{"id":"https://openalex.org/W2057690238","doi":"https://doi.org/10.1109/tit.2012.2232347","title":"Robust Lasso With Missing and Grossly Corrupted Observations","display_name":"Robust Lasso With Missing and Grossly Corrupted Observations","publication_year":2012,"publication_date":"2012-12-08","ids":{"openalex":"https://openalex.org/W2057690238","doi":"https://doi.org/10.1109/tit.2012.2232347","mag":"2057690238"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2232347","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2232347","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/A5103324660","display_name":"Nam H. Nguyen","orcid":"https://orcid.org/0000-0002-1254-0069"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nam H. Nguyen","raw_affiliation_strings":["Department of Electrical and Computer Engineering, John Hopkins University, Baltimore, MD, USA","Dept. of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, John Hopkins University, Baltimore, MD, USA","institution_ids":[]},{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101413113","display_name":"Trac D. Tran","orcid":"https://orcid.org/0000-0002-0421-8416"},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Trac D. Tran","raw_affiliation_strings":["Department of Electrical and Computer Engineering, John Hopkins University, Baltimore, MD, USA","Dept. of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, John Hopkins University, Baltimore, MD, USA","institution_ids":[]},{"raw_affiliation_string":"Dept. of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.4498,"has_fulltext":false,"cited_by_count":135,"citation_normalized_percentile":{"value":0.98557553,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"59","issue":"4","first_page":"2036","last_page":"2058"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9911999702453613,"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/computer-science","display_name":"Computer science","score":0.346821665763855},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3409181237220764}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.346821665763855},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3409181237220764}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2012.2232347","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2232347","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":81,"referenced_works":["https://openalex.org/W1480312878","https://openalex.org/W1560153690","https://openalex.org/W1573820523","https://openalex.org/W1800306869","https://openalex.org/W1838749730","https://openalex.org/W1967408078","https://openalex.org/W1979421731","https://openalex.org/W1994309289","https://openalex.org/W1995168330","https://openalex.org/W2003217181","https://openalex.org/W2010824638","https://openalex.org/W2032520928","https://openalex.org/W2034260606","https://openalex.org/W2045756756","https://openalex.org/W2064437806","https://openalex.org/W2077964948","https://openalex.org/W2081305621","https://openalex.org/W2089493818","https://openalex.org/W2092058109","https://openalex.org/W2093994886","https://openalex.org/W2095872233","https://openalex.org/W2096586829","https://openalex.org/W2099210013","https://openalex.org/W2109842006","https://openalex.org/W2115447612","https://openalex.org/W2116581043","https://openalex.org/W2120580172","https://openalex.org/W2124918466","https://openalex.org/W2125536150","https://openalex.org/W2126042536","https://openalex.org/W2127300249","https://openalex.org/W2128633079","https://openalex.org/W2129812935","https://openalex.org/W2135046866","https://openalex.org/W2138019504","https://openalex.org/W2141880952","https://openalex.org/W2145096794","https://openalex.org/W2145962650","https://openalex.org/W2147534083","https://openalex.org/W2147656689","https://openalex.org/W2150940164","https://openalex.org/W2151825876","https://openalex.org/W2161215690","https://openalex.org/W2161310686","https://openalex.org/W2162312215","https://openalex.org/W2164452299","https://openalex.org/W2168877202","https://openalex.org/W2593996946","https://openalex.org/W2950190315","https://openalex.org/W2951539721","https://openalex.org/W2962909343","https://openalex.org/W2963147719","https://openalex.org/W2963899927","https://openalex.org/W2964036110","https://openalex.org/W2997644599","https://openalex.org/W3098452830","https://openalex.org/W3098453412","https://openalex.org/W3098834468","https://openalex.org/W3099503819","https://openalex.org/W3099718522","https://openalex.org/W3100937728","https://openalex.org/W3100971749","https://openalex.org/W3101040439","https://openalex.org/W3101762025","https://openalex.org/W3104148512","https://openalex.org/W3105340263","https://openalex.org/W3105629641","https://openalex.org/W3106266785","https://openalex.org/W3106324661","https://openalex.org/W4301425558","https://openalex.org/W6638370976","https://openalex.org/W6649031020","https://openalex.org/W6658285354","https://openalex.org/W6665014229","https://openalex.org/W6675017388","https://openalex.org/W6681168328","https://openalex.org/W6682241100","https://openalex.org/W6682550672","https://openalex.org/W6683664273","https://openalex.org/W6684923232","https://openalex.org/W6766342068"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880","https://openalex.org/W1596801655","https://openalex.org/W2359140296"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,116,123,128,135,142,181],"problem":[4],"of":[5,97,137,152,159,189,223,235],"accurately":[6],"recovering":[7],"a":[8,64,79,85,156,178,220],"<i":[9,20,28,32,40,47,52,60,75,104,145,163,169,196,205,209,213],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[10,16,21,29,33,37,41,44,48,53,56,61,76,101,105,108,146,164,170,193,197,200,206,210,214],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</i>":[11,207],"-sparse":[12],"vector":[13,67],"\u03b2":[14,35,99,191],"<sup":[15,36,43,55,100,107,192,199],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">*</sup>":[17,38,45,57,102,109,194,201],"\u2208":[18,58],"\\BBR":[19,59],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</i>":[22,211],"from":[23,202],"highly":[24],"corrupted":[25],"linear":[26,221],"measurements":[27],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">y</i>":[30],"=":[31],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">X</i>":[34,147,165],"+":[39,46],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">e</i>":[42,54,106,198],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">w</i>":[49,77],",":[50],"where":[51],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</i>":[62,215],"is":[63,78,225,243],"sparse":[65,94],"error":[66],"whose":[68],"nonzero":[69],"entries":[70],"may":[71],"be":[72],"unbounded":[73],"and":[74,103,195],"stochastic":[80],"noise":[81],"term.":[82],"We":[83],"propose":[84],"so-called":[86],"extended":[87,117,138,182],"Lasso":[88,118,183],"optimization":[89],"which":[90,174],"takes":[91],"into":[92],"consideration":[93],"prior":[95],"information":[96],"both":[98,122,190],".":[110,148],"Our":[111,131,149,228],"first":[112],"result":[113],"shows":[114,231],"that":[115,232],"can":[119,176,184],"faithfully":[120],"recover":[121,185],"regression":[124],"as":[125,127],"well":[126],"corruption":[129],"vector.":[130],"analysis":[132,229],"relies":[133],"on":[134],"notion":[136],"restricted":[139],"eigenvalue":[140],"for":[141,173],"design":[143,161],"matrix":[144,162],"second":[150],"set":[151],"results":[153],"applies":[154],"to":[155,238],"general":[157],"class":[158],"Gaussian":[160],"with":[166],"i.i.d.":[167],"rows":[168],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</i>":[171],"(0,\u03a3),":[172],"we":[175],"establish":[177],"surprising":[179],"result:":[180],"exact":[186,240],"signed":[187,241],"supports":[188],"only":[203],"\u03a9(":[204],"log":[208,212],")":[216],"observations,":[217],"even":[218],"when":[219],"fraction":[222],"observations":[224,236],"grossly":[226],"corrupted.":[227],"also":[230],"this":[233],"amount":[234],"required":[237],"achieve":[239],"support":[242],"indeed":[244],"optimal.":[245]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}