{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T08:01:55Z","timestamp":1781856115090,"version":"3.54.5"},"reference-count":59,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T00:00:00Z","timestamp":1694995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"French Defense Agency","award":["ANR\/ASTRID HypFoM 15-ASTR-0019"],"award-info":[{"award-number":["ANR\/ASTRID HypFoM 15-ASTR-0019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>In a previous paper, we introduced (i) a specific hyperspectral mixing model for the sea bottom, based on a detailed physical analysis that includes the adjacency effect, and (ii) an associated unmixing method that is supervised (i.e., not blind) in the sense that it requires a prior estimation of various parameters of the mixing model, which is constraining. We here proceed much further, by first analytically showing that the above model can be seen as a specific member of the general class of mixing models involving spectral variability. Therefore, we then process such data with the IP-NMF unsupervised (i.e., blind) unmixing method that we proposed in previous works to handle spectral variability. Such variability especially occurs when the sea depth significantly varies over the considered scene. We show that IP-NMF then yields significantly better pure spectra estimates than a classical method from the literature that was not designed to handle such variability. We present test results obtained with realistic synthetic data. These tests address several reference water depths, up to 7.5 m, and clear or standard water. For instance, they show that when the reference depth is set to 7.5 m and the water is clear, the proposed approach is able to distinguish various classes of pure materials when the water depth varies up to \u00b10.2 m around this reference depth, over all pixels of the analyzed scene or over a \u201csubscene\u201d: the overall scene may first be segmented, to obtain smaller depths variations over each subscene. The proposed approach is therefore effective and can be used as a building block in performing the subpixel classification of the sea bottom for shallow water.<\/jats:p>","DOI":"10.3390\/rs15184583","type":"journal-article","created":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T05:59:06Z","timestamp":1695016746000},"page":"4583","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Modeling and Unsupervised Unmixing Based on Spectral Variability for Hyperspectral Oceanic Remote Sensing Data with Adjacency Effects"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8769-2446","authenticated-orcid":false,"given":"Yannick","family":"Deville","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Toulouse, UPS-CNRS-OMP-CNES, IRAP, 31400 Toulouse, 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Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/79.974727","article-title":"Spectral unmixing","volume":"19","author":"Keshava","year":"2002","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Deville, Y., Duarte, L.T., and Hosseini, S. (2021). Nonlinear Blind Source Separation and Blind Mixture Identification. METHODS for Bilinear, Linear-Quadratic and Polynomial Mixtures, Springer. Springer Briefs in Electrical and Computer Engineering, Springer Nature.","DOI":"10.1007\/978-3-030-64977-7"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1109\/TGRS.2013.2242475","article-title":"Linear-quadratic mixing model for reflectances in urban environments","volume":"52","author":"Meganem","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Deville, Y., and Duarte, L.T. (2015, January 25\u201328). An overview of blind source separation methods for linear-quadratic and post-nonlinear mixtures. Proceedings of the 12th International Conference on Latent Variable Analysis and Signal Separation (LVA\/ICA 2015), Liberec, Czech Republic. LNCS 9237.","DOI":"10.1007\/978-3-319-22482-4_18"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Deville, Y., and Hosseini, S. (2020, January 8\u201311). Blind source separation methods based on output nonlinear correlation for bilinear mixtures of an arbitrary number of possibly correlated signals. Proceedings of the Eleventh IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2020), Hangzhou, China.","DOI":"10.1109\/SAM48682.2020.9104220"},{"key":"ref_7","unstructured":"Meganem, I., Deville, Y., Hosseini, S., D\u00e9liot, P., Briottet, X., and Duarte, L.T. (September, January 29). Linear-quadratic and polynomial Non-negative Matrix Factorization; application to spectral unmixing. Proceedings of the 19th European Signal Processing Conference (EUSIPCO 2011), Barcelona, Spain."