{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T11:41:26Z","timestamp":1779882086250,"version":"3.53.1"},"reference-count":54,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2020,10,21]],"date-time":"2020-10-21T00:00:00Z","timestamp":1603238400000},"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, 61501098, 61671113"],"award-info":[{"award-number":["61571099, 61501098, 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 filtering is a key issue in interferometric synthetic aperture radar (InSAR) applications, such as deformation monitoring and topographic mapping. The accuracy of the deformation and terrain height is highly dependent on the quality of phase filtering. Researchers are committed to continuously improving the accuracy and efficiency of phase filtering. Inspired by the successful application of neural networks in SAR image denoising, in this paper we propose a phase filtering method that is based on deep learning to efficiently filter out the noise in the interferometric phase. In this method, the real and imaginary parts of the interferometric phase are filtered while using a scale recurrent network, which includes three single scale subnetworks based on the encoder-decoder architecture. The network can utilize the global structural phase information contained in the different-scaled feature maps, because RNN units are used to connect the three different-scaled subnetworks and transmit current state information among different subnetworks. The encoder part is used for extracting the phase features, and the decoder part restores detailed information from the encoded feature maps and makes the size of the output image the same as that of the input image. Experiments on simulated and real InSAR data prove that the proposed method is superior to three widely-used phase filtering methods by qualitative and quantitative comparisons. In addition, on the same simulated data set, the overall performance of the proposed method is better than another deep learning-based method (DeepInSAR). The runtime of the proposed method is only about 0.043s for an image with a size of 1024\u00d71024 pixels, which has the significant advantage of computational efficiency in practical applications that require real-time processing.<\/jats:p>","DOI":"10.3390\/rs12203453","type":"journal-article","created":{"date-parts":[[2020,10,22]],"date-time":"2020-10-22T20:51:00Z","timestamp":1603399860000},"page":"3453","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["A Phase Filtering Method with Scale Recurrent Networks for InSAR"],"prefix":"10.3390","volume":"12","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"}]},{"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"}]},{"given":"Yuanyuan","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"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,21]]},"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","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_3","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."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1456","DOI":"10.1109\/36.718849","article-title":"A new technique for noise filtering of SAR interferometric phase images","volume":"36","author":"Lee","year":"1998","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1109\/TGRS.2005.864142","article-title":"Intensity-driven adaptive-neighborhood technique for polarimetric and interferometric SAR parameters estimation","volume":"44","author":"Vasile","year":"2006","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1109\/TGRS.2012.2202911","article-title":"Directionally adaptive filter for synthetic aperture radar interferometric phase images","volume":"51","author":"Fu","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5315","DOI":"10.1109\/TGRS.2012.2234467","article-title":"Refined filtering of interferometric phase from InSAR data","volume":"51","author":"Chao","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1109\/LGRS.2006.883527","article-title":"An adaptive contoured window filter for interferometric synthetic aperture radar","volume":"4","author":"Yu","year":"2007","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"2114","DOI":"10.1109\/TGRS.2003.817212","article-title":"A modification to the Goldstein radar interferogram filter","volume":"41","author":"Baran","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1963","DOI":"10.1109\/36.729368","article-title":"Improving phase unwrapping techniques by the use of local frequency estimates","volume":"36","author":"Trouve","year":"1998","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1109\/LGRS.2013.2263554","article-title":"Improved Goldstein SAR interferogram filter based on empirical mode decomposition","volume":"11","author":"Song","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"096061","DOI":"10.1117\/1.JRS.9.096061","article-title":"Two-dimensional wavelet algorithm for interferometric synthetic aperture radar phase filtering enhancement","volume":"9","author":"Abdallah","year":"2015","journal-title":"J. Appl. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2553","DOI":"10.1109\/TGRS.2002.806997","article-title":"Modeling and reduction of SAR interferometric phase noise in the wavelet domain","volume":"40","author":"Fabregas","year":"2002","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1109\/LGRS.2008.916066","article-title":"Noise reduction in interferograms using the wavelet packet transform and wiener filtering","volume":"5","author":"Zha","year":"2008","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Fang, D., Lv, X., Wang, Y., Lin, X., and Qian, J. (2016). A sparsity-based InSAR phase denoising algorithm using nonlocal wavelet shrinkage. Remote Sens., 8.","DOI":"10.3390\/rs8100830"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1137\/040616024","article-title":"A review of image denoising algorithms, with a new one","volume":"4","author":"Buades","year":"2005","journal-title":"Multiscale Model. Simul."