{"id":"https://openalex.org/W3045385741","doi":"https://doi.org/10.1109/tit.2021.3067280","title":"What is the Largest Sparsity Pattern That Can Be Recovered by 1-Norm Minimization?","display_name":"What is the Largest Sparsity Pattern That Can Be Recovered by 1-Norm Minimization?","publication_year":2021,"publication_date":"2021-03-18","ids":{"openalex":"https://openalex.org/W3045385741","doi":"https://doi.org/10.1109/tit.2021.3067280","mag":"3045385741"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3067280","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3067280","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1910.05652","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070400780","display_name":"Mustafa Devrim Kaba","orcid":null},"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"]},{"id":"https://openalex.org/I4210150719","display_name":"eBay (United States)","ror":"https://ror.org/05cnabr44","country_code":"US","type":"company","lineage":["https://openalex.org/I4210150719"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mustafa D. Kaba","raw_affiliation_strings":["Johns Hopkins University, Baltimore, MD, USA","eBay Inc., San Jose, CA, USA","[Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]},{"raw_affiliation_string":"eBay Inc., San Jose, CA, USA","institution_ids":["https://openalex.org/I4210150719"]},{"raw_affiliation_string":"[Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD, USA]","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027718772","display_name":"Mengnan Zhao","orcid":"https://orcid.org/0000-0001-8319-4266"},"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":"Mengnan Zhao","raw_affiliation_strings":["Johns Hopkins University, Baltimore, MD, USA","Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA#TAB#","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011256828","display_name":"Ren\u00e9 Vidal","orcid":"https://orcid.org/0000-0003-1838-0761"},"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":"Rene Vidal","raw_affiliation_strings":["Johns Hopkins University, Baltimore, MD, USA","Mathematical Institute for Data Science, Johns Hopkins University, Baltimore, MD, USA","[Mathematical Inst. for Data Science, Johns Hopkins University, Baltimore, MD, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]},{"raw_affiliation_string":"Mathematical Institute for Data Science, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]},{"raw_affiliation_string":"[Mathematical Inst. for Data Science, Johns Hopkins University, Baltimore, MD, USA]","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082367556","display_name":"Daniel P. Robinson","orcid":"https://orcid.org/0000-0003-0251-4227"},"institutions":[{"id":"https://openalex.org/I186143895","display_name":"Lehigh University","ror":"https://ror.org/012afjb06","country_code":"US","type":"education","lineage":["https://openalex.org/I186143895"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel P. Robinson","raw_affiliation_strings":["Lehigh University, Bethlehem, PA, USA","Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehigh University, Bethlehem, PA, USA","institution_ids":["https://openalex.org/I186143895"]},{"raw_affiliation_string":"Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA#TAB#","institution_ids":["https://openalex.org/I186143895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032910355","display_name":"Enrique Mallada","orcid":"https://orcid.org/0000-0003-1568-1833"},"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":"Enrique Mallada","raw_affiliation_strings":["Johns Hopkins University, Baltimore, MD, USA","Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA#TAB#","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1783,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.42107448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"67","issue":"5","first_page":"3060","last_page":"3074"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9986000061035156,"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/norm","display_name":"Norm (philosophy)","score":0.556804895401001},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5190730690956116},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4988858699798584},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4582066535949707},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4508155286312103},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4500659704208374},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.44883933663368225},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43800753355026245},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41643738746643066},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32689332962036133},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2576829791069031}],"concepts":[{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.556804895401001},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5190730690956116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4988858699798584},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4582066535949707},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4508155286312103},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4500659704208374},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.44883933663368225},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43800753355026245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41643738746643066},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32689332962036133},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2576829791069031},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tit.2021.3067280","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3067280","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:1910.05652","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.05652","pdf_url":"https://arxiv.org/pdf/1910.05652","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":"doi:10.48550/arxiv.1910.05652","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1910.05652","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":"article"},{"id":"mag:3045385741","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1910.05652","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1910.05652","pdf_url":"https://arxiv.org/pdf/1910.05652","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/G285070763","display_name":null,"funder_award_id":"CAREER 