{"id":"https://openalex.org/W1991825408","doi":"https://doi.org/10.1109/cvpr.2012.6247927","title":"Matrix completion by Truncated Nuclear Norm Regularization","display_name":"Matrix completion by Truncated Nuclear Norm Regularization","publication_year":2012,"publication_date":"2012-06-01","ids":{"openalex":"https://openalex.org/W1991825408","doi":"https://doi.org/10.1109/cvpr.2012.6247927","mag":"1991825408"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2012.6247927","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2012.6247927","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-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/A5069785885","display_name":"Debing Zhang","orcid":"https://orcid.org/0000-0001-8965-3611"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Debing Zhang","raw_affiliation_strings":["State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China","State Key lab of CAD&CG, Zhejiang University, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"State Key lab of CAD&CG, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100666109","display_name":"Yao Hu","orcid":"https://orcid.org/0000-0003-4573-5740"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]},{"id":"https://openalex.org/I4210144662","display_name":"Xi'an Institute of Optics and Precision Mechanics","ror":"https://ror.org/0444j5556","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210144662"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yao Hu","raw_affiliation_strings":["Center for OPTical IMagery Analysis and Learning (OPTIMAL), Xi'an Institute of Optics and Precision Mechanics, Xi'an, Shaanxi, China","State Key lab of CAD&CG, Zhejiang University, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Center for OPTical IMagery Analysis and Learning (OPTIMAL), Xi'an Institute of Optics and Precision Mechanics, Xi'an, Shaanxi, China","institution_ids":["https://openalex.org/I4210144662"]},{"raw_affiliation_string":"State Key lab of CAD&CG, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010419481","display_name":"Jieping Ye","orcid":"https://orcid.org/0000-0001-8662-5818"},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]},{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Jieping Ye","raw_affiliation_strings":["State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China","Arizona University Tempe, AZ 85287"],"affiliations":[{"raw_affiliation_string":"State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"Arizona University Tempe, AZ 85287","institution_ids":["https://openalex.org/I138006243"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100740143","display_name":"Xuelong Li","orcid":"https://orcid.org/0000-0002-0019-4197"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Xuelong Li","raw_affiliation_strings":["Arizona University, Tempe, AZ","Center for OPTical IMagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences Xi'an 710119, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"Arizona University, Tempe, AZ","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Center for OPTical IMagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences Xi'an 710119, Shaanxi, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102013343","display_name":"Xiaofei He","orcid":"https://orcid.org/0000-0001-9887-5566"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaofei He","raw_affiliation_strings":["State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China","State Key lab of CAD&CG, Zhejiang University, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"State Key Lab of CAD&CG, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"State Key lab of CAD&CG, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5069785885"],"corresponding_institution_ids":["https://openalex.org/I76130692"],"apc_list":null,"apc_paid":null,"fwci":8.0342,"has_fulltext":false,"cited_by_count":166,"citation_normalized_percentile":{"value":0.97972243,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"2192","last_page":"2199"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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/T10057","display_name":"Face and Expression Recognition","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/matrix-norm","display_name":"Matrix norm","score":0.8841825723648071},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.7227118611335754},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.6935890913009644},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.640929102897644},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5351710319519043},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5038475394248962},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5015220642089844},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.48794764280319214},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47342661023139954},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46402508020401},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.44014257192611694},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.43970271944999695},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4344406723976135},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.41792091727256775},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37937480211257935},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3152385950088501},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23614326119422913},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1927242875099182},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14442989230155945},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.11853069067001343},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09665584564208984},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08321204781532288}],"concepts":[{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.8841825723648071},