{"id":"https://openalex.org/W2109379066","doi":"https://doi.org/10.1109/tit.2010.2059891","title":"Information Theoretic Bounds for Compressed Sensing","display_name":"Information Theoretic Bounds for Compressed Sensing","publication_year":2010,"publication_date":"2010-09-15","ids":{"openalex":"https://openalex.org/W2109379066","doi":"https://doi.org/10.1109/tit.2010.2059891","mag":"2109379066"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2010.2059891","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2059891","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0804.3439","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Shuchin Aeron","orcid":null},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shuchin Aeron","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA","institution_ids":["https://openalex.org/I111088046"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Venkatesh Saligrama","orcid":null},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Venkatesh Saligrama","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA","institution_ids":["https://openalex.org/I111088046"]}]},{"author_position":"last","author":{"id":null,"display_name":"Manqi Zhao","orcid":null},"institutions":[{"id":"https://openalex.org/I111088046","display_name":"Boston University","ror":"https://ror.org/05qwgg493","country_code":"US","type":"education","lineage":["https://openalex.org/I111088046"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Manqi Zhao","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA","institution_ids":["https://openalex.org/I111088046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I111088046"],"apc_list":null,"apc_paid":null,"fwci":18.1907,"has_fulltext":false,"cited_by_count":133,"citation_normalized_percentile":{"value":0.99576295,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"56","issue":"10","first_page":"5111","last_page":"5130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9620000123977661,"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":0.9620000123977661,"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/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.011599999852478504,"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"}},{"id":"https://openalex.org/T10964","display_name":"Wireless Communication Security Techniques","score":0.00419999985024333,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.6126999855041504},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.5680000185966492},{"id":"https://openalex.org/keywords/distortion","display_name":"Distortion (music)","score":0.5616999864578247},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5526000261306763},{"id":"https://openalex.org/keywords/noise-measurement","display_name":"Noise measurement","score":0.504800021648407},{"id":"https://openalex.org/keywords/superposition-principle","display_name":"Superposition principle","score":0.487199991941452},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4487999975681305},{"id":"https://openalex.org/keywords/signal-to-noise-ratio","display_name":"Signal-to-noise ratio (imaging)","score":0.39959999918937683},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.3905999958515167}],"concepts":[{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6126999855041504},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.5680000185966492},{"id":"https://openalex.org/C126780896","wikidata":"https://www.wikidata.org/wiki/Q899871","display_name":"Distortion (music)","level":4,"score":0.5616999864578247},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5526000261306763},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5260000228881836},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.504800021648407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49050000309944153},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.487199991941452},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4487999975681305},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.39959999918937683},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3991999924182892},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.38989999890327454},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.3707999885082245},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.3628000020980835},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.32019999623298645},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C137270730","wikidata":"https://www.wikidata.org/wiki/Q120811","display_name":"Detection theory","level":3,"score":0.27570000290870667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2750999927520752},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2750000059604645},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C181789720","wikidata":"https://www.wikidata.org/wiki/Q4812191","display_name":"Asymptotically optimal