{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T11:39:51Z","timestamp":1763811591353,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2024,11,3]],"date-time":"2024-11-03T00:00:00Z","timestamp":1730592000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"Postdoctoral Fellowship Program of CPSF","doi-asserted-by":"publisher","award":["GZC20242161"],"award-info":[{"award-number":["GZC20242161"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In order to enhance the detection of maritime vessel targets, considering the causal relationship between the motion of vessels and their wakes, as well as the characteristics of ship wakes such as large diffusion range and distinctive features, this paper proposes a data-driven method based on Dynamic Mode Decomposition (DMD) for detecting and analyzing ship wakes in sea surface videos. The method, named Multi-dimensional Dynamic Mode Decomposition (MDDMD), segments the video sequence into smaller blocks and analyzes them at various resolution levels, effectively addressing the data analysis issues of large and complex systems. The MDDMD algorithm not only extracts key dynamic features but also reveals the intrinsic structure of the system at different scales, providing new perspectives for the in-depth understanding of nonlinear systems. Comparative experimental results with existing DMD and PCA algorithms demonstrate that the MDDMD algorithm has higher accuracy and robustness in ship wake detection. This study offers valuable insights for ship wake detection under complex maritime conditions and holds potential for practical application in the field of maritime surveillance.<\/jats:p>","DOI":"10.3390\/rs16214110","type":"journal-article","created":{"date-parts":[[2024,11,4]],"date-time":"2024-11-04T09:52:54Z","timestamp":1730713974000},"page":"4110","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Detection of Ship Wakes in Dynamic Sea Surface Video Sequences: A Data-Driven Approach"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6634-7240","authenticated-orcid":false,"given":"Chengcheng","family":"Yu","sequence":"first","affiliation":[{"name":"School of Integrated Circuits and Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Yanmei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Integrated Circuits and Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Meifang","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Integrated Circuits and Electronic Engineering, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Zhibo","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Beihang University, Beijing 100191, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5207811","DOI":"10.1109\/TGRS.2023.3271905","article-title":"Ship Detection From Raw SAR Echo Data","volume":"61","author":"Leng","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Leng, X., Wang, J., Ji, K., and Kuang, G. (2022, January 17\u201322). Ship Detection in Range-Compressed SAR Data. Proceedings of the IGARSS 2022\u20142022 IEEE International Geoscience and Remote Sensing Symposium, Kuala Lumpur, Malaysia.","DOI":"10.1109\/IGARSS46834.2022.9884909"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/0167-8655(86)90009-7","article-title":"Linear feature detection and enhancement in noisy images via the Radon transform","volume":"4","author":"Murphy","year":"1986","journal-title":"Pattern Recognit. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1109\/TGRS.1990.572948","article-title":"Application Of Radon Transform Techniques To Wake Detection In Seasat-A SAR Images","volume":"28","author":"Rey","year":"1990","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1010","DOI":"10.1109\/36.508418","article-title":"An automatic ship and ship wake detection system for spaceborne SAR images in coastal regions","volume":"34","author":"Eldhuset","year":"1996","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_6","unstructured":"Tunaley, J. (2003, January 21\u201325). The estimation of ship velocity from SAR imagery. Proceedings of the IGARSS 2003. 2003 IEEE International Geoscience and Remote Sensing Symposium. Proceedings (IEEE Cat. No.03CH37477), Toulouse, France."