{"id":"https://openalex.org/W2585415590","doi":"https://doi.org/10.1109/tit.2018.2816685","title":"Weighted Matrix Completion and Recovery With Prior Subspace Information","display_name":"Weighted Matrix Completion and Recovery With Prior Subspace Information","publication_year":2018,"publication_date":"2018-03-16","ids":{"openalex":"https://openalex.org/W2585415590","doi":"https://doi.org/10.1109/tit.2018.2816685","mag":"2585415590"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2816685","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2816685","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1612.01720","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086280273","display_name":"Armin Eftekhari","orcid":"https://orcid.org/0000-0001-8202-6316"},"institutions":[{"id":"https://openalex.org/I4210128584","display_name":"The Alan Turing Institute","ror":"https://ror.org/035dkdb55","country_code":"GB","type":"facility","lineage":["https://openalex.org/I4210128584"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Armin Eftekhari","raw_affiliation_strings":["Alan Turing Institute, London, U.K","[Alan Turing Institute, London, U.K.]"],"raw_orcid":"https://orcid.org/0000-0001-8202-6316","affiliations":[{"raw_affiliation_string":"Alan Turing Institute, London, U.K","institution_ids":["https://openalex.org/I4210128584"]},{"raw_affiliation_string":"[Alan Turing Institute, London, U.K.]","institution_ids":["https://openalex.org/I4210128584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102747005","display_name":"Dehui Yang","orcid":"https://orcid.org/0000-0001-6984-9553"},"institutions":[{"id":"https://openalex.org/I167576493","display_name":"Colorado School of Mines","ror":"https://ror.org/04raf6v53","country_code":"US","type":"education","lineage":["https://openalex.org/I167576493"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dehui Yang","raw_affiliation_strings":["Department of Electrical Engineering, Colorado School of Mines, Golden, CO, USA","Department of Electrical Engineering , Colorado School of Mines , Golden , CO , USA"],"raw_orcid":"https://orcid.org/0000-0001-6984-9553","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Colorado School of Mines, Golden, CO, USA","institution_ids":["https://openalex.org/I167576493"]},{"raw_affiliation_string":"Department of Electrical Engineering , Colorado School of Mines , Golden , CO , USA","institution_ids":["https://openalex.org/I167576493"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065207980","display_name":"Michael B. Wakin","orcid":"https://orcid.org/0000-0002-2165-4586"},"institutions":[{"id":"https://openalex.org/I167576493","display_name":"Colorado School of Mines","ror":"https://ror.org/04raf6v53","country_code":"US","type":"education","lineage":["https://openalex.org/I167576493"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael B. Wakin","raw_affiliation_strings":["Department of Electrical Engineering, Colorado School of Mines, Golden, CO, USA","Department of Electrical Engineering , Colorado School of Mines , Golden , CO , USA"],"raw_orcid":"https://orcid.org/0000-0002-2165-4586","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Colorado School of Mines, Golden, CO, USA","institution_ids":["https://openalex.org/I167576493"]},{"raw_affiliation_string":"Department of Electrical Engineering , Colorado School of Mines , Golden , CO , USA","institution_ids":["https://openalex.org/I167576493"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00312819,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"64","issue":"6","first_page":"4044","last_page":"4071"},"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.8768873810768127},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.7523391246795654},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6474793553352356},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.647363543510437},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5742712020874023},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5149446129798889},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.491345077753067},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.453901469707489},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4442407786846161},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4394388794898987},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"Sample complexity","score":0.4390179514884949},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42583465576171875},{"id":"https://openalex.org/keywords/prior-information","display_name":"Prior information","score":0.4188104271888733},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.41189494729042053},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39782077074050903},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2619536519050598},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21121400594711304}],"concepts":[{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.8768873810768127},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.7523391246795654},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6474793553352356},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.647363543510437},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5742712020874023},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5149446129798889},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.491345077753067},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.453901469707489},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4442407786846161},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4394388794898987},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.4390179514884949},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42583465576171875},{"id":"https://openalex.org/C3020402766","wikidata":"https://www.wikidata.org/wiki/Q104376712","display_name":"Prior