{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:55:29Z","timestamp":1760151329739,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,2,22]],"date-time":"2022-02-22T00:00:00Z","timestamp":1645488000000},"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>3-D phase unwrapping (PU) methods based on the 2-D linear temporal coherencemodel have been widely used in time-series interferometric synthetic aperture radar (TS-InSAR) for measuring topography and monitoring subtle deformation. However, the linear temporal coherencemodel can not characterize the coherence of highly coherent pixels accurately in seasonal deformation areas, where nonlinear deformation is deterministic and nonnegligible. Especially, for urban areas with groundwater or thermal dilation seasonal changes or permafrost regions, the nonlinear deformation is usually associated with periodic temperature changes. In this work, a general multi-component temporal coherence model, which considers multiple components including the seasonal deformation, is proposed for 3-D PU of seasonal deformation areas. Moreover, the uncertainty evaluation criterion, based on Cram\u00e9r\u2013Rao bound (CRB), is derived for TS-InSAR. The experimental results, obtained by applying the multi-component temporal coherence model to a data set acquired from January 2012 to February 2016 over the Beijing Capital International Airport area, confirm the effectiveness of the proposed method. High phase consistency, accurate corrected digital elevation model (DEM) and deformation information monitoring with high-density and high-coverage PS pixels are achieved. Under the same iterations and TS-InSAR procedure, the enhanced performance by the proposed model is illustrated by comparing with that of linear model in terms of phase consistency of 3-D phase unwrapping, PSCs selection at each step, and final results evaluation. In summary, the number of phase-consistency edges after 3-D PU is increased by about 15%, the number of final PS pixels selected with the same coherence threshold constraint is increased by about 10%, and more PS pixels provide a low uncertainty in residual topography, mean deformation velocity and seasonal amplitude estimation.<\/jats:p>","DOI":"10.3390\/rs14051080","type":"journal-article","created":{"date-parts":[[2022,2,22]],"date-time":"2022-02-22T22:35:00Z","timestamp":1645569300000},"page":"1080","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Multicomponent Temporal Coherence Model for 3-D Phase Unwrapping in Time-Series InSAR of Seasonal Deformation Areas"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4910-608X","authenticated-orcid":false,"given":"Bo","family":"Yang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9559-3691","authenticated-orcid":false,"given":"Huaping","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1127-9823","authenticated-orcid":false,"given":"Liming","family":"Jiang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5637-0279","authenticated-orcid":false,"given":"Ronggang","family":"Huang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3965-5453","authenticated-orcid":false,"given":"Zhiwei","family":"Zhou","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3977-8886","authenticated-orcid":false,"given":"Hansheng","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Geodesy and Earth\u2019s Dynamics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2968-2888","authenticated-orcid":false,"given":"Wei","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield S1 3JD, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhu, X., Wang, Y., Montazeri, S., and Ge, N. (2018). A review of ten-year advances of multi-baseline SAR interferometry using TerraSAR-X data. Remote Sens., 10.","DOI":"10.3390\/rs10091374"},{"key":"ref_2","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_3","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_4","unstructured":"Kampes, B. (2005). Displacement Parameter Estimation Using Permanent Scatterer Interferometry. [Ph.D. Thesis, Delft University of Technology]."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.tecto.2011.10.013","article-title":"Recent advances in SAR interferometry time series analysis for measuring crustal deformation","volume":"514","author":"Hooper","year":"2012","journal-title":"Tectonophysics"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2006JB004763","article-title":"Persistent scatterer interferometric synthetic aperture radar for crustal deformation analysis, with application to Volc\u00e1n Alcedo, Gal\u00e1pagos","volume":"112","author":"Hooper","year":"2007","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_7","first-page":"248","article-title":"An iterative PS-InSAR method for the analysis of large spatio-temporal baseline data stacks for land subsidence estimation","volume":"74","author":"Foroughnia","year":"2019","journal-title":"Int. J. Appl. Earth Obs. Geoinf."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3497","DOI":"10.1109\/TGRS.2006.881748","article-title":"Imaging of single and double scatterers in urban areas via SAR tomography","volume":"44","author":"Fornaro","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/MGRS.2018.2873644","article-title":"Phase unwrapping in InSAR: A review","volume":"7","author":"Yu","year":"2019","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"10263","DOI":"10.1109\/TGRS.2019.2933024","article-title":"A triangle-oriented Spatial\u2013Temporal phase unwrapping algorithm based on irrotational constraints for time-series InSAR","volume":"57","author":"Li","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","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_12","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1109\/TGRS.2010.2102767","article-title":"A null-space method for the phase unwrapping of multitemporal SAR interferometric stacks","volume":"49","author":"Fornaro","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","unstructured":"Ghiglia, D., Ghiglia, D., Pritt, M., and Pritt, M. (1998). Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software, Wiley. Living Away from Home: Studies."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2865","DOI":"10.1109\/TIP.2011.2138148","article-title":"Residues cluster-based segmentation and outlier-detection method for large-scale phase unwrapping","volume":"20","author":"Yu","year":"2011","journal-title":"IEEE Trans. Image Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1109\/IGARSS.1999.773467","article-title":"A generalized phase unwrapping approach for sparse data","volume":"Volume 1","author":"Costantini","year":"1999","journal-title":"Proceedings of the IEEE 1999 International Geoscience and Remote Sensing Symposium\u2014IGARSS\u201999 (Cat. No. 99CH36293)"},{"key":"ref_16","unstructured":"Hooper, A. (December, January 30). A statistical-cost approach to unwrapping the phase of InSAR time series. Proceedings of the International Workshop on ERS SAR Interferometry, Frascati, Italy."