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1109\/TGRS.2011.2161586","article-title":"A nonlocal SAR image denoising algorithm based on LLMMSE wavelet shrinkage","volume":"50","author":"Parrilli","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1109\/LGRS.2013.2271650","article-title":"Fast adaptive nonlocal SAR despeckling","volume":"11","author":"Cozzolino","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1109\/TGRS.2010.2076376","article-title":"NL-InSAR: Nonlocal interferogram estimation","volume":"49","author":"Deledalle","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1109\/LGRS.2012.2225594","article-title":"Interferometric phase denoising by pyramid nonlocal means filter","volume":"10","author":"Chen","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1109\/LGRS.2014.2362952","article-title":"Nonlocal SAR interferometric phase filtering through higher order singular value decomposition","volume":"12","author":"Lin","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"6181","DOI":"10.1109\/TGRS.2013.2295431","article-title":"Two-step multitemporal nonlocal means for synthetic aperture radar images","volume":"52","author":"Su","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1109\/JSTARS.2015.2421554","article-title":"Nonlocal adaptive multilooking in SAR multipass differential interferometry","volume":"8","author":"Sica","year":"2015","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6469","DOI":"10.1109\/TGRS.2018.2839027","article-title":"A Nonlocal InSAR Filter for High-Resolution DEM Generation From TanDEM-X Interferograms","volume":"56","author":"Baier","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3456","DOI":"10.1109\/TGRS.2018.2800087","article-title":"INSAR-BM3D: A nonlocal filter for SAR interferometric phase restoration","volume":"56","author":"Sica","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","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_28","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_29","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_30","doi-asserted-by":"crossref","unstructured":"Hirose, A. (2012). Complex-Valued Neural Networks, Springer Science & Business Media.","DOI":"10.1007\/978-3-642-27632-3"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1763","DOI":"10.1109\/LSP.2017.2758203","article-title":"SAR image despeckling using a convolutional neural network","volume":"24","author":"Wang","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"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":"Zhang, Q., Yuan, Q., Li, J., Yang, Z., and Ma, X. (2018). Learning a dilated residual network for SAR image despeckling. Remote Sens., 10.","DOI":"10.3390\/rs10020196"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Mukherjee, S., Zimmer, A., Kottayil, N.K., Sun, X., Ghuman, P., and Cheng, I. (2018, January 28\u201331). CNN-Based InSAR Denoising and Coherence Metric. Proceedings of the 2018 IEEE SENSORS, New Delhi, India.","DOI":"10.1109\/ICSENS.2018.8589920"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Sun, X., Zimmer, A., Mukherjee, S., Kottayil, N.K., Ghuman, P., and Cheng, I. (2020). DeepInSAR\u2014A Deep Learning Framework for SAR Interferometric Phase Restoration and Coherence Estimation. Remote Sens., 12.","DOI":"10.3390\/rs12142340"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"6592","DOI":"10.1029\/2018JB015911","article-title":"Application of machine learning to classification of volcanic deformation in routinely generated InSAR data","volume":"123","author":"Anantrasirichai","year":"2018","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_37","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_38","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_39","doi-asserted-by":"crossref","first-page":"15100","DOI":"10.1364\/OE.27.015100","article-title":"One-step robust deep learning phase unwrapping","volume":"27","author":"Wang","year":"2019","journal-title":"Opt. Express"},{"key":"ref_40","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_41","unstructured":"Kingma, D.P., and Ba, J. (2014). Adam: A method for stochastic optimization. arXiv."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_43","unstructured":"Chung, J., Gulcehre, C., Cho, K., and Bengio, Y. (2014). Empirical evaluation of gated recurrent neural networks on sequence modeling. arXiv."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Lei, T., Zhang, Y., Wang, S.I., Dai, H., and Artzi, Y. (2017). Simple recurrent units for highly parallelizable recurrence. arXiv.","DOI":"10.18653\/v1\/D18-1477"},{"key":"ref_45","unstructured":"Matthew, D., and Fergus, R. (2014, January 6\u201312). Visualizing and understanding convolutional neural networks. Proceedings of the 13th European Conference Computer Vision and Pattern Recognition, Zurich, Switzerland."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_47","unstructured":"Mao, X., Shen, C., and Yang, Y.B. (2016, January 5\u201310). Image restoration using very deep convolutional encoder-decoder networks with symmetric skip connections. Proceedings of the 30th Conference on Neural Information Processing Systems, Barcelona, Spain."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"3116","DOI":"10.1109\/TIP.2010.2052820","article-title":"Automatic Parameter Selection for Denoising Algorithms Using a No-Reference Measure of Image Content","volume":"19","author":"Zhu","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_50","unstructured":"Glorot, X., and Bengio, Y. (2010, January 13\u201315). Understanding the difficulty of training deep feedforward neural networks. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, Chia Laguna Resort, Sardinia, Italy."},{"key":"ref_51","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_52","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_53","unstructured":"Coltelli, M., Fornaro, G., Franceschetti, G., Lanari, R., Migliaccio, M., Moreira, J.R., Papathanassiou, K.P., Puglisi, G., Riccio, D., and Schwabisch, M. (1996, January 31\u201331). On the survey of volcanic sites: The SIR-C\/X-SAR interferometry. Proceedings of the IGARSS\u201996, 1996 International Geoscience and Remote Sensing Symposium, Lincoln, NE, USA."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1109\/TGRS.2009.2037432","article-title":"The TerraSAR-X satellite","volume":"48","author":"Pitz","year":"2010","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/20\/3453\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:25:08Z","timestamp":1760178308000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/12\/20\/3453"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,21]]},"references-count":54,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2020,10]]}},"alternative-id":["rs12203453"],"URL":"https:\/\/doi.org\/10.3390\/rs12203453","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,21]]}}}