1752362","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G338337032","display_name":null,"funder_award_id":"IIS 1704458","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G372986997","display_name":null,"funder_award_id":"AMPS1736448","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5438380651","display_name":null,"funder_award_id":"CCF 1618637","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W143004564","https://openalex.org/W228380312","https://openalex.org/W1515135833","https://openalex.org/W1943159047","https://openalex.org/W1962147060","https://openalex.org/W1993962865","https://openalex.org/W2009505312","https://openalex.org/W2020390700","https://openalex.org/W2030449718","https://openalex.org/W2035816523","https://openalex.org/W2045385910","https://openalex.org/W2049502219","https://openalex.org/W2099641086","https://openalex.org/W2101675075","https://openalex.org/W2114595593","https://openalex.org/W2119667497","https://openalex.org/W2122340891","https://openalex.org/W2125680629","https://openalex.org/W2126833874","https://openalex.org/W2128633079","https://openalex.org/W2129131372","https://openalex.org/W2129812935","https://openalex.org/W2138002832","https://openalex.org/W2138019504","https://openalex.org/W2145096794","https://openalex.org/W2157872906","https://openalex.org/W2167401472","https://openalex.org/W2244252827","https://openalex.org/W2296616510","https://openalex.org/W2464641472","https://openalex.org/W2900264368","https://openalex.org/W2949382009","https://openalex.org/W2962904605","https://openalex.org/W2963840432","https://openalex.org/W2990281095","https://openalex.org/W3100940408","https://openalex.org/W3125735862","https://openalex.org/W4238591275","https://openalex.org/W4247549312","https://openalex.org/W4249667877","https://openalex.org/W4250955649","https://openalex.org/W6641049134","https://openalex.org/W6677581936","https://openalex.org/W6680496891","https://openalex.org/W6683194942","https://openalex.org/W6755846678"],"related_works":["https://openalex.org/W3138474759","https://openalex.org/W2980018270","https://openalex.org/W3100940408","https://openalex.org/W3104624268","https://openalex.org/W2577198532","https://openalex.org/W2919107126","https://openalex.org/W2258058088","https://openalex.org/W2964081564","https://openalex.org/W2784921731","https://openalex.org/W2120954952","https://openalex.org/W2951166537","https://openalex.org/W2964243449","https://openalex.org/W2618868144","https://openalex.org/W1829976833","https://openalex.org/W1597291075","https://openalex.org/W2949856292","https://openalex.org/W2533546402","https://openalex.org/W3035333509","https://openalex.org/W2169000144","https://openalex.org/W112980254"],"abstract_inverted_index":{"Much":[0],"of":[1,86,100,116,126,139,158,161,192,200],"the":[2,11,25,38,45,55,95,114,121,124,145,156,162,190,193,201,210],"existing":[3],"literature":[4],"in":[5,113,176],"sparse":[6,117,171],"recovery":[7,30,118,172],"is":[8,31,69,111,153,181],"concerned":[9],"with":[10],"following":[12],"question:":[13,40],"given":[14,41],"a":[15,19,42,67,72,76,127,132,165,221],"sparsity":[16,57,147,203],"pattern":[17,58,68,148,204],"and":[18,44,81,94,216],"corresponding":[20],"regularizer,":[21,53],"derive":[22],"conditions":[23],"on":[24,91,98],"dictionary":[26,43,122],"under":[27],"which":[28],"exact":[29],"possible.":[32],"In":[33,103,137,189],"this":[34,87,108,180],"paper,":[35],"we":[36,105,142,167],"study":[37,115],"opposite":[39],"<i":[46],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[47,50],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">l</i>":[48],"<sub":[49],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[51],"-norm":[52],"find":[54],"largest":[56,146,202],"that":[59,65,144,149,169,205],"can":[60,150,173,206],"be":[61,151,174,184,207,214,220],"recovered.":[62],"We":[63],"show":[64,106,143,168],"such":[66],"described":[70],"by":[71,155],"mathematical":[73],"object":[74],"called":[75],"\u201cmaximum":[77],"abstract":[78],"simplicial":[79],"complex,\u201d":[80],"provide":[82],"two":[83],"different":[84],"characterizations":[85],"object:":[88],"one":[89],"based":[90,97],"extreme":[92],"points":[93],"other":[96],"vectors":[99],"minimal":[101],"support.":[102],"addition,":[104],"how":[107],"new":[109],"framework":[110],"useful":[112],"problems":[119],"when":[120],"takes":[123],"form":[125],"graph":[128],"incidence":[129,140],"matrix":[130],"or":[131],"partial":[133,194],"discrete":[134,195],"Fourier":[135,196],"transform.":[136],"case":[138,191],"matrices,":[141],"recovered":[152,208],"determined":[154],"set":[157],"simple":[159],"cycles":[160],"graph.":[163],"As":[164],"byproduct,":[166],"standard":[170],"certified":[175],"polynomial":[177],"time,":[178],"although":[179],"known":[182],"to":[183,213,219],"NP-hard":[185],"for":[186],"general":[187],"matrices.":[188],"transform,":[197],"our":[198],"characterization":[199],"requires":[209],"unknown":[211],"signal":[212],"real":[215],"its":[217],"dimension":[218],"prime":[222],"number.":[223]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