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1506","DOI":"10.1109\/TGRS.2003.811998","article-title":"The application of wavelets correlator for ship wake detection in SAR images","volume":"41","author":"Kuo","year":"2003","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2335","DOI":"10.1109\/TGRS.2004.833390","article-title":"The speed and beam of a ship from its wake\u2019s SAR images","volume":"42","author":"Zilman","year":"2004","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1634","DOI":"10.1016\/j.sigpro.2005.02.013","article-title":"An improvement of ship wake detection based on the radon transform","volume":"85","author":"Courmontagne","year":"2005","journal-title":"Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Srivastava, R., and Christmas, J. (2022, January 21\u201324). Analysis of Sea Waves and Ship Wake Detection. Proceedings of the OCEANS 2022\u2014Chennai, Chennai, India.","DOI":"10.1109\/OCEANSChennai45887.2022.9775452"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5002016","DOI":"10.1109\/TIM.2024.3403211","article-title":"Deep Self-Representation Learning Framework for Hyperspectral Anomaly Detection","volume":"73","author":"Cheng","year":"2024","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5518118","DOI":"10.1109\/TGRS.2024.3399313","article-title":"Memory-Augmented Autoencoder with Adaptive Reconstruction and Sample Attribution Mining for Hyperspectral Anomaly Detection","volume":"62","author":"Huo","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5033016","DOI":"10.1109\/TIM.2024.3403211","article-title":"Deep Feature Aggregation Network for Hyperspectral Anomaly Detection","volume":"73","author":"Cheng","year":"2024","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5504205","DOI":"10.1109\/LGRS.2023.3271899","article-title":"Two-Stream Isolation Forest Based on Deep Features for Hyperspectral Anomaly Detection","volume":"20","author":"Cheng","year":"2023","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"6006505","DOI":"10.1109\/LGRS.2023.3283403","article-title":"Multiple Instances Complementary Detection and Difficulty Evaluation for Weakly Supervised Object Detection in Remote Sensing Images","volume":"20","author":"Huo","year":"2023","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Del Prete, R., Graziano, M.D., and Renga, A. (2021). First Results on Wake Detection in SAR Images by Deep Learning. Remote Sens., 13.","DOI":"10.3390\/rs13224573"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Jones, B., Ahmadibeni, A., and Shirkhodaie, A. (2021, January 1\u20135). Simulated SAR imagery generation of marine vehicles and associated wakes using electromagnetic modeling and simulation techniques. Proceedings of the Applications of Machine Learning 2021, San Diego, CA, USA.","DOI":"10.1117\/12.2600500"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5613622","DOI":"10.1109\/TGRS.2021.3128989","article-title":"Rethinking Automatic Ship Wake Detection: State-of-the-Art CNN-based Wake Detection via Optical Images","volume":"60","author":"Xue","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"113345","DOI":"10.1016\/j.rse.2022.113345","article-title":"Towards real-time detection of ships and wakes with lightweight deep learning model in Gaofen-3 SAR images","volume":"284","author":"Ding","year":"2022","journal-title":"Remote Sens. Environ."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Joshi, S.K., Baumgartner, S.V., da Silva, A.B.C., and Krieger, G. (2019). Range-Doppler Based CFAR Ship Detection with Automatic Training Data Selection. Remote Sens., 11.","DOI":"10.3390\/rs11111270"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"4004805","DOI":"10.1109\/LGRS.2024.3366749","article-title":"RCShip: A Dataset Dedicated to Ship Detection in Range-Compressed SAR Data","volume":"21","author":"Tan","year":"2024","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1665","DOI":"10.1109\/TGRS.2019.2947360","article-title":"Ship Wake Detection in SAR Images via Sparse Regularization","volume":"58","author":"Karakus","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Karakus, O., and Achim, A. (2019, January 12\u201317). Ship Wake Detection in X-band SAR Images Using Sparse GMC Regularization. Proceedings of the ICASSP 2019\u20142019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK.","DOI":"10.1109\/ICASSP.2019.8683489"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Graziano, M., Grasso, M., and D\u2019Errico, M. (2017). Performance Analysis of Ship Wake Detection on Sentinel-1 SAR Images. Remote Sens., 9.","DOI":"10.3390\/rs9111107"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Daniela Graziano, M. (2015, January 26\u201331). SAR-based ship route estimation by wake components detection and classification. Proceedings of the 2015 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Milan, Italy.","DOI":"10.1109\/IGARSS.2015.7326512"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4451","DOI":"10.1080\/01431161.2018.1425568","article-title":"Comparison of ship wake detectability on C-band and X-band SAR","volume":"39","author":"Tings","year":"2018","journal-title":"Int. J. