{"id":"https://openalex.org/W2050041778","doi":"https://doi.org/10.1109/tsp.2009.2025802","title":"A Convex Analysis-Based Minimum-Volume Enclosing Simplex Algorithm for Hyperspectral Unmixing","display_name":"A Convex Analysis-Based Minimum-Volume Enclosing Simplex Algorithm for Hyperspectral Unmixing","publication_year":2009,"publication_date":"2009-06-25","ids":{"openalex":"https://openalex.org/W2050041778","doi":"https://doi.org/10.1109/tsp.2009.2025802","mag":"2050041778"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2009.2025802","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2025802","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Transactions on Signal Processing","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/A5106725197","display_name":"Tsung\u2010Han Chan","orcid":null},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Tsung-Han Chan","raw_affiliation_strings":["Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan","[Inst. of Commun. Eng., Nat. Tsing Hua Univ., Hsinchu, Taiwan]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I25846049"]},{"raw_affiliation_string":"[Inst. of Commun. Eng., Nat. Tsing Hua Univ., Hsinchu, Taiwan]","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061813280","display_name":"Chong\u2010Yung Chi","orcid":"https://orcid.org/0000-0001-5004-7155"},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chong-Yung Chi","raw_affiliation_strings":["Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan","[Inst. of Commun. Eng., Nat. Tsing Hua Univ., Hsinchu, Taiwan]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I25846049"]},{"raw_affiliation_string":"[Inst. of Commun. Eng., Nat. Tsing Hua Univ., Hsinchu, Taiwan]","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001777935","display_name":"Yumin Huang","orcid":"https://orcid.org/0000-0001-8692-5781"},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yu-Min Huang","raw_affiliation_strings":["Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan","[Inst. of Commun. Eng., Nat. Tsing Hua Univ., Hsinchu, Taiwan]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Communications Engineering, National Tsing Hua University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I25846049"]},{"raw_affiliation_string":"[Inst. of Commun. Eng., Nat. Tsing Hua Univ., Hsinchu, Taiwan]","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016986549","display_name":"Wing\u2010Kin Ma","orcid":"https://orcid.org/0000-0001-7314-3537"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Wing-Kin Ma","raw_affiliation_strings":["Department of Electronic Engineering, Chinese University of Hong KOng, New Territories, Hong Kong, China","Dept. of Electron. Eng., Chinese Univ. of Hong Kong, Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Chinese University of Hong KOng, New Territories, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Dept. of Electron. Eng., Chinese Univ. of Hong Kong, Hong Kong, China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":42.8004,"has_fulltext":false,"cited_by_count":385,"citation_normalized_percentile":{"value":0.99886318,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"57","issue":"11","first_page":"4418","last_page":"4432"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10689","display_name":"Remote-Sensing Image Classification","score":1.0,"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":1.0,"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":0.9919000267982483,"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/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.9781000018119812,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperspectral-imaging","display_name":"Hyperspectral imaging","score":0.9511623382568359},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.8543972373008728},{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.7948210835456848},{"id":"https://openalex.org/keywords/endmember","display_name":"Endmember","score":0.684787929058075},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6061257719993591},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5798856019973755},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.472497820854187},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4416511356830597},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43217480182647705},{"id":"https://openalex.org/keywords/volume","display_name":"Volume (thermodynamics)","score":0.41601866483688354},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4110480844974518},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3942011892795563},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3782182037830353},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3675425052642822},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09539321064949036}],"concepts":[{"id":"https://openalex.org/C159078339","wikidata":"https://www.wikidata.org/wiki/Q959005","display_name":"Hyperspectral imaging","level":2,"score":0.9511623382568359},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.8543972373008728},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.7948210835456848},{"id":"https://openalex.org/C58237817","wikidata":"https://www.wikidata.org/wiki/Q5376204","display_name":"Endmember","level":3,"score":0.684787929058075},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6061257719993591},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5798856019973755},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.472497820854187},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4416511356830597},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43217480182647705},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.41601866483688354},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4110480844974518},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3942011892795563},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3782182037830353},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3675425052642822},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09539321064949036},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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":1,"locations":[{"id":"doi:10.1109/tsp.2009.2025802","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2025802","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Transactions on Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W846821018","https://openalex.org/W1489793438","https://openalex.org/W1514159701","https://openalex.org/W1537281681","https://openalex.org/W1555549210","https://openalex.org/W1582058549","https://openalex.org/W1902027874","https://openalex.org/W1967073510","https://openalex.org/W1970099214","https://openalex.org/W1976391658","https://openalex.org/W1978492002","https://openalex.org/W1989603283","https://openalex.org/W2005073772","https://openalex.org/W2007502829","https://openalex.org/W2012749606","https://openalex.org/W2021086890","https://openalex.org/W2035541108","https://openalex.org/W2066015174","https://openalex.org/W2069231830","https://openalex.org/W2070424424","https://openalex.org/W2078296814","https://openalex.org/W2093903024","https://openalex.org/W2101837437","https://openalex.org/W2107120407","https://openalex.org/W2114486983","https://openalex.org/W2115163184","https://openalex.org/W2117027921","https://openalex.org/W2118943995","https://openalex.org/W2119145296","https://openalex.org/W2122976738","https://openalex.org/W2127062304","https://openalex.org/W2127962925","https://openalex.org/W2136625467","https://openalex.org/W2140501674","https://openalex.org/W2145554279","https://openalex.org/W2156458885","https://openalex.org/W2157321686","https://openalex.org/W2163202748","https://openalex.org/W2165755981","https://openalex.org/W2169924573","https://openalex.org/W2170395949","https://openalex.org/W2222512263","https://openalex.org/W2295820431","https://openalex.org/W2296319761","https://openalex.org/W2406093411","https://openalex.org/W2545029332","https://openalex.org/W2998399533","https://openalex.org/W4233760599","https://openalex.org/W4250589301","https://openalex.org/W4301807748","https://openalex.org/W6623562790","https://openalex.org/W6633261909","https://openalex.org/W6634825034","https://openalex.org/W6655699792","https://openalex.org/W6675750237","https://openalex.org/W6684139228","https://openalex.org/W6729079846"],"related_works":["https://openalex.org/W2037328426","https://openalex.org/W1990914742","https://openalex.org/W3106536224","https://openalex.org/W2891033441","https://openalex.org/W2006559622","https://openalex.org/W2890371384","https://openalex.org/W2773863718","https://openalex.org/W2315521504","https://openalex.org/W2563324120","https://openalex.org/W2040756827"],"abstract_inverted_index":{"Hyperspectral":[0],"unmixing":[1,25,57,180],"aims":[2],"at":[3],"identifying":[4],"the":[5,39,61,66,76,106,137,154,169,172],"hidden":[6],"spectral":[7],"signatures":[8],"(or":[9,15],"endmembers)":[10],"and":[11,86,161],"their":[12],"corresponding":[13],"proportions":[14],"abundances)":[16],"from":[17],"an":[18,56],"observed":[19,77],"hyperspectral":[20,24,98,179],"scene.":[21],"Many":[22],"existing":[23,178],"algorithms":[26],"were":[27],"developed":[28,110],"under":[29],"a":[30,71,91,128,146],"commonly":[31],"used":[32],"assumption":[33,41],"that":[34],"pure":[35,140],"pixels":[36,141],"exist.":[37],"However,":[38],"pure-pixel":[40,62],"may":[42],"be":[43,117,145],"seriously":[44],"violated":[45],"for":[46,97,104,149],"highly":[47],"mixed":[48],"data.":[49],"Based":[50],"on":[51],"intuitive":[52],"grounds,":[53],"Craig":[54],"reported":[55],"criterion":[58,88],"without":[59],"requiring":[60],"assumption,":[63],"which":[64,115],"estimates":[65],"endmembers":[67],"by":[68,120],"vertices":[69],"of":[70,131,139,171],"minimum-volume":[72,92],"simplex":[73,94],"enclosing":[74,93],"all":[75],"pixels.":[78],"In":[79],"this":[80],"paper,":[81],"we":[82],"incorporate":[83],"convex":[84],"analysis":[85],"Craig's":[87],"to":[89,144,151,167],"develop":[90],"(MVES)":[95],"formulation":[96],"unmixing.":[99],"A":[100],"cyclic":[101],"minimization":[102],"algorithm":[103,175],"approximating":[105],"MVES":[107,133,150,174],"problem":[108,134],"is":[109,142],"using":[111],"linear":[112],"programs":[113],"(LPs),":[114],"can":[116],"practically":[118],"implemented":[119],"readily":[121],"available":[122],"LP":[123],"solvers.":[124],"We":[125],"also":[126],"provide":[127],"non-heuristic":[129],"guarantee":[130],"our":[132],"formulation,":[135],"where":[136],"existence":[138],"proved":[143],"sufficient":[147],"condition":[148],"perfectly":[152],"identify":[153],"true":[155],"endmembers.":[156],"Some":[157],"Monte":[158],"Carlo":[159],"simulations":[160],"real":[162],"data":[163],"experiments":[164],"are":[165],"presented":[166],"demonstrate":[168],"efficacy":[170],"proposed":[173],"over":[176],"several":[177],"methods.":[181]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":17},{"year":2021,"cited_by_count":32},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":23},{"year":2017,"cited_by_count":25},{"year":2016,"cited_by_count":35},{"year":2015,"cited_by_count":28},{"year":2014,"cited_by_count":31},{"year":2013,"cited_by_count":28},{"year":2012,"cited_by_count":32}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
