{"id":"https://openalex.org/W1896691890","doi":"https://doi.org/10.1109/tit.2012.2204535","title":"The Stability of Low-Rank Matrix Reconstruction: A Constrained Singular Value View","display_name":"The Stability of Low-Rank Matrix Reconstruction: A Constrained Singular Value View","publication_year":2012,"publication_date":"2012-06-13","ids":{"openalex":"https://openalex.org/W1896691890","doi":"https://doi.org/10.1109/tit.2012.2204535","mag":"1896691890"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2204535","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2204535","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":["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/A5101848896","display_name":"Gongguo Tang","orcid":"https://orcid.org/0000-0002-7879-1338"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gongguo Tang","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI, USA","Department of Electrical and Systems Engineering, Washington University of Saint Louis, Saint Louis, MO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"Department of Electrical and Systems Engineering, Washington University of Saint Louis, Saint Louis, MO, USA","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031212309","display_name":"Arye Nehorai","orcid":"https://orcid.org/0000-0002-9055-9865"},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arye Nehorai","raw_affiliation_strings":["Department of Electrical and Systems Engineering, Washington University of Saint Louis, Saint Louis, MO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, Washington University of Saint Louis, Saint Louis, MO, USA","institution_ids":["https://openalex.org/I204465549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101848896"],"corresponding_institution_ids":["https://openalex.org/I135310074","https://openalex.org/I204465549"],"apc_list":null,"apc_paid":null,"fwci":2.0959,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.85326416,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"58","issue":"9","first_page":"6079","last_page":"6092"},"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":0.9973999857902527,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.996399998664856,"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/notation","display_name":"Notation","score":0.5989196300506592},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4408879280090332},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.42853209376335144},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.42743825912475586},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.42040205001831055},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41807985305786133},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41652312874794006},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36568185687065125},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36233043670654297},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28764861822128296},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.0976211428642273},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.0854502022266388},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08058083057403564}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5989196300506592},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4408879280090332},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.42853209376335144},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.42743825912475586},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.42040205001831055},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41807985305786133},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41652312874794006},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36568185687065125},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36233043670654297},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28764861822128296},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.0976211428642273},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0854502022266388},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08058083057403564},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2012.2204535","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2204535","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:CiteSeerX.psu:10.1.1.747.789","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.747.789","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1006.4088.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W79421561","https://openalex.org/W156419107","https://openalex.org/W198837200","https://openalex.org/W339021664","https://openalex.org/W1499670810","https://openalex.org/W1529624360","https://openalex.org/W1546851689","https://openalex.org/W1577111082","https://openalex.org/W1577469824","https://openalex.org/W1591279474","https://openalex.org/W1601541039","https://openalex.org/W1817506613","https://openalex.org/W1966096622","https://openalex.org/W1980591506","https://openalex.org/W1990393033","https://openalex.org/W1993360063","https://openalex.org/W1997862149","https://openalex.org/W2001141328","https://openalex.org/W2009006054","https://openalex.org/W2011359124","https://openalex.org/W2015418199","https://openalex.org/W2046213250","https://openalex.org/W2047071281","https://openalex.org/W2053186076","https://openalex.org/W2054062969","https://openalex.org/W2066086960","https://openalex.org/W2070154657","https://openalex.org/W2109842006","https://openalex.org/W2116581043","https://openalex.org/W2118550318","https://openalex.org/W2129638195","https://openalex.org/W2142455269","https://openalex.org/W2145962650","https://openalex.org/W2162312215","https://openalex.org/W2162451874","https://openalex.org/W2165916500","https://openalex.org/W2176446742","https://openalex.org/W2296616510","https://openalex.org/W2327373345","https://openalex.org/W2586353914","https://openalex.org/W2611328865","https://openalex.org/W2950161800","https://openalex.org/W2950859181","https://openalex.org/W3099718522","https://openalex.org/W3106266785","https://openalex.org/W3148198191","https://openalex.org/W3179903767","https://openalex.org/W4250955649","https://openalex.org/W4285719527","https://openalex.org/W4301425558","https://openalex.org/W6635428452","https://openalex.org/W6638572029","https://openalex.org/W6657027774","https://openalex.org/W6683664273"],"related_works":["https://openalex.org/W2504004674","https://openalex.org/W1595229445","https://openalex.org/W2498744856","https://openalex.org/W4390482104","https://openalex.org/W2361403716","https://openalex.org/W2070653371","https://openalex.org/W2904061867","https://openalex.org/W4289115725","https://openalex.org/W3144644423","https://openalex.org/W2024384195"],"abstract_inverted_index":{"The":[0,15,116],"stability":[1,54],"of":[2,35,46,111,138,160],"low-rank":[3],"matrix":[4,58,149],"reconstruction":[5],"with":[6,52,103,147],"respect":[7],"to":[8,41,90,134],"noise":[9],"is":[10,39,113,169],"investigated":[11],"in":[12],"this":[13],"paper.":[14],"<formula":[16,27,67,92,117,139,161],"formulatype=\"inline\"":[17,28,68,93,118,140,162],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[18,29,69,94,119,141,163],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[19,70,95,142,164],"Notation=\"TeX\">$\\ell":[20,32,71,96,122,143,165],"_{\\ast}$</tex></formula>":[21,33,72,97,123,144,166],"-constrained":[22],"minimal":[23],"singular":[24],"value":[25],"(":[26],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[30,120],"<tex":[31,121],"-CMSV)":[34],"the":[36,43,53,57,62,109,136,148],"measurement":[37,86],"operator":[38],"shown":[40,89],"determine":[42],"recovery":[44],"performance":[45,63],"nuclear":[47],"norm":[48],"minimization-based":[49],"algorithms.":[50],"Compared":[51],"results":[55],"using":[56,66],"restricted":[59,150],"isometry":[60,151],"constant,":[61],"bounds":[64],"established":[65],"-CMSV":[73,124,145,167],"are":[74,80,88,129],"more":[75],"concise,":[76],"and":[77,84,132],"their":[78],"derivations":[79],"less":[81],"complex.":[82],"Isotropic":[83],"subgaussian":[85],"operators":[87,128],"have":[91],"-CMSVs":[98],"bounded":[99],"away":[100],"from":[101],"zero":[102],"high":[104],"probability,":[105],"as":[106,108],"long":[107],"number":[110],"measurements":[112],"relatively":[114],"large.":[115],"for":[125,172],"correlated":[126],"Gaussian":[127],"also":[130,154],"analyzed":[131],"used":[133],"illustrate":[135],"advantage":[137],"compared":[146],"constant.":[152],"We":[153],"provide":[155],"a":[156],"fixed":[157],"point":[158],"characterization":[159],"that":[168],"potentially":[170],"useful":[171],"its":[173],"computation.":[174]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}