{"id":"https://openalex.org/W2150224753","doi":"https://doi.org/10.1109/tit.2013.2278179","title":"Exact Recovery Conditions for Sparse Representations With Partial Support Information","display_name":"Exact Recovery Conditions for Sparse Representations With Partial Support Information","publication_year":2013,"publication_date":"2013-10-16","ids":{"openalex":"https://openalex.org/W2150224753","doi":"https://doi.org/10.1109/tit.2013.2278179","mag":"2150224753"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2013.2278179","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2278179","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/A5063342552","display_name":"C\u00e9dric Herzet","orcid":"https://orcid.org/0000-0003-3039-2669"},"institutions":[{"id":"https://openalex.org/I4210133778","display_name":"Inria Rennes - Bretagne Atlantique Research Centre","ror":"https://ror.org/04040yw90","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210133778"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Cedric Herzet","raw_affiliation_strings":["Bretagne Atlantique, INRIA Rennes, Rennes, France","FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences (France)"],"affiliations":[{"raw_affiliation_string":"Bretagne Atlantique, INRIA Rennes, Rennes, France","institution_ids":["https://openalex.org/I4210133778","https://openalex.org/I1326498283"]},{"raw_affiliation_string":"FLUMINANCE - Fluid Flow Analysis, Description and Control from Image Sequences (France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025224509","display_name":"Charles Soussen","orcid":"https://orcid.org/0000-0002-6837-6755"},"institutions":[{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]},{"id":"https://openalex.org/I4210110792","display_name":"Centre de Recherche en Automatique de Nancy","ror":"https://ror.org/022r5hc56","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210099203","https://openalex.org/I4210100260","https://openalex.org/I4210110792","https://openalex.org/I4210159245","https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Charles Soussen","raw_affiliation_strings":["Centre de Recherche en Automatique de Nancy, Facult\u00e9 des Sciences et Techniques, Vandoeuvre, France","CRAN - Centre de Recherche en Automatique de Nancy (Universit\u00e9 de Lorraine, Campus Sciences, BP 70239, 54506 Vandoeuvre-les-Nancy Cedex - France)"],"affiliations":[{"raw_affiliation_string":"Centre de Recherche en Automatique de Nancy, Facult\u00e9 des Sciences et Techniques, Vandoeuvre, France","institution_ids":["https://openalex.org/I4210110792"]},{"raw_affiliation_string":"CRAN - Centre de Recherche en Automatique de Nancy (Universit\u00e9 de Lorraine, Campus Sciences, BP 70239, 54506 Vandoeuvre-les-Nancy Cedex - France)","institution_ids":["https://openalex.org/I4210110792","https://openalex.org/I90183372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062028668","display_name":"J\u00e9r\u00f4me Idier","orcid":"https://orcid.org/0000-0003-4087-0302"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jerome Idier","raw_affiliation_strings":["Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, Nantes, France","IRCCyN - Institut de Recherche en Communications et en Cybern\u00e9tique de Nantes (1, rue de la No\u00eb BP92101 44321 Nantes Cedex 03 - France)"],"affiliations":[{"raw_affiliation_string":"Institut de Recherche en Communications et Cybern\u00e9tique de Nantes, Nantes, France","institution_ids":[]},{"raw_affiliation_string":"IRCCyN - Institut de Recherche en Communications et en Cybern\u00e9tique de Nantes (1, rue de la No\u00eb BP92101 44321 Nantes Cedex 03 - France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041230403","display_name":"R\u00e9mi Gribonval","orcid":"https://orcid.org/0000-0002-9450-8125"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210133778","display_name":"Inria Rennes - Bretagne Atlantique Research Centre","ror":"https://ror.org/04040yw90","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210133778"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Remi Gribonval","raw_affiliation_strings":["Bretagne Atlantique, INRIA Rennes, Rennes, France","PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Mod\u00e9lisation Audio (Campus de Beaulieu 35042 Rennes cedex - France)"],"affiliations":[{"raw_affiliation_string":"Bretagne Atlantique, INRIA Rennes, Rennes, France","institution_ids":["https://openalex.org/I4210133778","https://openalex.org/I1326498283"]},{"raw_affiliation_string":"PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Mod\u00e9lisation Audio (Campus de Beaulieu 35042 Rennes cedex - France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063342552"],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I4210133778"],"apc_list":null,"apc_paid":null,"fwci":5.9898,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.96673209,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"59","issue":"11","first_page":"7509","last_page":"7524"},"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":0.9994999766349792,"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/T11996","display_name":"Random lasers and scattering media","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3102","display_name":"Acoustics and Ultrasonics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.7596591711044312},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48614737391471863},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4061475992202759},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3833335340023041},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34810107946395874},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3437628746032715},{"id":"https://openalex.org/keywords/information-retrieval","display_name":"Information retrieval","score":0.34064650535583496},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.14604681730270386}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7596591711044312},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48614737391471863},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4061475992202759},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3833335340023041},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34810107946395874},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3437628746032715},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.34064650535583496},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.14604681730270386}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2013.2278179","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2013.2278179","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:10.1.1.636.1605","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.636.1605","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.univ-nantes.fr/docs/00/90/76/46/PDF/main_v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.742.9033","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.742.9033","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/1305.4008.