{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:40:32Z","timestamp":1760402432370,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,19]],"date-time":"2020-01-19T00:00:00Z","timestamp":1579392000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Key Research and Development Program","award":["2017YFB0502700"],"award-info":[{"award-number":["2017YFB0502700"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Interferometric phase filtering is a crucial step in multibaseline interferometric synthetic aperture radar (InSAR). Current multibaseline interferometric phase filtering methods mostly follow methods of single-baseline InSAR and do not bring its data superiority into full play. The joint filtering of multibaseline InSAR based on statistics is proposed in this paper. We study and analyze the fourth-order statistical quantity of interferometric phase: kurtosis. An empirical assumption that the kurtosis of interferograms with different baselines keeps constant is proposed and is named as the baseline-invariant property of kurtosis in this paper. Some numerical experiments and rational analyses confirm its validity and universality. The noise level estimation of nature images is extended to multibaseline InSAR by dint of the baseline-invariant property of kurtosis. A filtering method based on the non-subsampled shearlet transform (NSST) and Wiener filter with estimated noise variance is proposed then. Firstly, multi-scaled and multi-directional coefficients of interferograms are obtained by NSST. Secondly, the noise variance is represented as the solution of a constrained non-convex optimization problem. A pre-thresholded Wiener filtering with estimated noise variance is employed for shrinking or zeroing NSST coefficients. Finally, the inverse NSST is utilized to obtain the filtered interferograms. Experiments on simulated and real data show that the proposed method has excellent comprehensive performance and is superior to conventional single-baseline filtering methods.<\/jats:p>","DOI":"10.3390\/s20020551","type":"journal-article","created":{"date-parts":[[2020,1,21]],"date-time":"2020-01-21T03:04:43Z","timestamp":1579575883000},"page":"551","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Multibaseline Interferometric Phase Denoising Based on Kurtosis in the NSST Domain"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6524-2762","authenticated-orcid":false,"given":"Yanfang","family":"Liu","sequence":"first","affiliation":[{"name":"School of Electronic, Electrical and Communication Engineering, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Department of Space Microwave Remote Sensing System, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"}]},{"given":"Shiqiang","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Space Microwave Remote Sensing System, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"}]},{"given":"Heng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Space Microwave Remote Sensing System, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100190, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4993","DOI":"10.1029\/JB091iB05p04993","article-title":"Topographic Mapping From Interferometric Synthetic Aperture Radar Observations","volume":"91","author":"Zebker","year":"1986","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_2","unstructured":"Teng, W., Perissin, D., Liao, M., and Rocca, F. (2008, January 8\u201311). Deformation Monitoring by Long Term D-InSAR Analysis in Three Gorges Area, China. Proceedings of the IEEE International Geoscience & Remote Sensing Symposium (IGARSS 2008), Boston, MA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1109\/MAES.2005.1499278","article-title":"Multibaseline cross-track SAR interferometry: A signal processing perspective","volume":"20","author":"Gini","year":"2005","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_4","first-page":"12","article-title":"Synthetic aperture radar interferometry","volume":"14","author":"Bamler","year":"1999","journal-title":"Inverse Probl."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Roscoe, A.J., and Blair, S.M. (2016, January 28\u201330). Choice and properties of adaptive and tunable digital boxcar (moving average) filters for power systems and other signal processing applications. Proceedings of the 2016 IEEE International Workshop on Applied Measurements for Power Systems (AMPS), Aachen, Germany.","DOI":"10.1109\/AMPS.2016.7602853"},{"key":"ref_6","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_7","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_8","first-page":"1092","article-title":"Optimal integration-based adaptive direction filter for InSAR interferogram","volume":"13","author":"Yin","year":"2009","journal-title":"J. Remote Sens."},{"key":"ref_9","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_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.optlaseng.2019.03.008","article-title":"A novel two-step noise reduction approach for interferometric phase images","volume":"121","author":"Gao","year":"2019","journal-title":"Opt. Lasers Eng."},{"key":"ref_11","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_12","doi-asserted-by":"crossref","first-page":"4477","DOI":"10.1109\/TGRS.2018.2820725","article-title":"An Improved Phase Filter for Differential SAR Interferometry Based on an Iterative Method","volume":"56","author":"Selva","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","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_14","doi-asserted-by":"crossref","first-page":"1532","DOI":"10.1109\/83.862633","article-title":"Adaptive wavelet thresholding for image denoising and compression","volume":"9","author":"Chang","year":"2000","journal-title":"IEEE Trans. Image Process."