{"id":"https://openalex.org/W2057077945","doi":"https://doi.org/10.1109/isit.2013.6620199","title":"The minimax noise sensitivity in compressed sensing","display_name":"The minimax noise sensitivity in compressed sensing","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W2057077945","doi":"https://doi.org/10.1109/isit.2013.6620199","mag":"2057077945"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2013.6620199","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2013.6620199","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE International Symposium on Information Theory","raw_type":"proceedings-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/A5084396713","display_name":"Galen Reeves","orcid":"https://orcid.org/0000-0003-4230-0688"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Galen Reeves","raw_affiliation_strings":["Department of Statistics, Stanford University, USA","Dept. of Stat., Stanford Univ., Stanford, CA, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Stanford University, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Dept. of Stat., Stanford Univ., Stanford, CA, USA#TAB#","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065355421","display_name":"David L. Donoho","orcid":"https://orcid.org/0000-0003-1830-710X"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Donoho","raw_affiliation_strings":["Department of Statistics, Stanford University, USA","Dept. of Stat., Stanford Univ., Stanford, CA, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Stanford University, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Dept. of Stat., Stanford Univ., Stanford, CA, USA#TAB#","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":2.822,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.89792918,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"28","issue":null,"first_page":"116","last_page":"120"},"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":0.9969000220298767,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.7153709530830383},{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.6398221850395203},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.5767771005630493},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.571422815322876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5571679472923279},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.5088127255439758},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4187491536140442},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41576915979385376},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3551655411720276},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2802255153656006},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09769603610038757}],"concepts":[{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.7153709530830383},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.6398221850395203},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5767771005630493},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.571422815322876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5571679472923279},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.5088127255439758},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4187491536140442},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41576915979385376},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3551655411720276},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2802255153656006},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09769603610038757},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2013.6620199","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2013.6620199","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 IEEE International Symposium on Information Theory","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1560153690","https://openalex.org/W2050556604","https://openalex.org/W2072184935","https://openalex.org/W2085493178","https://openalex.org/W2097323375","https://openalex.org/W2114543434","https://openalex.org/W2116394223","https://openalex.org/W2123202508","https://openalex.org/W2138358551","https://openalex.org/W2164452299","https://openalex.org/W2164595191","https://openalex.org/W2478708596","https://openalex.org/W2550925785","https://openalex.org/W2949898670","https://openalex.org/W2963960675","https://openalex.org/W4205806204","https://openalex.org/W4229746864","https://openalex.org/W4302803504","https://openalex.org/W6729847528"],"related_works":["https://openalex.org/W2016058626","https://openalex.org/W2474724840","https://openalex.org/W2158224665","https://openalex.org/W2895916002","https://openalex.org/W2379589510","https://openalex.org/W1814049089","https://openalex.org/W4300044672","https://openalex.org/W2810730439","https://openalex.org/W1977348009","https://openalex.org/W2572355887"],"abstract_inverted_index":{"Consider":[0],"the":[1,23,30,33,44,49,58,72,81,85,108,131,142,152,165,191,205],"compressed":[2],"sensing":[3,97],"problem":[4],"of":[5,14,26,32,74,186,196,207],"estimating":[6],"an":[7],"unknown":[8],"k-sparse":[9],"n-vector":[10],"from":[11],"a":[12,65,157],"set":[13],"m":[15,115,123],"noisy":[16],"linear":[17],"equations.":[18],"Recent":[19],"work":[20],"focused":[21],"on":[22],"noise":[24,46,110,167],"sensitivity":[25,47,111,168],"particular":[27],"algorithms":[28,56],"-":[29,48],"scaling":[31],"reconstruction":[34],"error":[35],"with":[36],"added":[37],"noise.":[38],"In":[39],"this":[40],"paper,":[41],"we":[42,101],"study":[43,130],"minimax":[45,109,166],"minimum":[50],"is":[51,60,78,112,156,169,177,189],"over":[52,61,204],"all":[53,62,208],"possible":[54],"recovery":[55,75],"and":[57,120,145,162,176,198],"maximum":[59],"vectors":[63],"obeying":[64],"sparsity":[66,153],"constraint.":[67],"This":[68],"fundamental":[69],"quantity":[70],"characterizes":[71],"difficulty":[73],"when":[76],"nothing":[77],"known":[79],"about":[80],"vector":[82],"other":[83],"than":[84],"fact":[86],"that":[87,107,190],"it":[88],"has":[89],"at":[90],"most":[91],"k":[92,117,125],"nonzero":[93],"entries.":[94],"Assuming":[95],"random":[96],"matrices":[98],"(i.i.d.":[99],"Gaussian),":[100],"obtain":[102],"non-asymptotic":[103],"bounds":[104],"which":[105],"show":[106],"finite":[113],"if":[114,122],"\u2265":[116],"+":[118,126],"3":[119],"infinite":[121],"\u2264":[124],"1.":[127],"We":[128],"also":[129],"large":[132],"system":[133],"behavior":[134],"where":[135],"\u03b4":[136,173,181],"=":[137,147],"m/n":[138],"\u2208":[139,149],"(0,1)":[140,150],"denotes":[141,151],"undersampling":[143],"fraction":[144],"k/n":[146],"\u03b5":[148,175],"fraction.":[154],"There":[155],"phase":[158,194],"transition":[159],"separating":[160],"successful":[161],"unsuccessful":[163],"recovery:":[164],"bounded":[170],"for":[171,179],"any":[172,180],">":[174],"unbounded":[178],"<;":[182],"\u03b5.":[183],"One":[184],"consequence":[185],"our":[187],"results":[188],"Bayes":[192],"optimal":[193],"transitions":[195],"Wu":[197],"Verdu":[199],"can":[200],"be":[201],"obtained":[202],"uniformly":[203],"class":[206],"sparse":[209],"vectors.":[210]},"counts_by_year":[{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}