-parametric non-linear approach (NN-PSI), and the performance of the extended method is investigated by simulations and actual observation data processing with TerraSAR-X. In the simulation, non-linear displacements are modeled by the magnitudes and periods of the displacement, and the evaluation of NN-PSI is conducted. According to the simulation results, the maximum magnitude of the displacement that can be estimated by NN-PSI is two and a half times the magnitude of the SAR sensor\u2019s wavelength (2.5   \u03bb    that is roughly equivalent to 8 cm for X-band, 14 cm for C-band, and 60 cm for L-band), and the period of the displacement is about three months. However, this displacement cannot be reconstructed by the conventional PSI due to the limitation, known as the 2   \u03c0    displacement ambiguity. The result of the observation data processing shows that a large displacement with the 2   \u03c0    ambiguity can be estimated by NN-PSI as the simulation results show, but the conventional PSI cannot reconstruct it. In addition, a different approach, Small BAseline Subset (SBAS), is applied to the same data to ensure the accuracy of results, and the correlation between NN-PSI and SBAS is 0.95, while that between the conventional PSI and SBAS is \u22120.66. It is concluded that NN-PSI enables the reconstruction of non-linear displacements by the non-parametric approach and the expansion of applications to measure surface displacements that could not be measured due to the limitations of the traditional PSI methods.<\/jats:p>","DOI":"10.3390\/rs11212467","type":"journal-article","created":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T03:20:36Z","timestamp":1571973636000},"page":"2467","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Improvement of Persistent Scatterer Interferometry to Detect Large Non-Linear Displacements with the 2\u03c0 Ambiguity by a Non-Parametric Approach"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7702-9109","authenticated-orcid":false,"given":"Fumitaka","family":"Ogushi","sequence":"first","affiliation":[{"name":"Tokyo Institute of Technology, Yokohama 226-8502, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3061-5754","authenticated-orcid":false,"given":"Masashi","family":"Matsuoka","sequence":"additional","affiliation":[{"name":"Tokyo Institute of Technology, Yokohama 226-8502, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Defilippi","sequence":"additional","affiliation":[{"name":"sarmap S.A., 6987 Caslano, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paolo","family":"Pasquali","sequence":"additional","affiliation":[{"name":"sarmap S.A., 6987 Caslano, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1109\/5.838084","article-title":"Synthetic aperture radar interferometry","volume":"88","author":"Rosen","year":"2000","journal-title":"Proc. IEEE"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9183","DOI":"10.1029\/JB094iB07p09183","article-title":"Mapping small elevation changes over large areas\u2014Differential radar interferometry","volume":"94","author":"Gabriel","year":"1989","journal-title":"J. Geophys. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1038\/364138a0","article-title":"The displacement field of the Landers earthquake mapped by radar interferometry","volume":"364","author":"Massonnet","year":"1993","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1126\/science.268.5215.1333","article-title":"Surface Displacement of the 17 May 1993 Eureka Valley, California, Earthquake Observed by SAR Interferometry","volume":"268","author":"Peltzer","year":"1995","journal-title":"Science"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Hooper, A.J. (2008). A multi-temporal InSAR method incorporating both persistent scatterer and small baseline approaches. Geophys. Res. Lett., 35.","DOI":"10.1029\/2008GL034654"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Pasquali, P., Cantone, A., Riccardi, P., Defilippi, M., Ogushi, F., Gagliano, S., and Tamura, M. (2014). Mapping of Ground Deformations with Interferometric Stacking Techniques. Land Appl. Radar Remote Sens., 233\u2013259.","DOI":"10.5772\/58225"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/36.898661","article-title":"Permanent Scatterers in SAR Interferometry","volume":"39","author":"Ferretti","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.enggeo.2006.09.007","article-title":"Permanent Scatterers for landslide investigations: Outcomes from the ESA-SLAM project","volume":"88","author":"Farina","year":"2006","journal-title":"Eng. Geol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/j.enggeo.2006.09.013","article-title":"Investigating landslides with space-borne Synthetic Aperture Radar (SAR) interferometry","volume":"88","author":"Colesanti","year":"2006","journal-title":"Eng. Geol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1045","DOI":"10.3390\/rs5031045","article-title":"Persistent scatterer interferometry (PSI) technique for landslide characterization and monitoring","volume":"5","author":"Tofani","year":"2013","journal-title":"Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhao, F., and Mallorqui, J.J. (2018). Landslide Monitoring Using Multi-Temporal SAR Interferometry with Advanced Persistent Scatterers Identification Methods and Super High-Spatial Resolution TerraSAR-X Images. Remote Sens., 10.","DOI":"10.3390\/rs10060921"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"659","DOI":"10.5194\/nhess-13-659-2013","article-title":"Multi-temporal SAR interferometry reveals acceleration of bridge sinking before collapse","volume":"13","author":"Sousa","year":"2013","journal-title":"Nat. Hazards Earth Syst. Sci."},{"key":"ref_13","unstructured":"Lazecky, M., Perissin, D., Lei, L., Qin, Y., and Scaioni, M. (2013, January 9\u201311). Plover Cove dam monitoring with spaceborne InSAR technique in Hong Kong. Proceedings of the 2nd Joint International Symposium on Deformation Monitoring, Nottingham, UK."