},{"key":"ref_15","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_16","doi-asserted-by":"crossref","first-page":"2123","DOI":"10.1109\/TGRS.2014.2355592","article-title":"Sparse Regularization of Interferometric Phase and Amplitude for InSAR Image Formation Based on Bayesian Representation","volume":"53","author":"Xu","year":"2015","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1109\/LGRS.2010.2083631","article-title":"Adaptive InSAR Stack Multilooking Exploiting Amplitude Statistics: A Comparison Between Different Techniques and Practical Results","volume":"8","author":"Parizzi","year":"2011","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1109\/TGRS.2013.2238947","article-title":"Adaptive Multilooking of Airborne Single-Pass Multi-Baseline InSAR Stacks","volume":"52","author":"Schmitt","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3460","DOI":"10.1109\/TGRS.2011.2124465","article-title":"A New Algorithm for Processing Interferometric Data-Stacks: SqueeSAR","volume":"49","author":"Ferretti","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6807","DOI":"10.1109\/TGRS.2014.2303516","article-title":"Adaptive Covariance Matrix Estimation for Multi-Baseline InSAR Data Stacks","volume":"52","author":"Schmitt","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"135176","DOI":"10.1109\/ACCESS.2019.2942008","article-title":"A Phase Filter for Multi-Pass InSAR Stack Data by Hybrid Tensor Rank Representation","volume":"7","author":"You","year":"2019","journal-title":"IEEE Access"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1109\/LSP.2003.818225","article-title":"Wavelet domain image denoising by thresholding and Wiener filtering","volume":"10","author":"Kazubek","year":"2003","journal-title":"Signal Process. Lett. IEEE"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1109\/TIP.2016.2639447","article-title":"Noise level estimation for natural images based on scale-invariant kurtosis and piecewise stationarity","volume":"26","author":"Dong","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.acha.2005.07.002","article-title":"Wavelets with composite dilations and their MRA properties","volume":"20","author":"Guo","year":"2006","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"670","DOI":"10.1109\/TIP.2002.1014998","article-title":"The curvelet transform for image denoising","volume":"11","author":"Starck","year":"2002","journal-title":"IEEE Trans. Image Process."},{"key":"ref_26","unstructured":"H\u00e4user, S., and Steidl, G. (2012). Fast finite shearlet transform. arXiv."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1166","DOI":"10.1109\/TIP.2010.2041410","article-title":"The discrete shearlet transform: A new directional transform and compactly supported shearlet frames","volume":"19","author":"Lim","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.acha.2007.09.003","article-title":"Sparse directional image representations using the discrete shearlet transform","volume":"25","author":"Easley","year":"2008","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"59140U","DOI":"10.1117\/12.613494","article-title":"Sparse multidimensional representation using shearlets","volume":"5914","author":"Labate","year":"2005","journal-title":"Proc. SPIE"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1093\/biomet\/81.3.425","article-title":"Ideal spatial adaptation by wavelet shrinkage","volume":"81","author":"Donoho","year":"1994","journal-title":"Biometrika"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1109\/TCSVT.2014.2380196","article-title":"Noise estimation of natural images via statistical analysis and noise injection","volume":"25","author":"Tang","year":"2014","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zoran, D., and Weiss, Y. (October, January 29). Scale invariance and noise in natural images. Proceedings of the 2009 IEEE 12th International Conference on Computer Vision, Kyoto, Japan.","DOI":"10.1109\/ICCV.2009.5459476"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1661","DOI":"10.1109\/83.869177","article-title":"A mathematical analysis of the DCT coefficient distributions for images","volume":"9","author":"Lam","year":"2000","journal-title":"IEEE Trans. Image Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"930","DOI":"10.1109\/TCE.2010.5506022","article-title":"Gradient information-based image quality metric","volume":"56","author":"Kim","year":"2010","journal-title":"IEEE Trans. Consum. Electron."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1109\/TIP.2013.2293423","article-title":"Gradient magnitude similarity deviation: A highly efficient perceptual image quality index","volume":"23","author":"Xue","year":"2013","journal-title":"IEEE Trans. Image Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/2\/551\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:44:04Z","timestamp":1760363044000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/2\/551"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,19]]},"references-count":35,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["s20020551"],"URL":"https:\/\/doi.org\/10.3390\/s20020551","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,1,19]]}}}