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.7227118611335754},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.6935890913009644},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.640929102897644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5351710319519043},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5038475394248962},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5015220642089844},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.48794764280319214},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47342661023139954},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46402508020401},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.44014257192611694},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.43970271944999695},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4344406723976135},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.41792091727256775},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37937480211257935},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3152385950088501},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23614326119422913},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1927242875099182},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14442989230155945},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.11853069067001343},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09665584564208984},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08321204781532288},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cvpr.2012.6247927","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2012.6247927","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},{"id":"pmh:oai:eprints.bbk.ac.uk.oai2:7312","is_oa":false,"landing_page_url":"https://eprints.bbk.ac.uk/id/eprint/7312/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400466","display_name":"BIROn (Birkbeck, University of London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98259816","host_organization_name":"Birkbeck, University of London","host_organization_lineage":["https://openalex.org/I98259816"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"},{"id":"pmh:oai:ir.opt.ac.cn:181661/20536","is_oa":false,"landing_page_url":"http://ir.opt.ac.cn/handle/181661/20536","pdf_url":null,"source":{"id":"https://openalex.org/S4377196962","display_name":"Institutional Repository of Xi'an Institute of Optics and Fine Mechanics, Chinese Academy of Sciences (Xian Institute of Optics and Precision Mechanics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210144662","host_organization_name":"Xi'an Institute of Optics and Precision Mechanics","host_organization_lineage":["https://openalex.org/I4210144662"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"\u4f1a\u8bae\u8bba\u6587"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1573301526","https://openalex.org/W1574851760","https://openalex.org/W1998635907","https://openalex.org/W2000157792","https://openalex.org/W2047071281","https://openalex.org/W2091449379","https://openalex.org/W2100556411","https://openalex.org/W2103305137","https://openalex.org/W2103972604","https://openalex.org/W2109240917","https://openalex.org/W2111284169","https://openalex.org/W2124584309","https://openalex.org/W2134332047","https://openalex.org/W2137414835","https://openalex.org/W2144730813","https://openalex.org/W2164278908","https://openalex.org/W2611328865","https://openalex.org/W4240580737","https://openalex.org/W4292363360","https://openalex.org/W6634474516","https://openalex.org/W6673357430","https://openalex.org/W6764481259","https://openalex.org/W7073876970"],"related_works":["https://openalex.org/W2964006653","https://openalex.org/W2788826952","https://openalex.org/W2084983808","https://openalex.org/W1991825408","https://openalex.org/W4318564253","https://openalex.org/W4302315572","https://openalex.org/W1969698720","https://openalex.org/W1507830821","https://openalex.org/W2782047334","https://openalex.org/W2184500224"],"abstract_inverted_index":{"Estimating":[0],"missing":[1],"values":[2,50,98],"in":[3,10,63,153],"visual":[4],"data":[5],"is":[6,93,101],"a":[7,18,34,70,154],"challenging":[8],"problem":[9,134],"computer":[11],"vision,":[12],"which":[13],"can":[14,58,115],"be":[15,60,116],"considered":[16],"as":[17,33],"low":[19],"rank":[20,39,57,103,111],"matrix":[21,72,114],"approximation":[22],"problem.":[23],"Most":[24],"of":[25,37,96,104,112,141,157,162],"the":[26,30,38,44,48,56,77,86,94,102,105,110,113,120,132,137,144,160],"recent":[27],"studies":[28],"use":[29],"nuclear":[31,45,121],"norm":[32],"convex":[35],"relaxation":[36],"operator.":[40],"However,":[41],"by":[42,83,135],"minimizing":[43,85],"norm,":[46],"all":[47],"singular":[49,89,97],"are":[51],"simultaneously":[52],"minimized,":[53],"and":[54,99,143],"thus":[55],"not":[59],"well":[61],"approximated":[62,118],"practice.":[64],"In":[65,107],"this":[66,108],"paper,":[67],"we":[68],"propose":[69],"novel":[71],"completion":[73],"algorithm":[74],"based":[75],"on":[76],"Truncated":[78],"Nuclear":[79],"Norm":[80],"Regularization":[81],"(TNNR)":[82],"only":[84],"smallest":[87],"N-r":[88],"values,":[90],"where":[91],"N":[92],"number":[95],"r":[100],"matrix.":[106],"way,":[109],"better":[117],"than":[119],"norm.":[122],"We":[123],"further":[124],"develop":[125],"an":[126],"efficient":[127],"iterative":[128],"procedure":[129],"to":[130],"solve":[131],"optimization":[133],"using":[136],"alternating":[138],"direction":[139],"method":[140],"multipliers":[142],"accelerated":[145],"proximal":[146],"gradient":[147],"line":[148],"search":[149],"method.":[150],"Experimental":[151],"results":[152],"wide":[155],"range":[156],"applications":[158],"demonstrate":[159],"effectiveness":[161],"our":[163],"proposed":[164],"approach.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":19},{"year":2019,"cited_by_count":17},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}