{"id":"https://openalex.org/W2280409827","doi":"https://doi.org/10.1109/lsp.2016.2514845","title":"Complex and Quaternionic Principal Component Pursuit and Its Application to Audio Separation","display_name":"Complex and Quaternionic Principal Component Pursuit and Its Application to Audio Separation","publication_year":2016,"publication_date":"2016-01-05","ids":{"openalex":"https://openalex.org/W2280409827","doi":"https://doi.org/10.1109/lsp.2016.2514845","mag":"2280409827"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2016.2514845","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2016.2514845","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1801.03816","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068325856","display_name":"Tak-Shing Chan","orcid":"https://orcid.org/0000-0002-8302-3974"},"institutions":[{"id":"https://openalex.org/I4210086894","display_name":"Research Center for Information Technology Innovation, Academia Sinica","ror":"https://ror.org/000zgvm20","country_code":"TW","type":"facility","lineage":["https://openalex.org/I4210086894","https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Tak-Shing T. Chan","raw_affiliation_strings":["Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan"],"affiliations":[{"raw_affiliation_string":"Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan","institution_ids":["https://openalex.org/I4210086894"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101001413","display_name":"Yi-Hsuan Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210086894","display_name":"Research Center for Information Technology Innovation, Academia Sinica","ror":"https://ror.org/000zgvm20","country_code":"TW","type":"facility","lineage":["https://openalex.org/I4210086894","https://openalex.org/I84653119"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yi-Hsuan Yang","raw_affiliation_strings":["Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan"],"affiliations":[{"raw_affiliation_string":"Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan","institution_ids":["https://openalex.org/I4210086894"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068325856"],"corresponding_institution_ids":["https://openalex.org/I4210086894"],"apc_list":null,"apc_paid":null,"fwci":2.5505,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89842053,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"23","issue":"2","first_page":"287","last_page":"291"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10860","display_name":"Speech and Audio Processing","score":0.9998999834060669,"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/T10860","display_name":"Speech and Audio Processing","score":0.9998999834060669,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11698","display_name":"Underwater Acoustics Research","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.7802076935768127},{"id":"https://openalex.org/keywords/spectrogram","display_name":"Spectrogram","score":0.7673377990722656},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5990515947341919},{"id":"https://openalex.org/keywords/source-separation","display_name":"Source separation","score":0.5828537344932556},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5430914163589478},{"id":"https://openalex.org/keywords/singing","display_name":"Singing","score":0.5207917094230652},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.49140775203704834},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.485038697719574},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4624187648296356},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.41385698318481445},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.39439958333969116},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.369462788105011},{"id":"https://openalex.org/keywords/speech-recognition","display_name":"Speech recognition","score":0.36633598804473877},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3077099919319153},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2520620822906494},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.07523283362388611}],"concepts":[{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.7802076935768127},{"id":"https://openalex.org/C45273575","wikidata":"https://www.wikidata.org/wiki/Q578970","display_name":"Spectrogram","level":2,"score":0.7673377990722656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5990515947341919},{"id":"https://openalex.org/C2776864781","wikidata":"https://www.wikidata.org/wiki/Q52617913","display_name":"Source separation","level":2,"score":0.5828537344932556},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5430914163589478},{"id":"https://openalex.org/C44819458","wikidata":"https://www.wikidata.org/wiki/Q27939","display_name":"Singing","level":2,"score":0.5207917094230652},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.49140775203704834},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.485038697719574},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4624187648296356},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.41385698318481445},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.39439958333969116},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.369462788105011},{"id":"https://openalex.org/C28490314","wikidata":"https://www.wikidata.org/wiki/Q189436","display_name":"Speech recognition","level":1,"score":0.36633598804473877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3077099919319153},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2520620822906494},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.07523283362388611},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2016.2514845","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2016.2514845","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1801.03816","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.03816","pdf_url":"https://arxiv.org/pdf/1801.03816","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1801.03816","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.03816","pdf_url":"https://arxiv.org/pdf/1801.03816","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.5299999713897705,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1493852014","https://openalex.org/W1494757229","https://openalex.org/W1496920063","https://openalex.org/W1526336542","https://openalex.org/W1736339626","https://openalex.org/W1946620893","https://openalex.org/W1958349209","https://openalex.org/W1974042113","https://openalex.org/W2002016907","https://openalex.org/W2022086767","https://openalex.org/W2023334490","https://openalex.org/W2024283190","https://openalex.org/W2030958619","https://openalex.org/W2033772417","https://openalex.org/W2046233597","https://openalex.org/W2048127846","https://openalex.org/W2051275493","https://openalex.org/W2068071321","https://openalex.org/W2078681501","https://openalex.org/W2091741383","https://openalex.org/W2103972604","https://openalex.org/W2114113040","https://openalex.org/W2124539664","https://openalex.org/W2138019504","https://openalex.org/W2145962650","https://openalex.org/W2146842127","https://openalex.org/W2155996168","https://openalex.org/W2164098335","https://openalex.org/W2167480185","https://openalex.org/W2405580681","https://openalex.org/W4244591460","https://openalex.org/W6713480825","https://openalex.org/W6826570400"],"related_works":["https://openalex.org/W3094316140","https://openalex.org/W3133205200","https://openalex.org/W4289363934","https://openalex.org/W2898145319","https://openalex.org/W2098101267","https://openalex.org/W2898606530","https://openalex.org/W4289362680","https://openalex.org/W2403380333","https://openalex.org/W2059119686","https://openalex.org/W2761596192"],"abstract_inverted_index":{"Recently,":[0],"the":[1,29,55,63,77,99,112,121,125,130,136],"principal":[2,51,142],"component":[3,52,143],"pursuit":[4,53],"has":[5],"received":[6],"increasing":[7],"attention":[8],"in":[9,36,46,91,141],"signal":[10],"processing":[11],"research":[12],"ranging":[13],"from":[14,124],"source":[15],"separation":[16,115],"to":[17,54,60,111,119],"video":[18],"surveillance.":[19],"So":[20],"far,":[21],"all":[22],"existing":[23],"formulations":[24],"are":[25,108],"real-valued":[26],"and":[27,57,72,83,132],"lack":[28],"concept":[30],"of":[31,138],"phase,":[32],"which":[33,117],"is":[34],"inherent":[35],"inputs":[37],"such":[38,97],"as":[39,98],"complex":[40,56,71],"spectrograms":[41],"or":[42],"color":[43],"images.":[44],"Thus,":[45],"this":[47],"letter,":[48],"we":[49,68],"extend":[50],"quaternionic":[58,73],"cases":[59],"account":[61],"for":[62,76],"missing":[64],"phase":[65,139],"information.":[66],"Specifically,":[67],"present":[69],"both":[70],"proximity":[74],"operators":[75,87],"\u2113":[78],"<sub":[79],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[80],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[81],"-":[82],"trace-norm":[84],"regularizers.":[85],"These":[86],"can":[88],"be":[89],"used":[90],"conjunction":[92],"with":[93],"proximal":[94],"minimization":[95],"methods":[96],"inexact":[100],"augmented":[101],"Lagrange":[102],"multiplier":[103],"algorithm.":[104],"The":[105],"new":[106],"algorithms":[107],"then":[109],"applied":[110],"singing":[113,122],"voice":[114,123],"problem,":[116],"aims":[118],"separate":[120],"instrumental":[126],"accompaniment.":[127],"Results":[128],"on":[129],"iKala":[131],"MSD100":[133],"datasets":[134],"confirmed":[135],"usefulness":[137],"information":[140],"pursuit.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}