{"id":"https://openalex.org/W4312783285","doi":"https://doi.org/10.1109/jsait.2022.3220196","title":"A Coherence Parameter Characterizing Generative Compressed Sensing With Fourier Measurements","display_name":"A Coherence Parameter Characterizing Generative Compressed Sensing With Fourier Measurements","publication_year":2022,"publication_date":"2022-09-01","ids":{"openalex":"https://openalex.org/W4312783285","doi":"https://doi.org/10.1109/jsait.2022.3220196"},"language":"en","primary_location":{"id":"doi:10.1109/jsait.2022.3220196","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsait.2022.3220196","pdf_url":null,"source":{"id":"https://openalex.org/S4210211895","display_name":"IEEE Journal on Selected Areas in Information Theory","issn_l":"2641-8770","issn":["2641-8770"],"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 Journal on Selected Areas in Information Theory","raw_type":"journal-article"},"type":"article","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/A5018942420","display_name":"Aaron Berk","orcid":"https://orcid.org/0000-0001-9255-7030"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Aaron Berk","raw_affiliation_strings":["Department of Mathematics and Statistics, McGill University, Montreal, Canada"],"raw_orcid":"https://orcid.org/0000-0001-9255-7030","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McGill University, Montreal, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001768471","display_name":"Simone Brugiapaglia","orcid":"https://orcid.org/0000-0003-1927-8232"},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Simone Brugiapaglia","raw_affiliation_strings":["Department of Mathematics and Statistics, Concordia University, Montr&#x00E9;al, Canada"],"raw_orcid":"https://orcid.org/0000-0003-1927-8232","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Concordia University, Montr&#x00E9;al, Canada","institution_ids":["https://openalex.org/I60158472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078098304","display_name":"Babhru Joshi","orcid":"https://orcid.org/0000-0002-5187-6729"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Babhru Joshi","raw_affiliation_strings":["Department of Mathematics, The University of British Columbia, Vancouver, Canada"],"raw_orcid":"https://orcid.org/0000-0002-5187-6729","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of British Columbia, Vancouver, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018866413","display_name":"Yaniv Plan","orcid":"https://orcid.org/0000-0002-9930-0980"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yaniv Plan","raw_affiliation_strings":["Department of Mathematics, The University of British Columbia, Vancouver, Canada"],"raw_orcid":"https://orcid.org/0000-0002-9930-0980","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of British Columbia, Vancouver, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101898266","display_name":"Matthew Scott","orcid":"https://orcid.org/0000-0001-7761-6813"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Matthew Scott","raw_affiliation_strings":["Department of Mathematics, The University of British Columbia, Vancouver, Canada"],"raw_orcid":"https://orcid.org/0000-0001-7761-6813","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of British Columbia, Vancouver, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001594301","display_name":"\u00d6zg\u00fcr Y\u0131lmaz","orcid":"https://orcid.org/0000-0002-4349-3859"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"\u00d6zg\u00fcr Yilmaz","raw_affiliation_strings":["Department of Mathematics, The University of British Columbia, Vancouver, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of British Columbia, Vancouver, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5018942420"],"corresponding_institution_ids":["https://openalex.org/I5023651"],"apc_list":null,"apc_paid":null,"fwci":0.6645,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63392288,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"3","issue":"3","first_page":"502","last_page":"512"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9993000030517578,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.9975000023841858,"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/compressed-sensing","display_name":"Compressed sensing","score":0.8571398258209229},{"id":"https://openalex.org/keywords/restricted-isometry-property","display_name":"Restricted isometry property","score":0.7983607649803162},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.6102298498153687},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5631389021873474},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5177751779556274},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4924863278865814},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4688274562358856},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.45893168449401855},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.4439353942871094},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4395678639411926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4382333755493164},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.345450222492218},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2999522089958191},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.20197793841362},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15006116032600403}],"concepts":[{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.8571398258209229},{"id":"https://openalex.org/C17902559","wikidata":"https://www.wikidata.org/wiki/Q17099734","display_name":"Restricted isometry property","level":3,"score":0.7983607649803162},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.6102298498153687},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5631389021873474},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5177751779556274},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4924863278865814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4688274562358856},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.45893168449401855},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.4439353942871094},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4395678639411926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4382333755493164},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.345450222492218},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2999522089958191},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.20197793841362},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15006116032600403},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/jsait.2022.3220196","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jsait.2022.3220196","pdf_url":null,"source":{"id":"https://openalex.org/S4210211895","display_name":"IEEE