{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:12:13Z","timestamp":1760231533758,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2022,9,26]],"date-time":"2022-09-26T00:00:00Z","timestamp":1664150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42004129","2021YFC1523401","JJKH20210251KJ","JJKH20190879KJ"],"award-info":[{"award-number":["42004129","2021YFC1523401","JJKH20210251KJ","JJKH20190879KJ"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["42004129","2021YFC1523401","JJKH20210251KJ","JJKH20190879KJ"],"award-info":[{"award-number":["42004129","2021YFC1523401","JJKH20210251KJ","JJKH20190879KJ"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Education Department of Jilin Province","award":["42004129","2021YFC1523401","JJKH20210251KJ","JJKH20190879KJ"],"award-info":[{"award-number":["42004129","2021YFC1523401","JJKH20210251KJ","JJKH20190879KJ"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The GPR signals appear nonlinear and nonstationary during propagation. To evaluate the nonstationarity, the empirical mode decomposition (EMD) and its modifications have been proposed to localize the variations of energy and frequency components over time. Among the EMD\u2212based algorithms, the variational mode decomposition (VMD) is one of the representative methods. It eliminates the drawbacks of EMD, to some extent, but is still executed in one dimension. In this work, the multivariate variational mode decomposition (MVMD) algorithm is introduced for decomposing the GPR B-scans into several IMF-slices in two dimensions, which inherits the advantages of the VMD and considers the stratigraphic constraints. Then, by applying the Teager\u2013Kaiser energy operator (TKEO) within each IMF-slice, a novel energy attribute is formed and termed as the \u201cTKEO-slices\u201d. The proposed TKEO-slices can localize the energy attribute of geophysical information of different scales with good stratigraphic continuity. The proposed scheme is evaluated by the synthetic benchmark, model data, and field data. Compared with the VMD\u2212based scheme and the classic instantaneous amplitude, the proposed TKEO-slices show better resolution and lateral continuity.<\/jats:p>","DOI":"10.3390\/rs14194805","type":"journal-article","created":{"date-parts":[[2022,9,28]],"date-time":"2022-09-28T03:30:37Z","timestamp":1664335837000},"page":"4805","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["GPR Energy Attribute Slices Based on Multivariate Variational Mode Decomposition and Teager\u2013Kaiser Energy Operator"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2016-9420","authenticated-orcid":false,"given":"Xuebing","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Geomatics and Prospecting Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7898-4973","authenticated-orcid":false,"given":"Yuxiang","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Geomatics and Prospecting Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengkun","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Geomatics and Prospecting Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Geomatics and Prospecting Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7451-9145","authenticated-orcid":false,"given":"Xuan","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Geomatics and Prospecting Engineering, Jilin Jianzhu University, Changchun 130118, China"},{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuan","family":"Chai","sequence":"additional","affiliation":[{"name":"School of Geomatics and Prospecting Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1109\/78.492555","article-title":"Localization of the complex spectrum: The S transform","volume":"44","author":"Stockwell","year":"1996","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"SC1","DOI":"10.1190\/INT-2016-0041.1","article-title":"Application of bi-Gaussian S-transform in high-resolution seismic time-frequency analysis","volume":"5","author":"Cheng","year":"2017","journal-title":"Interpretation"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1109\/79.91217","article-title":"Wavelets and signal processing","volume":"8","author":"Rioul","year":"1991","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"P19","DOI":"10.1190\/1.2127113","article-title":"Spectral decomposition of seismic data with continuous-wavelet transform","volume":"70","author":"Sinha","year":"2005","journal-title":"Geophysics"},{"key":"ref_5","first-page":"177","article-title":"On instantaneous frequency","volume":"1","author":"Huang","year":"2009","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1098\/rspa.1998.0193","article-title":"The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis","volume":"454","author":"Huang","year":"1998","journal-title":"Proc. R. Soc. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S1793536909000047","article-title":"Ensemble empirical mode decomposition: A noise-assisted data analysis method","volume":"1","author":"Wu","year":"2011","journal-title":"Adv. Adapt. Data Anal."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Torres, M.E., Colominas, M.A., Schlotthauer, G., and Flandrin, P. (2011, January 22\u201327). A complete ensemble empirical mode decomposition with adaptive noise. Proceedings of the 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic.","DOI":"10.1109\/ICASSP.2011.5947265"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1615","DOI":"10.1109\/LGRS.2015.2415736","article-title":"GPR Signal Denoising and Target Extraction with the CEEMD Method","volume":"12","author":"Li","year":"2015","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational Mode Decomposition","volume":"62","author":"Dragomiretskiy","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"V365","DOI":"10.1190\/geo2015-0489.1","article-title":"Applications of variational mode decomposition in seismic time-frequency analysis","volume":"81","author":"Liu","year":"2016","journal-title":"Geophysics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6039","DOI":"10.1109\/TSP.2019.2951223","article-title":"Multivariate Variational Mode Decomposition","volume":"67","author":"Aftab","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","first-page":"5901214","article-title":"Ground-Roll Separation and Attenuation Using Curvelet-Based Multichannel Variational Mode Decomposition","volume":"60","author":"Liu","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Zhang, X., Nilot, E., Feng, X., Ren, Q., and Zhang, Z. (2018). IMF-Slices for GPR Data Processing Using Variational Mode Decomposition Method. Remote Sens., 10.","DOI":"10.3390\/rs10030476"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1007\/978-94-009-2037-8_10","article-title":"Evidence for nonlinear sound production mechanisms in the vocal tract","volume":"55","author":"Teager","year":"1990","journal-title":"Speech Prod. Speech Model."},{"key":"ref_16","unstructured":"Kaiser, J.F. (1990, January 3\u20136). On a simple algorithm to calculate the \u2018energy\u2019 of a signal. Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Albuquerque, NM, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1109\/LGRS.2017.2656158","article-title":"Spectral Decomposition for Hydrocarbon Detection Based on VMD and Teager\u2013Kaiser Energy","volume":"14","author":"Liu","year":"2017","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1093\/gji\/ggt530","article-title":"EMD and Teager\u2013Kaiser energy applied to hydrocarbon detection in a carbonate reservoir","volume":"197","author":"Xue","year":"2014","journal-title":"Geophys. J. Int."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1561\/2200000016","article-title":"Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers","volume":"3","author":"Boyd","year":"2011","journal-title":"Found. Trends Mach. Learn."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1016\/j.conbuildmat.2005.06.007","article-title":"Modelling ground penetrating radar by GprMax","volume":"19","author":"Giannopoulos","year":"2005","journal-title":"Constr. Build. Mater."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"D\u00e9robert, X., and Pajewski, L. (2018). TU1208 Open Database of Radargrams: The Dataset of the IFSTTAR Geophysical Test Site. Remote Sens., 10.","DOI":"10.3390\/rs10040530"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/19\/4805\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:39:54Z","timestamp":1760143194000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/19\/4805"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,26]]},"references-count":21,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["rs14194805"],"URL":"https:\/\/doi.org\/10.3390\/rs14194805","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,9,26]]}}}