algorithm","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.2653000056743622}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2010.2059891","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2010.2059891","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0804.3439","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0804.3439","pdf_url":"https://arxiv.org/pdf/0804.3439","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:0804.3439","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0804.3439","pdf_url":"https://arxiv.org/pdf/0804.3439","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1674742109","https://openalex.org/W2044199623","https://openalex.org/W2068691159","https://openalex.org/W2082102720","https://openalex.org/W2085000883","https://openalex.org/W2099111195","https://openalex.org/W2104357403","https://openalex.org/W2115447612","https://openalex.org/W2118040894","https://openalex.org/W2120327124","https://openalex.org/W2124140026","https://openalex.org/W2127300249","https://openalex.org/W2129131372","https://openalex.org/W2129638195","https://openalex.org/W2130199634","https://openalex.org/W2141556672","https://openalex.org/W2142337526","https://openalex.org/W2158973156","https://openalex.org/W2161279573","https://openalex.org/W4235461144","https://openalex.org/W4250955649"],"related_works":[],"abstract_inverted_index":{"In":[0,129,219],"this":[1,131],"paper,":[2],"we":[3,116,174,225,269,278],"derive":[4,98,113,275],"information":[5],"theoretic":[6],"performance":[7,242],"bounds":[8],"to":[9,60,70,97,158,211,282,285,307],"sensing":[10],"and":[11,33,54,68,77,106,156,189,258,265,289,313],"reconstruction":[12],"of":[13,48,64,94,104,152,162,180,200,234,261,302,316,329,337],"sparse":[14,339],"phenomena":[15],"from":[16],"noisy":[17],"projections.":[18],"We":[19,44,82,90,292,321],"consider":[20,45,83,270],"two":[21,46],"settings:":[22],"output":[23,171,266],"noise":[24,28,35,39,172,223,267],"models":[25,36],"where":[26,37],"the":[27,31,38,42,62,102,139,150,153,215,232,248,251,300,314,327,334,338],"enters":[29,40],"after":[30],"projection":[32],"input":[34,222,264],"before":[41],"projection.":[43],"types":[47],"distortion":[49,74,304,312],"for":[50,109,191,221,243,263],"reconstruction:":[51],"support":[52,84,136,193,201,228],"errors":[53,85,137,202],"mean-squared":[55,311],"errors.":[56],"Our":[57],"goal":[58],"is":[59,187],"relate":[61],"number":[63,103,233,260,315,328],"measurements,":[65],"m":[66],",":[67],"SNR,":[69],"signal":[71,78],"sparsity,":[72],"k,":[73],"level,":[75],"d,":[76],"dimension,":[79],"n":[80],".":[81],"in":[86,214],"a":[87,125,159,197,206,271,295],"worst-case":[88,252],"setting.":[89],"employ":[91],"different":[92],"variations":[93],"Fano's":[95,283],"inequality":[96,284],"necessary":[99,188,276],"conditions":[100],"on":[101,120,124],"measurements":[105,186,235,262,317,330],"SNR":[107,179,208,257,326],"required":[108],"exact":[110,192],"reconstruction.":[111],"To":[112,274],"sufficient":[114,190,213],"conditions,":[115,277],"develop":[117,279,294],"new":[118,296],"insights":[119],"max-likelihood":[121,297],"analysis":[122,146,161,298],"based":[123],"novel":[126,280],"superposition":[127],"property.":[128],"particular,":[130],"property":[132],"implies":[133],"that":[134,176,227,250,323],"small":[135,198],"are":[138],"dominant":[140],"error":[141],"events.":[142],"Consequently,":[143],"our":[144],"ML":[145],"does":[147],"not":[148],"suffer":[149],"conservatism":[151],"union":[154],"bound":[155],"leads":[157],"tighter":[160],"max-likelihood.":[163],"These":[164],"results":[165],"provide":[166],"order-wise":[167],"tight":[168],"bounds.":[169],"For":[170],"models,":[173,224,268],"show":[175,226,322],"asymptotically":[177],"an":[178],"((n))":[181],"together":[182],"with":[183,324,333],"(k":[184],"(n/k))":[185],"recovery.":[194],"Furthermore,":[195],"if":[196,231],"fraction":[199],"can":[203],"be":[204,212],"tolerated,":[205],"constant":[207,325],"turns":[209],"out":[210],"linear":[216],"sparsity":[217],"regime.":[218],"contrast":[220],"recovery":[229],"fails":[230],"scales":[236,331],"as":[237],"o(n(n)/SNR),":[238],"implying":[239],"poor":[240],"compression":[241],"such":[244],"cases.":[245],"Motivated":[246],"by":[247],"fact":[249],"setup":[253],"requires":[254],"significantly":[255],"high":[256],"substantial":[259],"Bayesian":[272],"setup.":[273],"extensions":[281],"handle":[286],"continuous":[287],"domains":[288],"arbitrary":[290],"distortions.":[291],"then":[293],"over":[299],"set":[301],"rate":[303],"quantization":[305],"points":[306],"characterize":[308],"tradeoffs":[309],"between":[310],"using":[318],"rate-distortion":[319,335],"theory.":[320],"linearly":[332],"function":[336],"phenomena.":[340]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":21},{"year":2012,"cited_by_count":24}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2016-06-24T00:00:00"}
