{"id":"https://openalex.org/W2165995740","doi":"https://doi.org/10.1162/neco.2009.08-08-846","title":"Estimation of Sparse Nonnegative Sources from Noisy Overcomplete Mixtures Using MAP","display_name":"Estimation of Sparse Nonnegative Sources from Noisy Overcomplete Mixtures Using MAP","publication_year":2009,"publication_date":"2009-09-18","ids":{"openalex":"https://openalex.org/W2165995740","doi":"https://doi.org/10.1162/neco.2009.08-08-846","mag":"2165995740","pmid":"https://pubmed.ncbi.nlm.nih.gov/19764872"},"language":"en","primary_location":{"id":"doi:10.1162/neco.2009.08-08-846","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco.2009.08-08-846","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5024870237","display_name":"C\u00e9sar F. Caiafa","orcid":"https://orcid.org/0000-0001-5437-6095"},"institutions":[{"id":"https://openalex.org/I2800939219","display_name":"RIKEN Center for Brain Science","ror":"https://ror.org/04j1n1c04","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800939219","https://openalex.org/I4210110652"]},{"id":"https://openalex.org/I24354313","display_name":"University of Buenos Aires","ror":"https://ror.org/0081fs513","country_code":"AR","type":"education","lineage":["https://openalex.org/I24354313"]}],"countries":["AR","JP"],"is_corresponding":true,"raw_author_name":"Cesar F. Caiafa","raw_affiliation_strings":["LABSP, RIKEN Brain Science Institute, Wako, Saitama 351-0198, Japan, and Engineering Faculty, University of Buenos Aires, Buenos Aires, C1063ACV, Argentina"],"affiliations":[{"raw_affiliation_string":"LABSP, RIKEN Brain Science Institute, Wako, Saitama 351-0198, Japan, and Engineering Faculty, University of Buenos Aires, Buenos Aires, C1063ACV, Argentina","institution_ids":["https://openalex.org/I2800939219","https://openalex.org/I24354313"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018676117","display_name":"Andrzej Cichocki","orcid":"https://orcid.org/0000-0002-8364-7226"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]},{"id":"https://openalex.org/I66083562","display_name":"Systems Research Institute","ror":"https://ror.org/0111cp837","country_code":"PL","type":"facility","lineage":["https://openalex.org/I66083562","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I4210110652","display_name":"RIKEN","ror":"https://ror.org/01sjwvz98","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"funder","lineage":["https://openalex.org/I99542240"]}],"countries":["JP","PL"],"is_corresponding":true,"raw_author_name":"Andrzej Cichocki","raw_affiliation_strings":["LABSP, RIKEN Brain Science Institute, Wako, Saitama 351-0198, Japan, and Warsaw University of Technology, Warsaw 00-661, Poland, and Systems Research Institute, Polish Academy of Sciences, Warsaw 01-447, Poland"],"affiliations":[{"raw_affiliation_string":"LABSP, RIKEN Brain Science Institute, Wako, Saitama 351-0198, Japan, and Warsaw University of Technology, Warsaw 00-661, Poland, and Systems Research Institute, Polish Academy of Sciences, Warsaw 01-447, Poland","institution_ids":["https://openalex.org/I66083562","https://openalex.org/I108403487","https://openalex.org/I4210110652","https://openalex.org/I99542240"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018676117","https://openalex.org/A5024870237"],"corresponding_institution_ids":["https://openalex.org/I108403487","https://openalex.org/I24354313","https://openalex.org/I2800939219","https://openalex.org/I4210110652","https://openalex.org/I66083562","https://openalex.org/I99542240"],"apc_list":null,"apc_paid":null,"fwci":1.4099,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.82404275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"12","first_page":"3487","last_page":"3518"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10640","display_name":"Spectroscopy and Chemometric Analyses","score":0.9836000204086304,"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"}},{"id":"https://openalex.org/T10860","display_name":"Speech and Audio Processing","score":0.9812999963760376,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/underdetermined-system","display_name":"Underdetermined system","score":0.7389732599258423},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.730088472366333},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5819059610366821},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5566655397415161},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5519676208496094},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48892584443092346},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.48752209544181824},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.48132574558258057},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.47525712847709656},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.47411540150642395},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39202243089675903},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36526763439178467},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.16004332900047302}],"concepts":[{"id":"https://openalex.org/C179690561","wikidata":"https://www.wikidata.org/wiki/Q4316110","display_name":"Underdetermined system","level":2,"score":0.7389732599258423},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.730088472366333},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5819059610366821},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5566655397415161},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5519676208496094},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48892584443092346},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.48752209544181824},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.48132574558258057},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.47525712847709656},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.47411540150642395},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39202243089675903},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36526763439178467},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.16004332900047302},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001499","descriptor_name":"Bayes Theorem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001499","descriptor_name":"Bayes Theorem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001499","descriptor_name":"Bayes