{"id":"https://openalex.org/W1839382729","doi":"https://doi.org/10.1109/isit.2015.7282516","title":"Isotropically random orthogonal matrices: Performance of LASSO and minimum conic singular values","display_name":"Isotropically random orthogonal matrices: Performance of LASSO and minimum conic singular values","publication_year":2015,"publication_date":"2015-06-01","ids":{"openalex":"https://openalex.org/W1839382729","doi":"https://doi.org/10.1109/isit.2015.7282516","mag":"1839382729"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2015.7282516","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2015.7282516","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 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/1503.07236","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024812488","display_name":"Christos Thrampoulidis","orcid":"https://orcid.org/0000-0001-9053-9365"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Christos Thrampoulidis","raw_affiliation_strings":["Department of Electrical Engineering, Caltech, Pasadena","[Department of Electrical Engineering, Caltech, Pasadena, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Caltech, Pasadena","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"[Department of Electrical Engineering, Caltech, Pasadena, USA]","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002430773","display_name":"Babak Hassibi","orcid":"https://orcid.org/0000-0002-1375-5838"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Babak Hassibi","raw_affiliation_strings":["Department of Electrical Engineering, Caltech, Pasadena","[Department of Electrical Engineering, Caltech, Pasadena, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Caltech, Pasadena","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"[Department of Electrical Engineering, Caltech, Pasadena, USA]","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024812488"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03748953,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"556","last_page":"560"},"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":0.9998000264167786,"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":0.9965999722480774,"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/gaussian","display_name":"Gaussian","score":0.7611956000328064},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.69713294506073},{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.6538019776344299},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6473352909088135},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5609733462333679},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.554124116897583},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4629664421081543},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.4489228427410126},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40096399188041687},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3878714442253113},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3513595461845398},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28127217292785645},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15711048245429993},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14233386516571045},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11913004517555237},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11800846457481384}],"concepts":[{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.7611956000328064},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.69713294506073},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.6538019776344299},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6473352909088135},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5609733462333679},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.554124116897583},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4629664421081543},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.4489228427410126},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40096399188041687},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3878714442253113},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3513595461845398},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28127217292785645},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15711048245429993},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14233386516571045},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11913004517555237},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11800846457481384},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"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":5,"locations":[{"id":"doi:10.1109/isit.2015.7282516","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2015.7282516","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1503.07236","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.07236","pdf_url":"https://arxiv.org/pdf/1503.07236","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":"mag:1839382729","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1503.07236.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":"pmh:oai:authors.library.caltech.edu:60805","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/60805/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"},{"id":"doi:10.48550/arxiv.1503.07236","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1503.07236","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:1503.07236","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.07236","pdf_url":"https://arxiv.org/pdf/1503.07236","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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1839382729.pdf","grobid_xml":"https://content.openalex.org/works/W1839382729.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W74946117","https://openalex.org/W271367557","https://openalex.org/W1583497301","https://openalex.org/W1689484996","https://openalex.org/W1976078268","https://openalex.org/W1984277078","https://openalex.org/W1986705681","https://openalex.org/W1997914379","https://openalex.org/W2050556604","https://openalex.org/W2077306951","https://openalex.org/W2089817321","https://openalex.org/W2122932035","https://openalex.org/W2123202508","https://openalex.org/W2164595191","https://openalex.org/W2167077875","https://openalex.org/W2220414877","https://openalex.org/W2554182088","https://openalex.org/W2950623019","https://openalex.org/W2953067105","https://openalex.org/W2964312599","https://openalex.org/W3103542348","https://openalex.org/W3124617746","https://openalex.org/W6610006199","https://openalex.org/W6637422517","https://openalex.org/W6638355909","https://openalex.org/W6638662542","https://openalex.org/W6644162585"],"related_works":["https://openalex.org/W2962776339","https://openalex.org/W1976078268","https://openalex.org/W2160051394","https://openalex.org/W2123202508","https://openalex.org/W2755876586","https://openalex.org/W3100056384","https://openalex.org/W2121716262","https://openalex.org/W2944860406","https://openalex.org/W2963859534","https://openalex.org/W2026686855","https://openalex.org/W2067157583","https://openalex.org/W2017304912","https://openalex.org/W3084552781","https://openalex.org/W2164595191","https://openalex.org/W2951002937","https://openalex.org/W2939812605","https://openalex.org/W2544357824","https://openalex.org/W2975231158","https://openalex.org/W2055602229","https://openalex.org/W2082324409"],"abstract_inverted_index":{"Recently,":[0],"the":[1,5,39,73,77,87,91,105,118,123,135,148,172],"precise":[2],"performance":[3,75,121],"of":[4,41,61,76,79,90,99,122,140,164],"Generalized":[6,92],"LASSO":[7,93],"algorithm":[8],"for":[9,58],"recovering":[10],"structured":[11],"signals":[12],"from":[13],"compressed":[14],"noisy":[15],"measurements,":[16],"obtained":[17],"via":[18],"i.i.d.":[19],"Gaussian":[20,43,51,112,152],"matrices,":[21],"has":[22],"been":[23,66],"characterized.":[24],"The":[25],"analysis":[26],"is":[27,145,175],"based":[28],"on":[29,38,50,134,151],"a":[30,47,54,96],"framework":[31,174],"introduced":[32],"by":[33],"Stojnic":[34],"and":[35,94,166],"heavily":[36],"relies":[37],"use":[40],"Gordon's":[42],"min-max":[44],"theorem":[45],"(GMT),":[46],"comparison":[48],"principle":[49],"processes.":[52],"As":[53],"result,":[55,128],"corresponding":[56,74,149],"characterizations":[57],"other":[59],"ensembles":[60],"measurement":[62],"matrices":[63,161],"have":[64],"not":[65],"developed.":[67],"In":[68],"this":[69],"work,":[70],"we":[71,158],"analyze":[72],"ensemble":[78],"isotropically":[80],"random":[81],"orthogonal":[82],"(i.r.o.)":[83],"measurements.":[84],"We":[85],"consider":[86],"constrained":[88],"version":[89],"derive":[95],"sharp":[97],"characterization":[98],"its":[100,111],"normalized":[101],"squared":[102],"error":[103],"in":[104,120,162],"large-system":[106],"limit.":[107],"When":[108],"compared":[109],"to":[110],"counterpart,":[113],"our":[114,156],"result":[115],"analytically":[116],"confirms":[117],"superiority":[119],"i.r.o.":[124,141,160],"ensemble.":[125],"Our":[126],"second":[127],"derives":[129],"an":[130],"asymptotic":[131],"lower":[132],"bound":[133,144,150],"minimum":[136],"conic":[137],"singular":[138],"values":[139],"matrices.":[142,153],"This":[143],"larger":[146],"than":[147],"To":[154],"prove":[155],"results":[157],"express":[159],"terms":[163],"Gaussians":[165],"show":[167],"that,":[168],"with":[169],"some":[170],"modifications,":[171],"GMT":[173],"still":[176],"applicable.":[177]},"counts_by_year":[],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}