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Benhalouche, F.Z., Deville, Y., Karoui, M.S., and Ouamri, A. (2016, January 13\u201316). Hyperspectral endmember spectra extraction based on constrained linear-quadratic matrix factorization using a projected gradient method. Proceedings of the 2016 IEEE International Workshop on Machine Learning for Signal Processing (MLSP 2016), Salerno, Italy.","DOI":"10.1109\/MLSP.2016.7738868"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Benhalouche, F.Z., Karoui, M.S., and Deville, Y. (2018, January 23\u201326). Linear-quadratic NMF-based urban hyperspectral data unmixing with some known endmembers. Proceedings of the 9th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS 2018), Amsterdam, The Netherlands.","DOI":"10.1109\/WHISPERS.2018.8747241"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Benhalouche, F.Z., Deville, Y., Karoui, M.S., and Ouamri, A. (2021). Hyperspectral unmixing based on constrained bilinear or linear-quadratic matrix factorization. Remote Sens., 13.","DOI":"10.3390\/rs13112132"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Benkouider, Y.K., Benhalouche, F.Z., Karoui, M.S., Deville, Y., and Hosseini, S. (2018, January 23\u201326). Bilinear matrix factorization using a gradient method for unmixing hyperspectral images combined with multispectral data. Proceedings of the 9th Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS 2018), Amsterdam, The Netherlands.","DOI":"10.1109\/WHISPERS.2018.8747126"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.dsp.2019.01.011","article-title":"From separability\/identifiability properties of bilinear and linear-quadratic mixture matrix factorization to factorization algorithms","volume":"87","author":"Deville","year":"2019","journal-title":"Digit. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1109\/LGRS.2013.2278993","article-title":"A bilinear-bilinear nonnegative matrix factorization method for hyperspectral unmixing","volume":"11","author":"Eches","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_14","unstructured":"Guerrero, A., Deville, Y., and Hosseini, S. (2018, January 2\u20135). A blind source separation method based on output nonlinear correlation for bilinear mixtures. Proceedings of the 14th International Conference on Latent Variable Analysis and Signal Separation (LVA\/ICA 2018), Guildford, UK. Part of Springer Nature 2018, LNCS 10891."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Huard, P., and Marion, R. (2011, January 6\u20139). Study of non-linear mixing in hyperspectral imagery\u2014A first attempt in the laboratory. Proceedings of the Third Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS 2011), Lisbon, Portugal.","DOI":"10.1109\/WHISPERS.2011.6080953"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Jarboui, L., Hosseini, S., Deville, Y., Guidara, R., and Hamida, A.B. (2014, January 17\u201319). A new unsupervised method for hyperspectral image unmixing using a linear-quadratic model. Proceedings of the First International Conference of Advanced Technologies for Signal and Image Processing (ATSIP 2014), Sousse, Tunisia.","DOI":"10.1109\/ATSIP.2014.6834649"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Jarboui, L., Hosseini, S., Guidara, R., Deville, Y., and Hamida, A.B. (2016, January 20\u201325). A MAP-based NMF approach to hyperspectral image unmixing using a linear-quadratic mixture model. Proceedings of the 2016 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2016), Shanghai, China.","DOI":"10.1109\/ICASSP.2016.7472299"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Meganem, I., D\u00e9liot, P., Briottet, X., Deville, Y., and Hosseini, S. (2011, January 6\u20139). Physical modelling and non-linear unmixing method for urban hyperspectral images. Proceedings of the Third Workshop on Hyperspectral Image and Signal Processing (WHISPERS 2011), Lisbon, Portugal.","DOI":"10.1109\/WHISPERS.2011.6080863"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1822","DOI":"10.1109\/TSP.2014.2306181","article-title":"Linear-quadratic blind source separation Using NMF to unmix urban hyperspectral images","volume":"62","author":"Meganem","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","unstructured":"Sigurdsson, J., Ulfarsson, M.O., and Sveinsson, J.R. (2018, January 22\u201327). Blind nonlinear hyperspectral unmixing using an lq regularizer. Proceedings of the 2018 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2018), Valencia, Spain."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Su, Y., Li, J., Qi, H., Gamba, P., Plaza, A., and Plaza, J. (August, January 28). Multi-task learning with low-rank matrix factorization for hyperspectral nonlinear unmixing. Proceedings of the 2019 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2019), Yokohama, Japan.","DOI":"10.1109\/IGARSS.2019.8899343"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Naik, G.R. (2018). Advances in Principal Component Analysis\u2014Research and Development, Springer.","DOI":"10.1007\/978-981-10-6704-4"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Revel, C., Deville, Y., Achard, V., Briottet, X., and Weber, C. (2018). Inertia-constrained pixel-by-pixel nonnegative matrix factorisation: A hyperspectral unmixing method dealing with intra-class variability. Remote Sens., 10.","DOI":"10.3390\/rs10111706"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1109\/MGRS.2021.3071158","article-title":"Spectral variability in hyperspectral data unmixing. A comprehensive review","volume":"9","author":"Borsoi","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1109\/MSP.2013.2279177","article-title":"Endmember variability in hyperspectral analysis","volume":"31","author":"Zare","year":"2014","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Cheng, Y., Zhao, L., Chen, S., and