{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T16:56:06Z","timestamp":1781110566980,"version":"3.54.1"},"reference-count":38,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2021,11,13]],"date-time":"2021-11-13T00:00:00Z","timestamp":1636761600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2017YFB0502700"],"award-info":[{"award-number":["2017YFB0502700"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61571099"],"award-info":[{"award-number":["61571099"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61501098"],"award-info":[{"award-number":["61501098"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61671113"],"award-info":[{"award-number":["61671113"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Phase unwrapping is a critical step in synthetic aperture radar interferometry (InSAR) data processing chains. In almost all phase unwrapping methods, estimating the phase gradient according to the phase continuity assumption (PGE-PCA) is an essential step. The phase continuity assumption is not always satisfied due to the presence of noise and abrupt terrain changes; therefore, it is difficult to get the correct phase gradient. In this paper, we propose a robust least squares phase unwrapping method that works via a phase gradient estimation network based on the encoder\u2013decoder architecture (PGENet) for InSAR. In this method, from a large number of wrapped phase images with topography features and different levels of noise, the deep convolutional neural network can learn global phase features and the phase gradient between adjacent pixels, so a more accurate and robust phase gradient can be predicted than that obtained by PGE-PCA. To get the phase unwrapping result, we use the traditional least squares solver to minimize the difference between the gradient obtained by PGENet and the gradient of the unwrapped phase. Experiments on simulated and real InSAR data demonstrated that the proposed method outperforms the other five well-established phase unwrapping methods and is robust to noise.<\/jats:p>","DOI":"10.3390\/rs13224564","type":"journal-article","created":{"date-parts":[[2021,11,14]],"date-time":"2021-11-14T20:51:53Z","timestamp":1636923113000},"page":"4564","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["A Robust InSAR Phase Unwrapping Method via Phase Gradient Estimation Network"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1197-3460","authenticated-orcid":false,"given":"Liming","family":"Pu","sequence":"first","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoling","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zenan","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4802-2447","authenticated-orcid":false,"given":"Liang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liming","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jun","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shunjun","family":"Wei","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MGRS.2013.2248301","article-title":"A tutorial on synthetic aperture radar","volume":"1","author":"Moreira","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_2","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_3","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_4","doi-asserted-by":"crossref","first-page":"R1","DOI":"10.1088\/0266-5611\/14\/4\/001","article-title":"Synthetic aperture radar interferometry","volume":"14","author":"Bamler","year":"1998","journal-title":"Inverse Probl."},{"key":"ref_5","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_6","doi-asserted-by":"crossref","first-page":"2470","DOI":"10.1364\/AO.21.002470","article-title":"Analysis of the phase unwrapping algorithm","volume":"21","author":"Itoh","year":"1982","journal-title":"Appl. Opt."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"7437","DOI":"10.1364\/AO.41.007437","article-title":"Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path","volume":"41","author":"Burton","year":"2002","journal-title":"Appl. Opt."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1109\/36.142934","article-title":"New approaches in interferometric SAR data processing","volume":"30","author":"Lin","year":"1992","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.optlaseng.2018.08.024","article-title":"A robust phase unwrapping algorithm based on reliability mask and weighted minimum least-squares method","volume":"112","author":"Yan","year":"2019","journal-title":"Opt. Lasers Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1109\/TIP.2006.888351","article-title":"Phase unwrapping via graph cuts","volume":"16","author":"Valadao","year":"2007","journal-title":"IEEE Trans. Image Process."},{"key":"ref_11","first-page":"80","article-title":"Minimum L 2-norm two dimensional phase unwrapping","volume":"1","author":"Zhang","year":"2005","journal-title":"J. Earth Sci. Enivron."