Journal on Selected Areas in Information Theory","issn_l":"2641-8770","issn":["2641-8770"],"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 Journal on Selected Areas in Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3829723756","display_name":null,"funder_award_id":"22R82411","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G4608520657","display_name":null,"funder_award_id":"RGPIN-2020-06766","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G524336552","display_name":null,"funder_award_id":"GR009284","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G7956423903","display_name":null,"funder_award_id":"GR007657","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320310984","display_name":"Pacific Institute for the Mathematical Sciences","ror":"https://ror.org/04w49dw51"},{"id":"https://openalex.org/F4320314331","display_name":"Centre de Recherches Math\u00e9matiques","ror":null},{"id":"https://openalex.org/F4320321588","display_name":"Concordia University","ror":"https://ror.org/0420zvk78"},{"id":"https://openalex.org/F4320330273","display_name":"Institut de Valorisation des Donn\u00e9es","ror":null},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W143004564","https://openalex.org/W641843003","https://openalex.org/W1522301498","https://openalex.org/W1959608418","https://openalex.org/W2007339694","https://openalex.org/W2011249813","https://openalex.org/W2029816571","https://openalex.org/W2055064119","https://openalex.org/W2109357213","https://openalex.org/W2119745496","https://openalex.org/W2137198385","https://openalex.org/W2145096794","https://openalex.org/W2154332973","https://openalex.org/W2194493324","https://openalex.org/W2284492459","https://openalex.org/W2288884963","https://openalex.org/W2480981092","https://openalex.org/W2786622092","https://openalex.org/W2787248994","https://openalex.org/W2801128564","https://openalex.org/W2883105305","https://openalex.org/W2898001268","https://openalex.org/W2946850335","https://openalex.org/W2948978827","https://openalex.org/W2963684088","https://openalex.org/W2966291568","https://openalex.org/W2967360854","https://openalex.org/W3003257820","https://openalex.org/W3003739484","https://openalex.org/W3012324700","https://openalex.org/W3035300465","https://openalex.org/W3128734291","https://openalex.org/W3163516179","https://openalex.org/W3188455524","https://openalex.org/W3211913805","https://openalex.org/W4206305733","https://openalex.org/W4212998291","https://openalex.org/W4213173722","https://openalex.org/W4250955649","https://openalex.org/W4281838023","https://openalex.org/W4286889237","https://openalex.org/W4287029002","https://openalex.org/W4294576319","https://openalex.org/W4298857773","https://openalex.org/W4300634415","https://openalex.org/W4301028776","https://openalex.org/W4312560805","https://openalex.org/W4318954422","https://openalex.org/W4320013936","https://openalex.org/W6631190155","https://openalex.org/W6640963894","https://openalex.org/W6677788992","https://openalex.org/W6685352114","https://openalex.org/W6735307612","https://openalex.org/W6745505307","https://openalex.org/W6746466744","https://openalex.org/W6748230616","https://openalex.org/W6753037639","https://openalex.org/W6755694737","https://openalex.org/W6762374284","https://openalex.org/W6773527042","https://openalex.org/W6799926150","https://openalex.org/W6802535065","https://openalex.org/W6804080674","https://openalex.org/W6839014182"],"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/W2568623927","https://openalex.org/W2952050240","https://openalex.org/W2085436476","https://openalex.org/W2025666718"],"abstract_inverted_index":{"In":[0],"Bora":[1],"et":[2,121],"al.":[3],"(2017),":[4],"a":[5,31,56,78,86,136,169,216],"mathematical":[6],"framework":[7],"was":[8],"developed":[9],"for":[10,98,172,204,219],"compressed":[11,39,100],"sensing":[12,40,101],"guarantees":[13],"in":[14],"the":[15,18,24,28,49,62,92,131,141,144,147,150,180],"setting":[16],"where":[17],"measurement":[19,50,66,151,181],"matrix":[20,51,80],"is":[21,27,128],"Gaussian":[22],"and":[23,106,149,160],"signal":[25,205],"structure":[26],"range":[29,145],"of":[30,38,77,119,146],"generative":[32,99],"neural":[33],"network":[34,53,148],"(GNN).":[35],"The":[36],"problem":[37,118],"with":[41,103,110,179,209,222],"GNNs":[42,174],"has":[43],"since":[44],"been":[45],"extensively":[46],"analyzed":[47],"when":[48],"and/or":[52],"weights":[54],"follow":[55],"subgaussian":[57,63],"distribution.":[58],"We":[59,183],"move":[60],"beyond":[61],"assumption,":[64],"to":[65,163,175],"matrices":[67],"that":[68,188,200],"are":[69],"derived":[70],"by":[71,130],"sampling":[72],"uniformly":[73],"at":[74],"random":[75],"rows":[76],"unitary":[79],"(including":[81],"subsampled":[82,104,223],"Fourier":[83],"measurements":[84,203],"as":[85,215],"special":[87],"case).":[88],"Specifically,":[89],"we":[90,167],"prove":[91],"first":[93],"known":[94],"restricted":[95],"isometry":[96],"guarantee":[97],"(GCS)":[102],"isometries,":[105],"provide":[107,184],"recovery":[108],"bounds":[109],"nearly":[111],"order-optimal":[112],"sample":[113],"complexity,":[114],"addressing":[115],"an":[116],"open":[117],"(Scarlett":[120],"al.,":[122],"2022,":[123],"p.":[124],"10).":[125],"Recovery":[126],"efficacy":[127],"characterized":[129],"<italic":[132],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[133],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">coherence</i>":[134],",":[135],"new":[137],"parameter,":[138],"which":[139],"measures":[140],"interplay":[142],"between":[143],"matrix.":[152],"Our":[153],"approach":[154],"relies":[155],"on":[156],"subspace":[157],"counting":[158],"arguments":[159],"ideas":[161],"central":[162],"high-dimensional":[164],"probability.":[165],"Furthermore,":[166],"propose":[168],"regularization":[170],"strategy":[171,195],"training":[173,192],"have":[176],"favourable":[177],"coherence":[178,198,214],"operator.":[182],"compelling":[185],"numerical":[186],"simulations":[187],"support":[189],"this":[190],"regularized":[191],"strategy:":[193],"our":[194,210],"yields":[196],"low":[197],"networks":[199],"require":[201],"fewer":[202],"recovery.":[206],"This,":[207],"together":[208],"theoretical":[211],"results,":[212],"supports":[213],"natural":[217],"quantity":[218],"characterizing":[220],"GCS":[221],"isometries.":[224]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
