{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,11]],"date-time":"2026-01-11T17:44:22Z","timestamp":1768153462648,"version":"3.49.0"},"reference-count":69,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T00:00:00Z","timestamp":1697760000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["42276257"],"award-info":[{"award-number":["42276257"]}]},{"name":"National Natural Science Foundation of China","award":["41876230"],"award-info":[{"award-number":["41876230"]}]},{"name":"National Natural Science Foundation of China","award":["41941006"],"award-info":[{"award-number":["41941006"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Radio-echo sounding (RES) is widely used for polar ice sheet detection due to its wide coverage and high efficiency. The multivariate variational mode decomposition (MVMD) algorithm for the processing of RES data is an improvement to the variational mode decomposition (VMD) algorithm. It processes data encompassing multiple channels. Determining the most effective component combination of the penalty parameter (\u03b1) and the number of intrinsic mode functions (IMFs) (K) is fundamental and affects the decomposition results. \u03b1 and K in traditional MVMD are provided by subjective experience. We integrated the particle swarm optimization (PSO) algorithm to iteratively optimize these parameters\u2014specifically, \u03b1 and K\u2014with high precision. This was then combined with the four quantitative parameters: energy entropy, signal-to-noise ratio (SNR), peak signal-to-noise ratio (PSNR), and root-mean-square error (RMSE). The RES signal decomposition results were judged, and the most effective component combination for noise suppression was selected. We processed the airborne RES data from the East Antarctic ice sheet using the combined PSO\u2013MVMD method. The results confirmed the quality of the proposed method in attenuating the RES signal noise, enhancing the weak signal of the ice base, and improving the SNR. This combined PSO\u2013MVMD method may help to enhance weak signals in deeper parts of ice sheets and may be an effective tool for RES data interpretation.<\/jats:p>","DOI":"10.3390\/rs15205041","type":"journal-article","created":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T07:25:22Z","timestamp":1697786722000},"page":"5041","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Airborne Radio-Echo Sounding Data Denoising Using Particle Swarm Optimization and Multivariate Variational Mode Decomposition"],"prefix":"10.3390","volume":"15","author":[{"given":"Yuhan","family":"Chen","sequence":"first","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, No. 938 Ximinzhu Street, Changchun 130026, China"},{"name":"Key Laboratory of Polar Science of Ministry of Natural Resources (MNR), Polar Research Institute of China, Shanghai 200136, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6660-6780","authenticated-orcid":false,"given":"Sixin","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, No. 938 Ximinzhu Street, Changchun 130026, China"}]},{"given":"Kun","family":"Luo","sequence":"additional","affiliation":[{"name":"The Institute for Interdisciplinary and Innovate Research, Xi\u2019an University of Architecture and Technology, Xi\u2019an 710055, China"}]},{"given":"Lijuan","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Polar Science of Ministry of Natural Resources (MNR), Polar Research Institute of China, Shanghai 200136, China"},{"name":"College of Surveying and Geo-Informatics, Tongji University, No. 1239 Siping Road, Shanghai 200092, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6226-4891","authenticated-orcid":false,"given":"Xueyuan","family":"Tang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Polar Science of Ministry of Natural Resources (MNR), Polar Research Institute of China, Shanghai 200136, China"},{"name":"School of Oceanography, Shanghai Jiao Tong University, Shanghai 200030, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4929","DOI":"10.5194\/tc-15-4929-2021","article-title":"Nunataks as Barriers to Ice Flow: Implications for Palaeo Ice Sheet Reconstructions","volume":"15","author":"Newall","year":"2021","journal-title":"Cryosphere"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1038\/nature25026","article-title":"Initiation and Long-Term Instability of the East Antarctic Ice Sheet","volume":"552","author":"Gulick","year":"2017","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1038\/nature17447","article-title":"Repeated Large-Scale Retreat and Advance of Totten Glacier Indicated by Inland Bed Erosion","volume":"533","author":"Aitken","year":"2016","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1038\/s41586-022-04946-0","article-title":"Response of the East Antarctic Ice Sheet to Past and Future Climate Change","volume":"608","author":"Stokes","year":"2022","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"e2019GL086663","DOI":"10.1029\/2019GL086663","article-title":"Englacial Architecture and Age-Depth Constraints Across the West Antarctic Ice Sheet","volume":"47","author":"Ashmore","year":"2020","journal-title":"Geophys. 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