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"728","DOI":"10.1109\/36.499752","article-title":"Phase unwrapping by means of multigrid techniques for interferometric SAR","volume":"34","author":"Pritt","year":"1996","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1364\/JOSAA.11.000107","article-title":"Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods","volume":"11","author":"Ghiglia","year":"1994","journal-title":"JOSA A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1109\/TGRS.2002.802453","article-title":"Phase unwrapping for large SAR interferograms: Statistical segmentation and generalized network models","volume":"40","author":"Chen","year":"2002","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1364\/JOSAA.17.000401","article-title":"Network approaches to two-dimensional phase unwrapping: Intractability and two new algorithms","volume":"17","author":"Chen","year":"2000","journal-title":"JOSA A"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Liang, J., Zhang, J., Shao, J., Song, B., Yao, B., and Liang, R. (2020). Deep Convolutional Neural Network Phase Unwrapping for Fringe Projection 3D Imaging. Sensors, 20.","DOI":"10.3390\/s20133691"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"23173","DOI":"10.1364\/OE.27.023173","article-title":"Rapid and robust two-dimensional phase unwrapping via deep learning","volume":"27","author":"Zhang","year":"2019","journal-title":"Opt. Express"},{"key":"ref_18","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_19","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_20","unstructured":"Sica, F., Calvanese, F., Scarpa, G., and Rizzoli, P. (2020). A CNN-Based Coherence-Driven Approach for InSAR Phase Unwrapping. IEEE Geosci. Remote Sens. Lett., early access."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4653","DOI":"10.1109\/TGRS.2020.2965918","article-title":"Deep Convolutional Neural Network-Based Robust Phase Gradient Estimation for Two-Dimensional Phase Unwrapping Using SAR Interferograms","volume":"58","author":"Zhou","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/MGRS.2021.3065811","article-title":"Artificial Intelligence In Interferometric Synthetic Aperture Radar Phase Unwrapping: A Review","volume":"9","author":"Zhou","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7840","DOI":"10.1109\/JSTARS.2021.3099485","article-title":"A Novel Quality-Guided Two-Dimensional InSAR Phase Unwrapping Method via GAUNet","volume":"14","author":"Wang","year":"2021","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"033104","DOI":"10.1117\/1.OE.55.3.033104","article-title":"Identifying the phase discontinuities in the wrapped phase maps by a classification framework","volume":"55","author":"Ahmad","year":"2016","journal-title":"Opt. Eng."},{"key":"ref_25","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_26","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1117\/12.227137","article-title":"Weighted least squares phase unwrapping by means of multigrid techniques","volume":"Volume 2584","author":"Pritt","year":"1995","journal-title":"Proceedings of the Synthetic Aperture Radar and Passive Microwave Sensing"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.optlaseng.2014.06.007","article-title":"Robust phase unwrapping algorithm based on least squares","volume":"63","author":"Guo","year":"2014","journal-title":"Opt. Lasers Eng."},{"key":"ref_28","first-page":"2802","article-title":"Image restoration using very deep convolutional encoder-decoder networks with symmetric skip connections","volume":"29","author":"Mao","year":"2016","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Tao, X., Gao, H., Shen, X., Wang, J., and Jia, J. (2018, January 18\u201323). Scale-recurrent network for deep image deblurring. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00853"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P., and Brox, T. (2015, January 5\u20139). U-net: Convolutional networks for biomedical image segmentation. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Munich, Germany.","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Nah, S., Hyun Kim, T., and Mu Lee, K. (2017, January 21\u201326). Deep multi-scale convolutional neural network for dynamic scene deblurring. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.35"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Shi, J., Yang, X., Wang, C., Kumar, D., Wei, S., and Zhang, X. (2019). Deep multi-scale recurrent network for synthetic aperture radar images despeckling. Remote Sens., 11.","DOI":"10.3390\/rs11212462"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Pu, L., Zhang, X., Zhou, Z., Shi, J., Wei, S., and Zhou, Y. (2020). A Phase Filtering Method with Scale Recurrent Networks for InSAR. Remote Sens., 12.","DOI":"10.3390\/rs12203453"},{"key":"ref_34","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1007\/s00365-006-0663-2","article-title":"On early stopping in gradient descent learning","volume":"26","author":"Yao","year":"2007","journal-title":"Constr. Approx."},{"key":"ref_36","first-page":"335","article-title":"Early stopping and non-parametric regression: An optimal data-dependent stopping rule","volume":"15","author":"Raskutti","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"4035","DOI":"10.1029\/1998GL900033","article-title":"Radar interferogram filtering for geophysical applications","volume":"25","author":"Goldstein","year":"1998","journal-title":"Geophys. Res. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.isprsjprs.2016.01.013","article-title":"Modified patch-based locally optimal Wiener method for interferometric SAR phase filtering","volume":"114","author":"Wang","year":"2016","journal-title":"ISPRS J. Photogramm. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/22\/4564\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:29:46Z","timestamp":1760167786000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/22\/4564"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,13]]},"references-count":38,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["rs13224564"],"URL":"https:\/\/doi.org\/10.3390\/rs13224564","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,13]]}}}