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1109\/LGRS.2012.2218214","article-title":"Bridge Thermal Dilation Monitoring with Millimeter Sensitivity via Multidimensional SAR Imaging","volume":"10","author":"Fornaro","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_15","first-page":"81","article-title":"Rating health and stability of engineering structures via classification indexes of InSAR Persistent Scatterers","volume":"40","author":"Pratesi","year":"2015","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_16","first-page":"95","article-title":"Heterogeneous surface displacement pattern at the Hatchobaru geothermal field inferred from SAR interferometry time-series","volume":"44","author":"Ishitsuka","year":"2016","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1109\/TGRS.2009.2030792","article-title":"Nonuniform Ground Motion Monitoring with TerraSAR-X Persistent Scatterer Interferometry","volume":"48","author":"Walter","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.jappgeo.2009.02.003","article-title":"Validation and intercomparison of Persistent Scatterers Interferometry: PSIC4 project results","volume":"68","author":"Raucoules","year":"2009","journal-title":"J. Appl. Geophys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.enggeo.2014.03.003","article-title":"Investigating landslides and unstable slopes with satellite Multi Temporal Interferometry: Current issues and future perspectives","volume":"174","author":"Wasowski","year":"2014","journal-title":"Engineering Geology"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1016\/j.isprsjprs.2015.10.011","article-title":"Persistent Scatterer Interferometry: A review","volume":"115","author":"Crosetto","year":"2016","journal-title":"Isprs. J. Photogramm. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2202","DOI":"10.1109\/36.868878","article-title":"Nonlinear Subsidence Rate Estimation Using Permanent Scatterers in Differential SAR Interferometry","volume":"38","author":"Ferretti","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1685","DOI":"10.1109\/TGRS.2003.813278","article-title":"SAR Monitoring of Progressive and Seasonal Ground Deformation Using the Permanent Scatterers Technique","volume":"41","author":"Colesanti","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1109\/TGRS.2010.2052625","article-title":"Modeling PSInSAR Time Series Without Phase Unwrapping","volume":"49","author":"Zhang","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","first-page":"3231","article-title":"Higher-order permanent scatterers analysis","volume":"2005","author":"Ferretti","year":"2005","journal-title":"EURASIP J. Appl. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/TGRS.2004.838371","article-title":"Differential tomography: A new framework for SAR interferometry","volume":"43","author":"Lombardini","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1109\/TGRS.2008.2000837","article-title":"Four-dimensional SAR imaging for height estimation and monitoring of single and double scatterers","volume":"47","author":"Fornaro","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1109\/LGRS.2010.2103298","article-title":"Let\u2019s Do the Time Warp: Multicomponent Nonlinear Motion Estimation in Differential SAR Tomography","volume":"8","author":"Zhu","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Budillon, A., Crosetto, M., Johnsy, A.C., Monserrat, O., Krishnakumar, V., and Schirinzi, G. (2018). Comparison of Persistent Scatterer Interferometry and SAR Tomography Using Sentinel-1 in Urban Environment. Remote Sens., 10.","DOI":"10.3390\/rs10121986"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Berardino, P., Fornaro, G., Lanari, R., and Sansosti, E. (2002, January 24\u201328). A new algorithm for monitoring localized deformation phenomena based on small baseline differential SAR interferograms. Proceedings of the IEEE International Geoscience and Remote Sensing Symposium, Toronto, ON, Canada.","DOI":"10.1109\/TGRS.2002.803792"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2374","DOI":"10.1109\/TGRS.2006.873207","article-title":"On the Extension of the Minimum Cost Flow Algorithm for Phase Unwrapping of Multitemporal Differential SAR Interferograms","volume":"44","author":"Pepe","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1109\/36.298013","article-title":"The wavenumber shift in SAR interferometry","volume":"32","author":"Gatelli","year":"1994","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_32","unstructured":"Pasquali, P., Prati, C., Rocca, F., Seymour, M., Fortuny, J., Ohlmer, E., and Sieber, A.J. (1995, January 10\u201314). A 3-D SAR Experiment with EMSL Data. Proceedings of the 1995 International Geoscience and Remote Sensing Symposium, IGARSS\u201995, Quantitative Remote Sensing for Science and Application, Firenze, Italy."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2142","DOI":"10.1109\/36.868873","article-title":"First Demonstration of Airborne SAR Tomography Using Multibaseline L-Band Data","volume":"38","author":"Reigber","year":"2000","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_34","first-page":"41","article-title":"Tomographic Processing of Interferometric SAR Data","volume":"50","author":"Lombardini","year":"2014","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1109\/TGRS.2003.809934","article-title":"Three-dimensional focusing with multipass SAR data","volume":"41","author":"Fornaro","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2284","DOI":"10.1109\/TGRS.2008.2011632","article-title":"Detection of Single Scatterers in Multidimensional SAR Imaging","volume":"47","author":"Maio","year":"2009","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","unstructured":"Peter, K. (2019, September 17). Space Monitor for Hong Kong Settlement. Available online: https:\/\/tunneltalk.com\/Satellite-imaging-Sep11-Satellite-eye-on-settlement.php."},{"key":"ref_38","unstructured":"Corne, E. (2015, January 11\u201313). Satellite technology as an aid to map and monitor construction\/infrastructure sites anywhere in the world. Proceedings of Geomatics Indaba, Ekurhuleni, South Africa."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/21\/2467\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:28:46Z","timestamp":1760189326000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/21\/2467"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,23]]},"references-count":38,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["rs11212467"],"URL":"https:\/\/doi.org\/10.3390\/rs11212467","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2019,10,23]]}}}