{"id":"https://openalex.org/W2782693723","doi":"https://doi.org/10.1109/isit.2018.8437468","title":"Frame Moments and Welch Bound with Erasures","display_name":"Frame Moments and Welch Bound with Erasures","publication_year":2018,"publication_date":"2018-06-01","ids":{"openalex":"https://openalex.org/W2782693723","doi":"https://doi.org/10.1109/isit.2018.8437468","mag":"2782693723"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2018.8437468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2018.8437468","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1801.04548","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072814303","display_name":"Marina Haikin","orcid":null},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Marina Haikin","raw_affiliation_strings":["EE - Systems Department, Tel Aviv University, Tel Aviv, Israel","Tel Aviv University, EE - Systems Department, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"EE - Systems Department, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, EE - Systems Department, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027550575","display_name":"Ram Zamir","orcid":"https://orcid.org/0000-0003-1800-3886"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ram Zamir","raw_affiliation_strings":["EE - Systems Department, Tel Aviv University, Tel Aviv, Israel","Tel Aviv University, EE - Systems Department, Tel Aviv, Israel"],"affiliations":[{"raw_affiliation_string":"EE - Systems Department, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"Tel Aviv University, EE - Systems Department, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013235677","display_name":"Matan Gavish","orcid":"https://orcid.org/0000-0001-6747-6888"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Matan Gavish","raw_affiliation_strings":["School of Computer Science and Engineering, The Hebrew University, Jerusalem, Israel","The Hebrew University, School of Computer Science and Engineering, Jerusalem, Israel#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, The Hebrew University, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"The Hebrew University, School of Computer Science and Engineering, Jerusalem, Israel#TAB#","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072814303"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":0.9681863,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.67765812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7277542352676392},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7131614685058594},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6905629634857178},{"id":"https://openalex.org/keywords/equiangular-polygon","display_name":"Equiangular polygon","score":0.5558882355690002},{"id":"https://openalex.org/keywords/gramian-matrix","display_name":"Gramian matrix","score":0.492652952671051},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46431848406791687},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3957057595252991},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20654278993606567},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.16158592700958252},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1502322554588318},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14548027515411377},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09542375802993774},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.0873134434223175}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7277542352676392},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7131614685058594},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6905629634857178},{"id":"https://openalex.org/C41779539","wikidata":"https://www.wikidata.org/wiki/Q2543717","display_name":"Equiangular polygon","level":3,"score":0.5558882355690002},{"id":"https://openalex.org/C77246614","wikidata":"https://www.wikidata.org/wiki/Q1409400","display_name":"Gramian matrix","level":3,"score":0.492652952671051},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46431848406791687},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3957057595252991},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20654278993606567},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.16158592700958252},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1502322554588318},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14548027515411377},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09542375802993774},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.0873134434223175},{"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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/isit.2018.8437468","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2018.8437468","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1801.04548","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.04548","pdf_url":"https://arxiv.org/pdf/1801.04548","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":"","raw_type":"text"},{"id":"mag:2782693723","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1801.04548.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1801.04548","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1801.04548","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1801.04548","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.04548","pdf_url":"https://arxiv.org/pdf/1801.04548","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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2782693723.pdf","grobid_xml":"https://content.openalex.org/works/W2782693723.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1988487377","https://openalex.org/W2015418199","https://openalex.org/W2072184935","https://openalex.org/W2081825044","https://openalex.org/W2110140246","https://openalex.org/W2133553014","https://openalex.org/W2138548210","https://openalex.org/W2270451106","https://openalex.org/W2576310190","https://openalex.org/W2734391606","https://openalex.org/W2949876750","https://openalex.org/W2963169799","https://openalex.org/W4229746864"],"related_works":["https://openalex.org/W2039971134","https://openalex.org/W3152829224","https://openalex.org/W3111905764","https://openalex.org/W2963750720","https://openalex.org/W3012485420","https://openalex.org/W2953261448","https://openalex.org/W2289991267","https://openalex.org/W128487529","https://openalex.org/W2892564615","https://openalex.org/W2952425385","https://openalex.org/W2890959015","https://openalex.org/W3000435524","https://openalex.org/W2797403927","https://openalex.org/W2959342769","https://openalex.org/W2491158392","https://openalex.org/W3047485863","https://openalex.org/W3113130384","https://openalex.org/W2951868426","https://openalex.org/W2301931005","https://openalex.org/W2346276749"],"abstract_inverted_index":{"The":[0,164],"Welch":[1,42,92,102],"Bound":[2],"is":[3,86,139,178],"a":[4,48,74,79,152,187,199],"lower":[5,49],"bound":[6,43,50,93,118,135,165],"on":[7,51,58,104,190],"the":[8,20,37,41,52,59,62,91,99,105,109,113,121,133,140,143,191],"root":[9],"mean":[10],"square":[11],"cross":[12],"correlation":[13],"between":[14],"$n$":[15,156],"unit-norm":[16],"vectors":[17],"$f_1,...,f_n$":[18],"in":[19,72,198],"$m$":[21],"dimensional":[22],"space":[23],"($\\mathbb{R}":[24],"^m$":[25],"or":[26],"$\\mathbb{C}":[27],"^m$),":[28],"for":[29,132,136,171],"$n\\geq":[30],"m$.":[31],"Letting":[32],"$F":[33],"=":[34,173],"[f_1|...|f_n]$":[35],"denote":[36],"$m$-by-$n$":[38],"frame":[39],"matrix,":[40],"can":[44],"be":[45],"viewed":[46],"as":[47],"second":[53],"moment":[54,124,145],"of":[55,61,78,82,87,108,112,125,142,146,193,201],"$F$,":[56],"namely":[57],"trace":[60],"squared":[63],"Gram":[64,110],"matrix":[65,111],"$(F'F)^2$.":[66],"We":[67,89,127],"consider":[68],"an":[69,179],"erasure":[70,101],"setting,":[71],"which":[73,138],"reduced":[75,114],"frame,":[76],"composed":[77],"random":[80],"subset":[81],"Bernoulli":[83],"selected":[84],"vectors,":[85],"interest.":[88],"extend":[90],"to":[94,120,158],"this":[95,117],"setting":[96],"and":[97,151,209],"present":[98],"{\\em":[100],"bound}":[103],"expected":[106],"value":[107],"frame.":[115],"Interestingly,":[116],"generalizes":[119],"$d$-th":[122,144],"order":[123],"$F$.":[126],"provide":[128],"simple,":[129],"explicit":[130],"formulae":[131],"generalized":[134],"$d=2,3,4$,":[137],"sum":[141],"Wachter's":[147],"classical":[148],"MANOVA":[149],"distribution":[150],"vanishing":[153],"term":[154],"(as":[155],"goes":[157],"infinity":[159],"with":[160,167],"$\\frac{m}{n}$":[161],"held":[162],"constant).":[163],"holds":[166],"equality":[168],"if":[169],"(and":[170],"$d":[172],"4$":[174],"only":[175],"if)":[176],"$F$":[177],"Equiangular":[180],"Tight":[181],"Frame":[182],"(ETF).":[183],"Our":[184],"results":[185],"offer":[186],"novel":[188],"perspective":[189],"superiority":[192],"ETFs":[194],"over":[195],"other":[196],"frames":[197],"variety":[200],"applications,":[202],"including":[203],"spread":[204],"spectrum":[205],"communications,":[206],"compressed":[207],"sensing":[208],"analog":[210],"coding.":[211]},"counts_by_year":[{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":3}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}