Li, X. (2023). Hyperspectral unmixing network accounting for spectral variability based on a modified scaled and a perturbed linear mixing model. Remote Sens., 15.","DOI":"10.3390\/rs15153890"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Imbiriba, T., Borsoi, R.A., and Bermudez, J.C.M. (2018, January 15\u201320). Generalized linear mixing model accounting for endmember variability. Proceedings of the 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2018), Calgary, AB, Canada.","DOI":"10.1109\/ICASSP.2018.8462214"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Brezini, S.E., Deville, Y., Karoui, M.S., Benhalouche, F.Z., and Ouamri, A. (2021, January 11\u201316). A penalization-based NMF approach for hyperspectral unmixing addressing spectral variability with an additively-tuned mixing model. Proceedings of the 2021 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2021), Brussels, Belgium.","DOI":"10.1109\/IGARSS47720.2021.9553366"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"108214","DOI":"10.1016\/j.sigpro.2021.108214","article-title":"Linear mixing model with scaled bundle dictionary for hyperspectral unmixing with spectral variability","volume":"188","author":"Azar","year":"2021","journal-title":"Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Benhalouche, F.Z., Karoui, M.S., and Deville, Y. (2021, January 11\u201316). Gradient-based NMF methods for hyperspectral unmixing addressing spectral variability with a multiplicative-tuning linear mixing model. Proceedings of the 2021 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2021), Brussels, Belgium.","DOI":"10.1109\/IGARSS47720.2021.9554445"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"103838","DOI":"10.1016\/j.dsp.2022.103838","article-title":"An NMF-based method for jointly handling mixture nonlinearity and intraclass variability in hyperspectral blind source separation","volume":"133","author":"Deville","year":"2023","journal-title":"Digit. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3890","DOI":"10.1109\/TIP.2016.2579259","article-title":"Blind hyperspectral unmixing using an extended linear mixing model to address spectral variability","volume":"25","author":"Drumetz","year":"2016","journal-title":"IEEE Trans. Image Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1109\/JSTSP.2018.2877497","article-title":"SULoRA: Subspace unmixing with low-rank attribute embedding for hyperspectral data analysis","volume":"12","author":"Hong","year":"2018","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1109\/TIP.2018.2878958","article-title":"An augmented linear mixing model to address spectral variability for hyperspectral unmixing","volume":"28","author":"Hong","year":"2019","journal-title":"IEEE Trans. Image Process."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Karoui, M.S., Benhalouche, F.Z., and Deville, Y. (2022, January 7\u20139). Hyperspectral unmixing with a modified augmented linear mixing model addressing spectral variability. Proceedings of the 2022 IEEE Mediterranean and Middle-East Geoscience and Remote Sensing Symposium (M2GARSS 2022), Istanbul, Turkey.","DOI":"10.1109\/M2GARSS52314.2022.9839710"},{"key":"ref_36","first-page":"5503515","article-title":"Bayesian unmixing of hyperspectral image sequence with composite priors for abundance and endmember variability","volume":"60","author":"Liu","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"5501713","DOI":"10.1109\/TGRS.2023.3236471","article-title":"Orthogonal subspace unmixing to address spectral variability for hyperspectral image","volume":"61","author":"Ren","year":"2023","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Sahadevan, A.S., Ahmad, T., Lyngdoh, R.B., and Kumar, D.N. (Adv. Space Res., 2023). Endmember variability based abundance estimation of red and black soil over sparsely vegetated area using AVIRIS-NG hyperspectral image, Adv. Space Res., in press.","DOI":"10.1016\/j.asr.2023.05.027"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Salehani, Y.E., Arabnejad, E., and Gazor, S. (2021, January 6\u201311). Augmented Gaussian linear mixture model for spectral variability in hyperspectral unmixing. Proceedings of the 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2021), Toronto, ON, Canada.","DOI":"10.1109\/ICASSP39728.2021.9414358"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Shi, S., Zhao, M., Zhang, L., and Chen, J. (2021, January 6\u201311). Variational autoencoders for hyperspectral unmixing with endmember variability. Proceedings of the 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2021), Toronto, ON, Canada.","DOI":"10.1109\/ICASSP39728.2021.9414940"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Su, L., Liu, J., Yuan, Y., and Chen, Q. (2023). A multi-attention autoencoder for hyperspectral unmixing based on the extended linear mixing model. Remote Sens., 15.","DOI":"10.3390\/rs15112898"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1109\/TSP.2015.2486746","article-title":"Hyperspectral unmixing with spectral variability using a perturbed linear mixing model","volume":"64","author":"Thouvenin","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"5506805","DOI":"10.1109\/LGRS.2023.3295398","article-title":"Manifold regularized sparse archetype analysis considering endmember variability","volume":"20","author":"Xu","year":"2023","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"112359","DOI":"10.1016\/j.rse.2021.112359","article-title":"A novel inequality-constrained weighted linear mixture model for endmember variability","volume":"257","author":"Yu","year":"2021","journal-title":"Remote Sens. Environ."