{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:02:19Z","timestamp":1760238139821,"version":"build-2065373602"},"reference-count":71,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T00:00:00Z","timestamp":1595203200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-15-NMED- 0002-02","ANR-3IA Artificial and Natural Intelligence Toulouse Institute (ANITI)"],"award-info":[{"award-number":["ANR-15-NMED- 0002-02","ANR-3IA Artificial and Natural Intelligence Toulouse Institute (ANITI)"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Seventh Framework Programme","award":["ERANETMED JC-WATER MapInvPlnt"],"award-info":[{"award-number":["ERANETMED JC-WATER MapInvPlnt"]}]},{"DOI":"10.13039\/501100004718","name":"Universit\u00e9 de Toulouse","doi-asserted-by":"publisher","award":["IDEX ATS MUESLI Project"],"award-info":[{"award-number":["IDEX ATS MUESLI Project"]}],"id":[{"id":"10.13039\/501100004718","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Accounting for endmember variability is a challenging issue when unmixing hyperspectral data. This paper models the variability that is associated with each endmember as a conical hull defined by extremal pixels from the data set. These extremal pixels are considered as so-called prototypal endmember spectra that have meaningful physical interpretation. Capitalizing on this data-driven modeling, the pixels of the hyperspectral image are then described as combinations of these prototypal endmember spectra weighted by bundling coefficients and spatial abundances. The proposed unmixing model not only extracts and clusters the prototypal endmember spectra, but also estimates the abundances of each endmember. The performance of the approach is illustrated thanks to experiments conducted on simulated and real hyperspectral data and it outperforms state-of-the-art methods.<\/jats:p>","DOI":"10.3390\/rs12142326","type":"journal-article","created":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T10:59:38Z","timestamp":1595242778000},"page":"2326","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Hierarchical Sparse Nonnegative Matrix Factorization for Hyperspectral Unmixing with Spectral Variability"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9228-6947","authenticated-orcid":false,"given":"Tatsumi","family":"Uezato","sequence":"first","affiliation":[{"name":"IRIT\/INP-ENSEEIHT, University of Toulouse, CEDEX 7, 31071 Toulouse, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3304-6932","authenticated-orcid":false,"given":"Mathieu","family":"Fauvel","sequence":"additional","affiliation":[{"name":"CESBIO, CNES\/CNRS\/IRD\/UPS\/INRAE, University of Toulouse, CEDEX 9, 31401 Toulouse, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8127-350X","authenticated-orcid":false,"given":"Nicolas","family":"Dobigeon","sequence":"additional","affiliation":[{"name":"IRIT\/INP-ENSEEIHT, University of Toulouse, CEDEX 7, 31071 Toulouse, France"},{"name":"Institut Universitaire de France, Minist\u00e8re de l\u2019\u00c9ducation Nationale, de l\u2019Enseignement Sup\u00e9rieur et de la Recherche, 1 rue Descartes, CEDEX 05, 75231 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1016\/j.rse.2007.07.028","article-title":"Recent advances in techniques for hyperspectral image processing","volume":"113","author":"Plaza","year":"2009","journal-title":"Remote Sens. 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