{"id":"https://openalex.org/W2123519167","doi":"https://doi.org/10.1109/allerton.2009.5394883","title":"A restricted isometry property for structurally-subsampled unitary matrices","display_name":"A restricted isometry property for structurally-subsampled unitary matrices","publication_year":2009,"publication_date":"2009-09-01","ids":{"openalex":"https://openalex.org/W2123519167","doi":"https://doi.org/10.1109/allerton.2009.5394883","mag":"2123519167"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2009.5394883","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2009.5394883","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5028718006","display_name":"Waheed U. Bajwa","orcid":"https://orcid.org/0000-0003-4406-5263"},"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/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Waheed U. Bajwa","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Wisconsin, Madison, USA","The Program in Applied and Computational Mathematics, Princeton University, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Wisconsin, Madison, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"The Program in Applied and Computational Mathematics, Princeton University, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064613937","display_name":"A.M. Sayeed","orcid":"https://orcid.org/0009-0005-4066-1908"},"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Akbar M. Sayeed","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Wisconsin, Madison, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Wisconsin, Madison, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106921483","display_name":"Robert D. Nowak","orcid":"https://orcid.org/0000-0001-8743-0887"},"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert Nowak","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Wisconsin, Madison, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Wisconsin, Madison, USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.044,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.94121455,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"70","issue":null,"first_page":"1005","last_page":"1012"},"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":0.9995999932289124,"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/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/restricted-isometry-property","display_name":"Restricted isometry property","score":0.8716226816177368},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.7086941599845886},{"id":"https://openalex.org/keywords/unitary-matrix","display_name":"Unitary matrix","score":0.6690170764923096},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5480180382728577},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.520913302898407},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5159664750099182},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5038599371910095},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.48692405223846436},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.3685912489891052},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.341593861579895}],"concepts":[{"id":"https://openalex.org/C17902559","wikidata":"https://www.wikidata.org/wiki/Q17099734","display_name":"Restricted isometry property","level":3,"score":0.8716226816177368},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.7086941599845886},{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.6690170764923096},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5480180382728577},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.520913302898407},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5159664750099182},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5038599371910095},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.48692405223846436},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.3685912489891052},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.341593861579895},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/allerton.2009.5394883","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2009.5394883","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.295.9114","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.295.9114","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.rci.rutgers.edu/~wub1/pubs/allerton09_ssum.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.296.8860","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.296.8860","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://nowak.ece.wisc.edu/allerton09.pdf","raw_type":"text"},{"id":"pmh:oai:alma.01RUT_INST:11665027500004646","is_oa":false,"landing_page_url":"https://scholarship.libraries.rutgers.edu/esploro/outputs/conferenceProceeding/A-restricted-isometry-property-for-structurally-subsampled/991031665707804646","pdf_url":null,"source":{"id":"https://openalex.org/S4210197018","display_name":"View","issn_l":"2688-268X","issn":["2688-268X","2688-3988"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Conference Proceedings"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W188867022","https://openalex.org/W203533378","https://openalex.org/W595252221","https://openalex.org/W1546372806","https://openalex.org/W1632225057","https://openalex.org/W1966637115","https://openalex.org/W1976709621","https://openalex.org/W1997834106","https://openalex.org/W2029816571","https://openalex.org/W2030449718","https://openalex.org/W2034260606","https://openalex.org/W2050994160","https://openalex.org/W2055064119","https://openalex.org/W2129131372","https://openalex.org/W2129638195","https://openalex.org/W2137628444","https://openalex.org/W2141116650","https://openalex.org/W2145096794","https://openalex.org/W2163137659","https://openalex.org/W2166873702","https://openalex.org/W2170311302","https://openalex.org/W2188449898","https://openalex.org/W2610335499","https://openalex.org/W3105340263","https://openalex.org/W4301425558"],"related_works":["https://openalex.org/W1595179898","https://openalex.org/W2949399405","https://openalex.org/W4301619540","https://openalex.org/W4297570801","https://openalex.org/W1639246335","https://openalex.org/W116214155","https://openalex.org/W2952050240","https://openalex.org/W2568623927","https://openalex.org/W2085436476","https://openalex.org/W2025666718"],"abstract_inverted_index":{"Subsampled":[0],"(or":[1],"partial)":[2],"Fourier":[3],"matrices":[4,43,117,169],"were":[5],"originally":[6],"introduced":[7],"in":[8,18,68,87,105,173,194],"the":[9,35,54,58,66,70,107,114,119,137,141,146,158,195,202,212],"compressive":[10],"sensing":[11,47,84,108,154],"literature":[12],"by":[13,20],"Candes":[14,21],"et":[15],"al.":[16],"Later,":[17],"papers":[19],"and":[22,24,26,181],"Tao":[23],"Rudelson":[25],"Vershynin,":[27],"it":[28],"was":[29],"shown":[30],"that":[31,53,81,170,221],"(random)":[32],"subsampling":[33,112],"of":[34,37,41,56,103,113,116,118,125,140,162,166,191,197,205,214],"rows":[36,55,95,115],"many":[38],"other":[39],"classes":[40],"unitary":[42,59,149,168],"also":[44],"yield":[45],"effective":[46],"matrices.":[48,155],"The":[49],"key":[50],"requirement":[51],"is":[52,72,129],"U,":[57],"matrix,":[60],"must":[61],"be":[62,209],"highly":[63],"incoherent":[64,89],"with":[65],"basis":[67],"which":[69,106],"signal":[71],"sparse.":[73],"In":[74,184],"this":[75,192,206],"paper,":[76],"we":[77,186],"consider":[78,99],"acquisition":[79,142],"systems":[80,104],"-":[82,91],"despite":[83],"sparse":[85,223],"signals":[86],"an":[88,188],"domain":[90],"cannot":[92],"randomly":[93],"subsample":[94],"from":[96],"U.":[97],"We":[98,144,156],"a":[100,131,163],"general":[101],"class":[102,165],"matrix":[109,133],"corresponds":[110],"to":[111,151,211],"form":[120],"\u00bf":[121],"=":[122],"RU":[123],"(instead":[124],"U),":[126],"where":[127,201],"R":[128],"typically":[130],"low-rank":[132],"whose":[134],"structure":[135],"reflects":[136],"physical/technological":[138],"constraints":[139],"system.":[143],"use":[145],"term":[147],"\u00bfstructurally-subsampled":[148],"matrices\u00bf":[150],"describe":[152],"such":[153,176],"investigate":[157],"restricted":[159],"isometry":[160],"property":[161],"particular":[164],"structurally-subsampled":[167],"arise":[171],"naturally":[172],"application":[174,190],"areas":[175],"as":[177],"multiple-antenna":[178,215],"channel":[179,199],"estimation":[180,213],"sub-nyquist":[182],"sampling.":[183],"addition,":[185],"discuss":[187],"immediate":[189],"work":[193],"area":[196],"wireless":[198],"estimation,":[200],"main":[203],"results":[204],"paper":[207],"can":[208],"applied":[210],"orthogonal":[216],"frequency":[217],"division":[218],"multiplexing":[219],"channels":[220],"have":[222],"impulse":[224],"responses.":[225]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}