Theorem","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D006801","descriptor_name":"Humans","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012815","descriptor_name":"Signal Processing, Computer-Assisted","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D013598","descriptor_name":"Systems Theory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013598","descriptor_name":"Systems Theory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013598","descriptor_name":"Systems Theory","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D025341","descriptor_name":"Principal Component Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D025341","descriptor_name":"Principal Component Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D025341","descriptor_name":"Principal Component Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1162/neco.2009.08-08-846","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco.2009.08-08-846","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:19764872","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19764872","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural computation","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.6200000047683716,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":62,"referenced_works":["https://openalex.org/W36294837","https://openalex.org/W119641611","https://openalex.org/W1489793438","https://openalex.org/W1514159701","https://openalex.org/W1542782021","https://openalex.org/W1548802052","https://openalex.org/W1598962862","https://openalex.org/W1634005169","https://openalex.org/W1902027874","https://openalex.org/W1939438719","https://openalex.org/W1986931325","https://openalex.org/W1992431015","https://openalex.org/W2002418905","https://openalex.org/W2010161441","https://openalex.org/W2039844283","https://openalex.org/W2045887127","https://openalex.org/W2046756894","https://openalex.org/W2049226298","https://openalex.org/W2054295885","https://openalex.org/W2058670155","https://openalex.org/W2059745395","https://openalex.org/W2065919982","https://openalex.org/W2095715335","https://openalex.org/W2097323375","https://openalex.org/W2105345414","https://openalex.org/W2106440213","https://openalex.org/W2110111686","https://openalex.org/W2111031731","https://openalex.org/W2114147096","https://openalex.org/W2115909066","https://openalex.org/W2116148865","https://openalex.org/W2117509237","https://openalex.org/W2118718620","https://openalex.org/W2126344578","https://openalex.org/W2130855892","https://openalex.org/W2135029798","https://openalex.org/W2140499889","https://openalex.org/W2141188596","https://openalex.org/W2142940228","https://openalex.org/W2147460091","https://openalex.org/W2151693816","https://openalex.org/W2152279006","https://openalex.org/W2152435897","https://openalex.org/W2153909896","https://openalex.org/W2154332973","https://openalex.org/W2160482844","https://openalex.org/W2160547390","https://openalex.org/W2162165657","https://openalex.org/W2163886718","https://openalex.org/W2166471851","https://openalex.org/W2168092484","https://openalex.org/W2404400936","https://openalex.org/W2492794003","https://openalex.org/W2533352123","https://openalex.org/W2534217604","https://openalex.org/W2535202871","https://openalex.org/W3101375842","https://openalex.org/W3143596294","https://openalex.org/W4205778870","https://openalex.org/W4247969042","https://openalex.org/W4251649775","https://openalex.org/W4299338613"],"related_works":["https://openalex.org/W2549922247","https://openalex.org/W2300663769","https://openalex.org/W1523391825","https://openalex.org/W2152231009","https://openalex.org/W1939631077","https://openalex.org/W2735239078","https://openalex.org/W2152589265","https://openalex.org/W2071589878","https://openalex.org/W2963414100","https://openalex.org/W2372875289"],"abstract_inverted_index":{"In":[0,20],"this":[1],"letter,":[2],"we":[3,22],"propose":[4],"a":[5,14,106,149,174,196],"new":[6,118],"algorithm":[7,104,168,179,183],"for":[8,120,130,154,169,186],"estimating":[9,187],"sparse":[10,44,96,111],"nonnegative":[11],"sources":[12,32,41,135,193],"from":[13],"set":[15,202],"of":[16,88,98,133,144,176,203,211],"noisy":[17],"linear":[18],"mixtures.":[19],"particular,":[21],"consider":[23],"difficult":[24],"situations":[25],"with":[26,57,83,100,180],"high":[27],"noise":[28],"levels":[29],"and":[30,47,62,95,160,191],"more":[31],"than":[33,68],"sensors":[34,67],"(underdetermined":[35],"case).":[36],"We":[37,126],"show":[38],"that":[39],"when":[40],"are":[42,163],"very":[43,58],"in":[45,85,195],"time":[46],"overlapped":[48,155],"at":[49],"some":[50],"locations,":[51],"they":[52],"can":[53],"be":[54],"recovered":[55],"even":[56],"low":[59],"signal-to-noise":[60],"ratio,":[61],"by":[63,109,165],"using":[64,166],"many":[65],"fewer":[66],"sources.":[69],"A":[70,200],"theoretical":[71],"analysis":[72,129],"based":[73],"on":[74],"Bayesian":[75,107],"estimation":[76],"tools":[77],"is":[78,184,206],"included":[79,207],"showing":[80,208],"strong":[81],"connections":[82],"algorithms":[84,153],"related":[86],"areas":[87],"research":[89],"such":[90,157],"as":[91,158],"ICA,":[92],"NMF,":[93],"FOCUSS,":[94],"representation":[97],"data":[99],"overcomplete":[101],"dictionaries.":[102],"Our":[103],"uses":[105],"approach":[108],"modeling":[110],"signals":[112,171],"through":[113],"mixed-state":[114],"random":[115],"variables.":[116],"This":[117],"model":[119],"priors":[121],"imposes":[122],"l(0)":[123],"norm-based":[124],"sparsity.":[125],"start":[127],"our":[128,177,212],"the":[131,142,145,167,181,188,192,209],"case":[132],"nonoverlapped":[134],"(1-sparse),":[136],"which":[137],"allows":[138],"us":[139],"to":[140],"simplify":[141],"search":[143],"posterior":[146],"maximum":[147],"avoiding":[148],"combinatorial":[150],"search.":[151],"General":[152],"cases,":[156],"2-sparse":[159],"k-sparse":[161],"sources,":[162],"derived":[164],"1-sparse":[170],"recursively.":[172],"Additionally,":[173],"combination":[175],"MAP":[178],"NN-KSVD":[182],"proposed":[185],"mixing":[189],"matrix":[190],"simultaneously":[194],"real":[197],"blind":[198],"fashion.":[199],"complete":[201],"simulation":[204],"results":[205],"performance":[210],"algorithm.":[213]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}