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/LGRS.2017.2777264","article-title":"Low-Rank Plus Sparse Decomposition and Localized Radon Transform for Ship-Wake Detection in Synthetic Aperture Radar Images","volume":"15","author":"Biondi","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1146\/annurev-fluid-010816-060042","article-title":"Model Reduction for Flow Analysis and Control","volume":"49","author":"Rowley","year":"2017","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.dsp.2013.11.006","article-title":"Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking","volume":"25","author":"Mihaylova","year":"2014","journal-title":"Digit. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.physd.2004.06.015","article-title":"Comparison of systems with complex behavior","volume":"197","author":"Banaszuk","year":"2004","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s11071-005-2824-x","article-title":"Spectral Properties of Dynamical Systems, Model Reduction and Decompositions","volume":"41","year":"2005","journal-title":"Nonlinear Dyn."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1017\/S0022112010001217","article-title":"Dynamic mode decomposition of numerical and experimental data","volume":"656","author":"Schmid","year":"2010","journal-title":"J. Fluid Mech."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1017\/S0022112009992059","article-title":"Spectral analysis of nonlinear flows","volume":"641","author":"Rowley","year":"2009","journal-title":"J. Fluid Mech."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1073\/pnas.17.5.315","article-title":"Hamiltonian Systems and Transformation in Hilbert Space","volume":"17","author":"Koopman","year":"1931","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1146\/annurev-fluid-011212-140652","article-title":"Analysis of Fluid Flows via Spectral Properties of the Koopman Operator","volume":"45","year":"2013","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Brunton, S.L., Brunton, B.W., Proctor, J.L., and Kutz, J.N. (2016). Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control. PLoS ONE, 11.","DOI":"10.1371\/journal.pone.0150171"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1017\/jfm.2018.283","article-title":"Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis","volume":"847","author":"Towne","year":"2018","journal-title":"J. Fluid Mech."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"024103","DOI":"10.1063\/1.4863670","article-title":"Sparsity-promoting dynamic mode decomposition","volume":"26","author":"Schmid","year":"2014","journal-title":"Phys. Fluids"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1017\/jfm.2016.678","article-title":"Recursive dynamic mode decomposition of transient and post-transient wake flows","volume":"809","author":"Noack","year":"2016","journal-title":"J. Fluid Mech."},{"key":"ref_40","first-page":"20220576","article-title":"Physics-informed dynamic mode decomposition","volume":"479","author":"Baddoo","year":"2023","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Boull\u00e9, N., and Colbrook, M. (2024). Multiplicative Dynamic Mode Decomposition. arXiv.","DOI":"10.1016\/bs.hna.2024.05.004"},{"key":"ref_42","unstructured":"Ch\u00e1vez-Dorado, J., Scherl, I., and DiBenedetto, M. (2024). Wave and turbulence separation using dynamic mode decomposition. arXiv."},{"key":"ref_43","unstructured":"Colbrook, M., Drysdale, C., and Horning, A. (2024). Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators. arXiv."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"053501","DOI":"10.1063\/1.5027419","article-title":"Dynamic mode decomposition for plasma diagnostics and validation","volume":"89","author":"Taylor","year":"2018","journal-title":"Rev. Sci. Instruments"},{"key":"ref_45","unstructured":"Hirsh, S., Brunton, B., and Kutz, J. (2018). Data-driven Spatiotemporal Modal Decomposition for Time Frequency Analysis. arXiv."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Kutz, J., Brunton, S., Brunton, B., and Proctor, J. (2016). Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, SIAM-Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9781611974508"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/21\/4110\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:27:37Z","timestamp":1760113657000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/21\/4110"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,3]]},"references-count":46,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["rs16214110"],"URL":"https:\/\/doi.org\/10.3390\/rs16214110","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,11,3]]}}}