{"id":"https://openalex.org/W2085267075","doi":"https://doi.org/10.1109/lsp.2015.2402206","title":"Restricted Isometry Property of Subspace Projection Matrix Under Random Compression","display_name":"Restricted Isometry Property of Subspace Projection Matrix Under Random Compression","publication_year":2015,"publication_date":"2015-02-10","ids":{"openalex":"https://openalex.org/W2085267075","doi":"https://doi.org/10.1109/lsp.2015.2402206","mag":"2085267075"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2015.2402206","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2402206","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1502.02245","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Xinyue Shen","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinyue Shen","raw_affiliation_strings":["Department of Electronic Engineering, Tsinghua University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":null,"display_name":"Yuantao Gu","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuantao Gu","raw_affiliation_strings":["Department of Electronic Engineering, Tsinghua University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, Tsinghua University, Beijing, China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":0.3351,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.61977635,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"9","first_page":"1326","last_page":"1330"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.8144999742507935,"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":0.8144999742507935,"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/T11716","display_name":"Random Matrices and Applications","score":0.04729999974370003,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.01810000091791153,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/restricted-isometry-property","display_name":"Restricted isometry property","score":0.8349999785423279},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.6990000009536743},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.6819999814033508},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.6574000120162964},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.5486000180244446},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.545199990272522},{"id":"https://openalex.org/keywords/random-projection","display_name":"Random projection","score":0.46549999713897705},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.46299999952316284},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.45489999651908875}],"concepts":[{"id":"https://openalex.org/C17902559","wikidata":"https://www.wikidata.org/wiki/Q17099734","display_name":"Restricted isometry property","level":3,"score":0.8349999785423279},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.6990000009536743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6948000192642212},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.6819999814033508},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6574000120162964},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.5486000180244446},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.545199990272522},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4729999899864197},{"id":"https://openalex.org/C2777036070","wikidata":"https://www.wikidata.org/wiki/Q18393452","display_name":"Random projection","level":2,"score":0.46549999713897705},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.46299999952316284},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.45489999651908875},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.4546999931335449},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C2777121530","wikidata":"https://www.wikidata.org/wiki/Q7512739","display_name":"Signal subspace","level":4,"score":0.3878999948501587},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.38519999384880066},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.35030001401901245},{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3215000033378601},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3206000030040741},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3073999881744385},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.30379998683929443},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.2953999936580658},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28870001435279846},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.27410000562667847},{"id":"https://openalex.org/C94947713","wikidata":"https://www.wikidata.org/wiki/Q12806125","display_name":"Hollow matrix","level":5,"score":0.2669000029563904},{"id":"https://openalex.org/C49996920","wikidata":"https://www.wikidata.org/wiki/Q17089185","display_name":"Essential matrix","level":5,"score":0.2597000002861023},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.2558000087738037}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2015.2402206","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2402206","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1502.02245","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1502.02245","pdf_url":"https://arxiv.org/pdf/1502.02245","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1502.02245","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1502.02245","pdf_url":"https://arxiv.org/pdf/1502.02245","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":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1495302720","https://openalex.org/W1974973278","https://openalex.org/W1977196460","https://openalex.org/W1986736933","https://openalex.org/W1997516668","https://openalex.org/W2015418199","https://openalex.org/W2030449718","https://openalex.org/W2037757210","https://openalex.org/W2118550318","https://openalex.org/W2119667497","https://openalex.org/W2125874614","https://openalex.org/W2130320772","https://openalex.org/W2132743051","https://openalex.org/W2147631863","https://openalex.org/W2150414161","https://openalex.org/W2157878484","https://openalex.org/W2162451874","https://openalex.org/W2962834831","https://openalex.org/W4205293427","https://openalex.org/W4293203252","https://openalex.org/W6605953395","https://openalex.org/W6675827639","https://openalex.org/W6683496805"],"related_works":[],"abstract_inverted_index":{"Structures":[0],"play":[1],"a":[2,12,41],"significant":[3],"role":[4],"in":[5,33,105,117],"the":[6,71,84,95,129,154],"field":[7],"of":[8,14,43,55,73,86,101,132,151,156],"signal":[9,35],"processing.":[10,36],"As":[11],"representative":[13],"structural":[15],"data,":[16],"low":[17,44],"rank":[18,45],"matrix":[19,39,46,77,89,159],"along":[20],"with":[21,47],"its":[22,56,64],"restricted":[23],"isometry":[24],"property":[25],"(RIP)":[26],"has":[27],"been":[28],"an":[29,111],"important":[30],"research":[31],"topic":[32],"compressive":[34],"Subspace":[37],"projection":[38,76,88,99,158],"is":[40,126,143,160],"kind":[42],"additional":[48],"structure,":[49],"which":[50,67],"allows":[51],"for":[52,62],"further":[53],"reduction":[54],"intrinsic":[57],"dimension.":[58],"This":[59],"leaves":[60],"room":[61],"improving":[63],"own":[65],"RIP,":[66],"could":[68],"work":[69],"as":[70],"foundation":[72],"compressed":[74],"subspace":[75,87,98,157],"recovery.":[78],"In":[79],"this":[80],"work,":[81],"we":[82],"study":[83],"RIP":[85,155],"under":[90],"random":[91,152],"orthonormal":[92],"compression.":[93],"Considering":[94],"fact":[96],"that":[97,144],"matrices":[100],"s":[102],"dimensional":[103,115],"subspaces":[104],"R":[106,118,136],"<sup":[107,119,137],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[108,120,138],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</sup>":[109],"form":[110],"s(N":[112],"-":[113,147],"s)":[114],"submanifold":[116,134],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N\u00d7N</sup>":[121,139],",":[122],"our":[123],"main":[124],"concern":[125],"transformed":[127],"to":[128],"stable":[130],"embedding":[131],"such":[133],"into":[135],".":[140],"The":[141],"result":[142],"by":[145],"O(s(N":[146],"s)log":[148],"N)":[149],"number":[150],"measurements":[153],"guaranteed.":[161]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2016-06-24T00:00:00"}