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1364\/JOSAA.18.000338","article-title":"Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization","volume":"18","author":"Chen","year":"2001","journal-title":"JOSA A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1029\/RS023i004p00713","article-title":"Satellite radar interferometry: Two-dimensional phase unwrapping","volume":"23","author":"Goldstein","year":"1988","journal-title":"Radio Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1109\/36.673674","article-title":"A novel phase unwrapping method based on network programming","volume":"36","author":"Costantini","year":"1998","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"4862","DOI":"10.1109\/TIP.2020.2977213","article-title":"Phasenet 2.0: Phase unwrapping of noisy data based on deep learning approach","volume":"29","author":"Spoorthi","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_21","first-page":"4003705","article-title":"A CNN-based coherence-driven approach for InSAR phase unwrapping","volume":"19","author":"Sica","year":"2020","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2737","DOI":"10.1364\/JOSAA.24.002737","article-title":"Phase unwrapping in three dimensions with application to InSAR time series","volume":"24","author":"Hooper","year":"2007","journal-title":"JOSA A"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1364\/JOSAA.27.000605","article-title":"Edgelist phase unwrapping algorithm for time series InSAR analysis","volume":"27","author":"Shanker","year":"2010","journal-title":"JOSA A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"758","DOI":"10.1109\/TGRS.2011.2162630","article-title":"A general formulation for redundant integration of finite differences and phase unwrapping on a sparse multidimensional domain","volume":"50","author":"Costantini","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1857","DOI":"10.1109\/TGRS.2019.2949926","article-title":"A new 3-D minimum cost flow phase unwrapping algorithm based on closure phase","volume":"58","author":"Liu","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","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_27","doi-asserted-by":"crossref","first-page":"4062","DOI":"10.1109\/TGRS.2011.2135371","article-title":"New advances of the extended minimum cost flow phase unwrapping algorithm for SBAS-DInSAR analysis at full spatial resolution","volume":"49","author":"Pepe","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4606","DOI":"10.1109\/TGRS.2011.2143722","article-title":"A new method for temporal phase unwrapping of persistent scatterers InSAR time series","volume":"49","author":"Cuenca","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2446","DOI":"10.1109\/TGRS.2004.835222","article-title":"Ambiguity resolution for permanent scatterer interferometry","volume":"42","author":"Kampes","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1109\/LGRS.2010.2103298","article-title":"Let us 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_31","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_32","unstructured":"Kay, S.M. (1993). Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice-Hall, Inc."},{"key":"ref_33","unstructured":"KAY, S.M. (1998). Fundamentals of Statistical Signal Processing, Prentice Hall."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1109\/MSP.2014.2365593","article-title":"Cram\u00e9r-rao bound analog of bayes\u2019 rule [lecture notes]","volume":"32","author":"Zachariah","year":"2015","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"622","DOI":"10.1109\/TSP.2012.2226165","article-title":"Cram\u00e9r\u2013Rao-type bounds for sparse Bayesian learning","volume":"61","author":"Prasad","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"720","DOI":"10.1109\/29.17564","article-title":"MUSIC, maximum likelihood, and Cramer\u2013Rao bound","volume":"37","author":"Stoica","year":"1989","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1049\/iet-rsn.2012.0139","article-title":"Cramer\u2013Rao bound of parameters estimation and coherence performance for next generation radar","volume":"7","author":"Sun","year":"2013","journal-title":"IET Radar Sonar Navig."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1109\/TMI.2018.2873704","article-title":"Optimal experiment design for magnetic resonance fingerprinting: Cramer\u2013Rao bound meets spin dynamics","volume":"38","author":"Zhao","year":"2018","journal-title":"IEEE Trans. Med. Imag."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1109\/TGRS.2011.2160183","article-title":"Super-resolution power and robustness of compressive sensing for spectral estimation with application to spaceborne tomographic SAR","volume":"50","author":"Zhu","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2429","DOI":"10.1109\/JSTARS.2018.2834950","article-title":"Realistic lower bound on elevation estimation for tomographic SAR","volume":"11","author":"Yang","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Zhou, C., Gong, H., Zhang, Y., Warner, T.A., and Wang, C. (2018). Spatiotemporal evolution of land subsidence in the Beijing plain 2003\u20132015 using persistent scatterer interferometry (PSI) with multi-source SAR data. Remote Sens., 10.","DOI":"10.3390\/rs10040552"},{"key":"ref_42","first-page":"16","article-title":"Structure Design of Beijing Capital International Airport Terminal 3","volume":"38","author":"Wang","year":"2008","journal-title":"Build. Struct."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.patrec.2019.08.011","article-title":"A non-fuzzy interferometric phase estimation algorithm based on modified Fully Convolutional Network","volume":"128","author":"Li","year":"2019","journal-title":"Pattern Recognit. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.tecto.2016.10.016","article-title":"InSAR time-series investigation of long-term ground displacement at Beijing Capital International Airport, China","volume":"691","author":"Gao","year":"2016","journal-title":"Tectonophysics"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.isprsjprs.2015.04.012","article-title":"Multi-dimensional SAR tomography for monitoring the deformation of newly built concrete buildings","volume":"106","author":"Ma","year":"2015","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"111282","DOI":"10.1016\/j.rse.2019.111282","article-title":"Remotely sensing large-and small-scale ground subsidence: A case study of the Guangdong\u2013Hong Kong\u2013Macao Greater Bay Area of China","volume":"232","author":"Ma","year":"2019","journal-title":"Remote Sens. Environ."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/5\/1080\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:25:19Z","timestamp":1760135119000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/5\/1080"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,22]]},"references-count":46,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["rs14051080"],"URL":"https:\/\/doi.org\/10.3390\/rs14051080","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,2,22]]}}}