information","level":2,"score":0.4188104271888733},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.41189494729042053},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39782077074050903},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2619536519050598},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21121400594711304},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2018.2816685","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2816685","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1612.01720","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.01720","pdf_url":"https://arxiv.org/pdf/1612.01720","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"},{"id":"mag:2585415590","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1612.01720","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1612.01720","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1612.01720","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1612.01720","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.01720","pdf_url":"https://arxiv.org/pdf/1612.01720","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":[],"awards":[{"id":"https://openalex.org/G2677335170","display_name":null,"funder_award_id":"CCF-1409258","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4066840050","display_name":null,"funder_award_id":"CCF-1149225","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4500485203","display_name":"The Alan Turing Institute","funder_award_id":"EP/N510129/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G8597009950","display_name":null,"funder_award_id":"EP/N510129/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W143004564","https://openalex.org/W2032782431","https://openalex.org/W2047071281","https://openalex.org/W2057763140","https://openalex.org/W2074471762","https://openalex.org/W2107861471","https://openalex.org/W2108753466","https://openalex.org/W2111297856","https://openalex.org/W2111394763","https://openalex.org/W2113642685","https://openalex.org/W2117377454","https://openalex.org/W2118550318","https://openalex.org/W2120387782","https://openalex.org/W2120872934","https://openalex.org/W2136912397","https://openalex.org/W2143075842","https://openalex.org/W2166163936","https://openalex.org/W2171046470","https://openalex.org/W2184497579","https://openalex.org/W2345050207","https://openalex.org/W2511257454","https://openalex.org/W2550752607","https://openalex.org/W2611328865","https://openalex.org/W2804931894","https://openalex.org/W2950201748","https://openalex.org/W2953310052","https://openalex.org/W2962904925","https://openalex.org/W2963705450","https://openalex.org/W6636904114","https://openalex.org/W6639038035","https://openalex.org/W6676665419","https://openalex.org/W6677959539","https://openalex.org/W6678101856","https://openalex.org/W6680391196","https://openalex.org/W6681872947","https://openalex.org/W6686515677","https://openalex.org/W6686968995","https://openalex.org/W6729214561","https://openalex.org/W6750968397"],"related_works":["https://openalex.org/W1604604340","https://openalex.org/W2941311521","https://openalex.org/W2853949691","https://openalex.org/W3011302148","https://openalex.org/W2963155938","https://openalex.org/W2952716509","https://openalex.org/W3173745758","https://openalex.org/W2557895864","https://openalex.org/W2966293209","https://openalex.org/W3026590303","https://openalex.org/W2952622379","https://openalex.org/W3037211805","https://openalex.org/W2891849478","https://openalex.org/W3004722026","https://openalex.org/W2948440434","https://openalex.org/W152374499","https://openalex.org/W2467768057","https://openalex.org/W2100282471","https://openalex.org/W3019637614","https://openalex.org/W2950180286"],"abstract_inverted_index":{"An":[0],"incoherent":[1],"low-rank":[2],"matrix":[3,48,64,90,118],"can":[4],"be":[5],"efficiently":[6],"reconstructed":[7],"after":[8],"observing":[9],"a":[10,20,67,93],"few":[11],"of":[12,46,89,117],"its":[13],"entries":[14],"at":[15],"random,":[16],"and":[17,43,96],"then,":[18],"solving":[19],"convex":[21],"program":[22],"that":[23,81],"minimizes":[24],"the":[25,41,47,53,86,97,113],"nuclear":[26,69],"norm.":[27],"In":[28,55,75],"many":[29],"applications,":[30],"in":[31,63,79,100],"addition":[32],"to":[33,52],"these":[34],"entries,":[35],"potentially":[36],"valuable":[37],"prior":[38,61,83],"knowledge":[39,62,84],"about":[40],"column":[42],"row":[44],"spaces":[45],"is":[49,103],"also":[50,108],"available":[51],"practitioner.":[54],"this":[56,60],"paper,":[57],"we":[58,77],"incorporate":[59],"completion-by":[65],"minimizing":[66],"weighted":[68],"norm-and":[70],"precisely":[71],"quantify":[72],"any":[73],"improvements.":[74],"particular,":[76],"find":[78],"theory":[80],"reliable":[82],"reduces":[85],"sample":[87],"complexity":[88],"completion":[91],"by":[92],"logarithmic":[94],"factor,":[95],"observed":[98],"improvement":[99],"numerical":[101],"simulations":[102],"considerably":[104],"more":[105],"magnified.":[106],"We":[107],"present":[109],"similar":[110],"results":[111],"for":[112],"closely":[114],"related":[115],"problem":[116],"recovery":[119],"from":[120],"generic":[121],"linear":[122],"measurements.":[123]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}