{"id":"https://openalex.org/W2025907697","doi":"https://doi.org/10.1109/lgrs.2013.2278993","title":"A Bilinear\u2013Bilinear Nonnegative Matrix Factorization Method for Hyperspectral Unmixing","display_name":"A Bilinear\u2013Bilinear Nonnegative Matrix Factorization Method for Hyperspectral Unmixing","publication_year":2013,"publication_date":"2013-09-11","ids":{"openalex":"https://openalex.org/W2025907697","doi":"https://doi.org/10.1109/lgrs.2013.2278993","mag":"2025907697"},"language":"en","primary_location":{"id":"doi:10.1109/lgrs.2013.2278993","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lgrs.2013.2278993","pdf_url":null,"source":{"id":"https://openalex.org/S126920919","display_name":"IEEE Geoscience and Remote Sensing Letters","issn_l":"1545-598X","issn":["1545-598X","1558-0571"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Geoscience and Remote Sensing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000091092","display_name":"Olivier Eches","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210125985","display_name":"Institut Fresnel","ror":"https://ror.org/03br1wy20","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210095849","https://openalex.org/I4210125985","https://openalex.org/I4210142724"]},{"id":"https://openalex.org/I4210142724","display_name":"Centrale Marseille","ror":"https://ror.org/040baw385","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Olivier Eches","raw_affiliation_strings":["Ecole Centrale Marseille, Aix Marseille Universit\u00e9, CNRS, Institut Fresnel UMR 7122, Marseille, France","[Inst. Fresnel, Aix Marseille Univ., Marseille, France]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Centrale Marseille, Aix Marseille Universit\u00e9, CNRS, Institut Fresnel UMR 7122, Marseille, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210125985","https://openalex.org/I4210142724"]},{"raw_affiliation_string":"[Inst. Fresnel, Aix Marseille Univ., Marseille, France]","institution_ids":["https://openalex.org/I21491767"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022577086","display_name":"Mireille Guillaume","orcid":"https://orcid.org/0000-0002-6125-1159"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210125985","display_name":"Institut Fresnel","ror":"https://ror.org/03br1wy20","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210095849","https://openalex.org/I4210125985","https://openalex.org/I4210142724"]},{"id":"https://openalex.org/I4210142724","display_name":"Centrale Marseille","ror":"https://ror.org/040baw385","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mireille Guillaume","raw_affiliation_strings":["Ecole Centrale Marseille, Aix Marseille Universit\u00e9, CNRS, Institut Fresnel UMR 7122, Marseille, France","[Inst. Fresnel, Aix Marseille Univ., Marseille, France]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Centrale Marseille, Aix Marseille Universit\u00e9, CNRS, Institut Fresnel UMR 7122, Marseille, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210125985","https://openalex.org/I4210142724"]},{"raw_affiliation_string":"[Inst. Fresnel, Aix Marseille Univ., Marseille, France]","institution_ids":["https://openalex.org/I21491767"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":8.2643,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.97380899,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"11","issue":"4","first_page":"778","last_page":"782"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10689","display_name":"Remote-Sensing Image Classification","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10689","display_name":"Remote-Sensing Image Classification","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/1602","display_name":"Analytical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperspectral-imaging","display_name":"Hyperspectral imaging","score":0.9440868496894836},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.901160478591919},{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.8077735900878906},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.6172292232513428},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5671142935752869},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4693497121334076},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4634210169315338},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.45450928807258606},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42229175567626953},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.4187110662460327},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3904799222946167},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3458523154258728},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3348710536956787},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14094850420951843},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.13195699453353882},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09359541535377502},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.06992453336715698}],"concepts":[{"id":"https://openalex.org/C159078339","wikidata":"https://www.wikidata.org/wiki/Q959005","display_name":"Hyperspectral imaging","level":2,"score":0.9440868496894836},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.901160478591919},{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.8077735900878906},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.6172292232513428},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5671142935752869},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4693497121334076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4634210169315338},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.45450928807258606},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42229175567626953},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.4187110662460327},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3904799222946167},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3458523154258728},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3348710536956787},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14094850420951843},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.13195699453353882},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09359541535377502},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.06992453336715698},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lgrs.2013.2278993","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lgrs.2013.2278993","pdf_url":null,"source":{"id":"https://openalex.org/S126920919","display_name":"IEEE Geoscience and Remote Sensing Letters","issn_l":"1545-598X","issn":["1545-598X","1558-0571"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Geoscience and Remote Sensing Letters","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01279618v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01279618","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.grss-ieee.org/publication-category/grsl/","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1902027874","https://openalex.org/W2042626896","https://openalex.org/W2059745395","https://openalex.org/W2065441953","https://openalex.org/W2078222544","https://openalex.org/W2088259770","https://openalex.org/W2101837437","https://openalex.org/W2110096996","https://openalex.org/W2110340688","https://openalex.org/W2112965385","https://openalex.org/W2118718620","https://openalex.org/W2125678373","https://openalex.org/W2127062304","https://openalex.org/W2127827417","https://openalex.org/W2136637647","https://openalex.org/W2140692918","https://openalex.org/W2145597631","https://openalex.org/W2155759219","https://openalex.org/W2157321686","https://openalex.org/W2159379102","https://openalex.org/W2163886442","https://openalex.org/W2404400936","https://openalex.org/W2999905431","https://openalex.org/W6676349960","https://openalex.org/W6677759377","https://openalex.org/W6683609202"],"related_works":["https://openalex.org/W4308269461","https://openalex.org/W4281395053","https://openalex.org/W2020769413","https://openalex.org/W2766940489","https://openalex.org/W2127243424","https://openalex.org/W4390394189","https://openalex.org/W2037504162","https://openalex.org/W2539013788","https://openalex.org/W2792706544","https://openalex.org/W1568451138"],"abstract_inverted_index":{"Spectral":[0],"unmixing":[1,22,41],"of":[2,6,24,83],"hyperspectral":[3],"images":[4],"consists":[5],"estimating":[7],"pure":[8],"material":[9],"spectra":[10,60],"with":[11],"their":[12],"corresponding":[13],"proportions":[14],"(or":[15],"abundances).":[16],"Nonlinear":[17],"mixing":[18],"models":[19],"for":[20],"spectral":[21],"are":[23,86],"very":[25],"recent":[26,95],"interest":[27],"within":[28],"the":[29,44,89,94],"signal":[30],"and":[31,48,62,65,78,92],"image":[32],"processing":[33],"community.":[34],"This":[35],"letter":[36],"proposes":[37],"a":[38,73],"new":[39],"nonlinear":[40,96],"approach":[42,91],"using":[43,72],"Fan":[45],"bilinear-bilinear":[46],"model":[47],"nonnegative":[49],"matrix":[50],"factorization":[51],"method":[52,69,85],"that":[53],"takes":[54],"into":[55],"account":[56],"physical":[57],"constraints":[58],"on":[59,76],"(positivity)":[61],"abundances":[63],"(positivity":[64],"sum-to-one).":[66],"The":[67,81],"proposed":[68],"is":[70],"tested":[71],"projected-gradient":[74],"algorithm":[75],"synthetic":[77],"real":[79],"data.":[80],"performances":[82],"this":[84],"compared":[87],"to":[88,93],"linear":[90],"approach.":[97]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