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"6014605","DOI":"10.1109\/LGRS.2022.3214843","article-title":"Spectral variability augmented two-stream network for hyperspectral sparse unmixing","volume":"19","author":"Zhang","year":"2022","journal-title":"IEEE Geosci. Remote. Sens. Lett."},{"key":"ref_46","first-page":"5521914","article-title":"A 3-D-CNN framework for hyperspectral unmixing with spectral variability","volume":"60","author":"Zhao","year":"2022","journal-title":"IEEE Trans. Geosci. Remote. Sens."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Karoui, M.S., Benhalouche, F.Z., and Deville, Y. (2022, January 17\u201322). A gradient-based method for the modified augmented linear mixing model addressing spectral variability for hyperspectral unmixing. Proceedings of the 2022 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2022), Kuala Lumpur, Malaysia.","DOI":"10.1109\/IGARSS46834.2022.9883849"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"A319","DOI":"10.1364\/OE.27.00A319","article-title":"Analysis and quantification of seabed adjacency effects in the subsurface upward radiance in shallow waters","volume":"27","author":"Chami","year":"2019","journal-title":"Opt. Express"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"6633","DOI":"10.1109\/TGRS.2019.2907567","article-title":"Blind hyperspectral unmixing considering the adjacency effect","volume":"57","author":"Wang","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Guillaume, M., Juste, L., Lenot, X., Deville, Y., Lafrance, B., Chami, M., Jay, S., Minghelli, A., Briottet, X., and Serfaty, V. (2018, January 23\u201326). NMF hyperspectral unmixing of the sea bottom: Influence of the adjacency effects, model and method. Proceedings of the WHISPERS 2018, Amsterdam, The Netherlands.","DOI":"10.1109\/WHISPERS.2018.8747064"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Deville, Y., Brezini, S.E., Benhalouche, F.Z., Karoui, M.S., Guillaume, M., Lenot, X., Lafrance, B., Chami, M., Jay, S., and Minghelli, A. (August, January 28). Hyperspectral oceanic remote sensing with adjacency effects: From spectral-variability-based modeling to performance of associated blind unmixing methods. Proceedings of the 2019 IEEE International Geoscience and Remote Sensing Symposium (IGARSS 2019), Yokohama, Japan.","DOI":"10.1109\/IGARSS.2019.8898430"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Cichocki, A., Zdunek, R., Phan, A.H., and Amari, S.-I. (2009). Nonnegative Matrix and Tensor Factorizations. Applications to Exploratory Multi-Way Data Analysis and Blind Source Separation, Wiley.","DOI":"10.1002\/9780470747278"},{"key":"ref_53","unstructured":"Comon, P., and Jutten, C. (2010). Handbook of Blind Source Separation. Independent Component Analysis and Applications, Academic Press."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1109\/TGRS.2005.844293","article-title":"Vertex component analysis: A fast algorithm to unmix hyperspectral data","volume":"43","author":"Nascimento","year":"2005","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1109\/36.911111","article-title":"Fully constrained least squares linear spectral mixture analysis method for material quantification in hyperspectral imagery","volume":"39","author":"Heinz","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Lawson, C.L., and Hanson, R.J. (1995). Solving Least Squares Problems, SIAM\u2019s Classics in Applied Mathematics, Prentice-Hall.","DOI":"10.1137\/1.9781611971217"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"27829","DOI":"10.1364\/OE.23.027829","article-title":"OSOAA: A vector radiative transfer model of coupled atmosphere-ocean system for a rough sea surface application to the estimates of the directional variations of the water leaving reflectance to better process multi-angular satellite sensors data over the ocean","volume":"23","author":"Chami","year":"2015","journal-title":"Opt. Express"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0034-4257(93)90013-N","article-title":"The spectral image processing system (SIPS)\u2014Interactive visualization and analysis of imaging spectrometer data","volume":"44","author":"Kruse","year":"1993","journal-title":"Remote Sens. Environ."},{"key":"ref_59","unstructured":"(2019, February 01). L3HARRIS Geospatial, ENVI Software. Available online: https:\/\/www.l3harrisgeospatial.com\/docs\/spectralanglemapper.html."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/18\/4583\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:52:49Z","timestamp":1760129569000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/18\/4583"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,18]]},"references-count":59,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["rs15184583"],"URL":"https:\/\/doi.org\/10.3390\/rs15184583","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,18]]}}}