Citation: Deville, Y.; Brezini, S.-E.; Benhalouche, F.Z.; Karoui, M.S.; Guillaume, M.; Lenot, X.; Lafrance, B.; Chami, M.; Jay, S.; Minghelli, A.; Briottet, X.; Serfaty, V. Modeling and Unsupervised Unmixing Based on Spectral Variability for Hyperspectral Oceanic Remote Sensing Data with Adjacency Effects. Remote Sens. 2023, 15, 4583. https://doi.org/10.3390/ rs15184583 Academic Editors: Paul Scheunders and Danfeng Hong Received: 29 June 2023 Revised: 13 September 2023 Accepted: 14 September 2023 Published: 18 September 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). remote sensing Article Modeling and Unsupervised Unmixing Based on Spectral Variability for Hyperspectral Oceanic Remote Sensing Data with Adjacency Effects Yannick Deville 1, * ,† , Salah-Eddine Brezini 1,2,† , Fatima Zohra Benhalouche 1,2,3,† , Moussa Sofiane Karoui 1,2,3,† , Mireille Guillaume 4,† , Xavier Lenot 5,† , Bruno Lafrance 5,† , Malik Chami 6,† , Sylvain Jay 4,† , Audrey Minghelli 7,8,† , Xavier Briottet 9,† and Véronique Serfaty 10,† 1 Université de Toulouse, UPS-CNRS-OMP-CNES, IRAP, 31400 Toulouse, France; salaheddine.brezini@univ-usto.dz (S.-E.B.); fatima.benhalouche@irap.omp.eu (F.Z.B.); sofiane.karoui@irap.omp.eu (M.S.K.) 2 Université des Sciences et de la Technologie d’Oran-Mohamed Boudiaf, LSI, Bir El Djir, Oran 31000, Algeria 3 Algerian Space Agency (ASAL), Centre des Techniques Spatiales (CTS), Arzew 31200, Algeria 4 Aix Marseille University, CNRS, Centrale Marseille, Institut Fresnel, 13013 Marseille, France; mireille.guillaume@fresnel.fr 5 CS GROUP, CEDEX 05, 31506 Toulouse, France; xavier.lenot@csgroup.eu (X.L.); bruno.lafrance@csgroup.eu (B.L.) 6 Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Sorbonne Université (UFR 918), Laboratoire Lagrange, CS 34229, CEDEX 4, 06304 Nice, France; malik.chami@upmc.fr 7 Laboratoire d’Informatique et Système (LIS), Université de Toulon, CNRS UMR 7020, 83041 Toulon, France; audrey.minghelli@univ-tln.fr 8 Laboratoire d’Informatique et Système (LIS), Aix Marseille Université, 13288 Marseille, France 9 Université de Toulouse, ONERA/DOTA, CEDEX 4, 31055 Toulouse, France; xavier.briottet@onera.fr 10 DGA/AID, CEDEX 15, 75509 Paris, France; veronique.serfaty@intradef.gouv.fr * Correspondence: yannick.deville@irap.omp.eu; Tel.: +33-5-61-33-28-24 † These authors contributed equally to this work. Abstract: 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 ±0.2 m around this reference depth, over all pixels of the analyzed scene or over a “subscene”: 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. Keywords: hyperspectral unsupervised unmixing; hyperspectral blind unmixing; spectral variability; intraclass variability; sea bottom unmixing; adjacency effect; nonnegative matrix factorization Remote Sens. 2023, 15, 4583. https://doi.org/10.3390/rs15184583 https://www.mdpi.com/journal/remotesensing