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00907646v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-00907646","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2013, 59 (11), pp.7509-7524. &#x27E8;10.1109/TIT.2013.2278179&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W43282915","https://openalex.org/W1027701583","https://openalex.org/W1591116419","https://openalex.org/W1786681852","https://openalex.org/W1906972028","https://openalex.org/W1974198688","https://openalex.org/W1978885364","https://openalex.org/W1986931325","https://openalex.org/W1988529089","https://openalex.org/W2012961725","https://openalex.org/W2015418199","https://openalex.org/W2018324106","https://openalex.org/W2019741018","https://openalex.org/W2028781966","https://openalex.org/W2028878677","https://openalex.org/W2046658845","https://openalex.org/W2058428247","https://openalex.org/W2065829287","https://openalex.org/W2075506710","https://openalex.org/W2091893102","https://openalex.org/W2098704159","https://openalex.org/W2099100030","https://openalex.org/W2099641086","https://openalex.org/W2102380305","https://openalex.org/W2111067490","https://openalex.org/W2111394763","https://openalex.org/W2116148865","https://openalex.org/W2119197726","https://openalex.org/W2119323121","https://openalex.org/W2122315118","https://openalex.org/W2127271355","https://openalex.org/W2128659236","https://openalex.org/W2129131372","https://openalex.org/W2134074206","https://openalex.org/W2134474909","https://openalex.org/W2136235822","https://openalex.org/W2151693816","https://openalex.org/W2154332973","https://openalex.org/W2157969180","https://openalex.org/W2160979406","https://openalex.org/W2185568723","https://openalex.org/W2289917018","https://openalex.org/W2407409608","https://openalex.org/W2537682809","https://openalex.org/W2762625016","https://openalex.org/W2949125413","https://openalex.org/W2952062907","https://openalex.org/W3098515897","https://openalex.org/W4235713725","https://openalex.org/W6601779987","https://openalex.org/W6639887155","https://openalex.org/W6713532222"],"related_works":["https://openalex.org/W2504004674","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W1595229445","https://openalex.org/W2498744856","https://openalex.org/W4390482104","https://openalex.org/W322408318","https://openalex.org/W149041114","https://openalex.org/W2963177394","https://openalex.org/W1965815883"],"abstract_inverted_index":{"We":[0,50,163],"address":[1],"the":[2,15,23,31,38,63,91,100,104,115,128,142,181,201,207,216,230,237,253,262,266,277],"exact":[3,208],"recovery":[4,116,209],"of":[5,33,37,65,99,117,147,178,218],"a":[6,35,52,196],"<formula":[7,70,93,107,119,133,148,156,219,245,268,281],"formulatype=\"inline\"":[8,71,94,108,120,134,149,157,220,246,269,282],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,72,95,109,121,135,150,158,221,247,270,283],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex":[10,73,96,110,151,159,222,248],"Notation=\"TeX\">$k$</tex></formula>":[11,124],"-sparse":[12,125],"vector":[13,126],"in":[14,127,229,260],"noiseless":[16],"setting":[17],"when":[18,141,244],"some":[19,59,66,171],"partial":[20,28,254],"information":[21,29],"on":[22,69,90,200],"support":[24,40,144],"is":[25,88,145,168,188,250],"available.":[26],"This":[27],"takes":[30],"form":[32],"either":[34],"subset":[36,44],"true":[39],"or":[41],"an":[42,241],"approximate":[43],"including":[45],"wrong":[46,161],"atoms":[47,154],"as":[48],"well.":[49],"derive":[51],"new":[53],"sufficient":[54],"and":[55,81,102,155,206,227,276],"worst-case":[56],"necessary":[57],"(in":[58],"sense)":[60],"condition":[61,106,167,187,210],"for":[62,256,265,280],"success":[64],"procedures":[67,226],"based":[68,89,199],"Notation=\"TeX\">$\\ell":[74,223,273],"_{p}$</tex></formula>":[75,224],"-relaxation,":[76],"orthogonal":[77,82],"matching":[78],"pursuit":[79],"(OMP),":[80],"least":[83],"squares":[84],"(OLS).":[85],"Our":[86],"result":[87],"coherence":[92,186],"Notation=\"TeX\">$\\mu":[97,111,138],"$</tex></formula>":[98],"dictionary":[101],"relaxes":[103],"well-known":[105],"&lt;":[112,139],"1/(2k-1)$</tex></formula>":[113],"ensuring":[114],"any":[118],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[122,136,271,284],"<tex":[123,137,272,285],"noninformed":[129],"setup.":[130,232],"It":[131],"reads":[132],"1/(2k-g+b-1)$</tex></formula>":[140],"informed":[143,231,267],"composed":[146],"Notation=\"TeX\">$g$</tex></formula>":[152],"good":[153],"Notation=\"TeX\">$b$</tex></formula>":[160],"atoms.":[162],"emphasize":[164,235],"that":[165,176,236],"our":[166],"complementary":[169],"to":[170,190],"restricted-isometry-based":[172],"conditions":[173],"by":[174],"showing":[175],"none":[177],"them":[179],"implies":[180,259],"other.":[182],"Because":[183],"this":[184],"mutual":[185],"common":[189],"all":[191],"procedures,":[192],"we":[193,234],"carry":[194],"out":[195],"finer":[197],"analysis":[198],"null":[202],"space":[203],"property":[204,243],"(NSP)":[205],"(ERC).":[211],"Connections":[212],"are":[213],"established":[214],"regarding":[215],"characterization":[217],"-relaxation":[225],"OMP":[228,257],"First,":[233],"truncated":[238,263,278],"NSP":[239,264,279],"enjoys":[240],"ordering":[242],"Notation=\"TeX\">$p$</tex></formula>":[249],"decreased.":[251],"Second,":[252],"ERC":[255],"(ERC-OMP)":[258],"turn":[261],"_{1}$</tex></formula>":[274],"problem,":[275],"Notation=\"TeX\">$p&lt;":[286],"1$</tex></formula>":[287],".":[288]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
