{"id":"https://openalex.org/W2123457453","doi":"https://doi.org/10.1109/tsp.2011.2112650","title":"Sensitivity to Basis Mismatch in Compressed Sensing","display_name":"Sensitivity to Basis Mismatch in Compressed Sensing","publication_year":2011,"publication_date":"2011-02-11","ids":{"openalex":"https://openalex.org/W2123457453","doi":"https://doi.org/10.1109/tsp.2011.2112650","mag":"2123457453"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2011.2112650","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2112650","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","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/A5053809095","display_name":"Yuejie Chi","orcid":"https://orcid.org/0000-0002-6766-5459"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yuejie Chi","raw_affiliation_strings":["Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080469112","display_name":"Louis L. Scharf","orcid":"https://orcid.org/0000-0003-1764-9335"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Louis L. Scharf","raw_affiliation_strings":["Department of Electrical and Computer Engineering, and the Department of Statistics, Colorado State University, Fort Collins, CO, USA","Dept. of Electr. and Comput. Eng., Colorado State Univ., Fort Collins, CO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, and the Department of Statistics, Colorado State University, Fort Collins, CO, USA","institution_ids":["https://openalex.org/I92446798"]},{"raw_affiliation_string":"Dept. of Electr. and Comput. Eng., Colorado State Univ., Fort Collins, CO, USA","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028995727","display_name":"Ali Pezeshki","orcid":"https://orcid.org/0000-0002-7142-5685"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ali Pezeshki","raw_affiliation_strings":["Department of Electrical and Computer Engineering, and the Department of Statistics, Colorado State University, Fort Collins, CO, USA","Dept. of Electr. and Comput. Eng., Colorado State Univ., Fort Collins, CO, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, and the Department of Statistics, Colorado State University, Fort Collins, CO, USA","institution_ids":["https://openalex.org/I92446798"]},{"raw_affiliation_string":"Dept. of Electr. and Comput. Eng., Colorado State Univ., Fort Collins, CO, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111958277","display_name":"A.R. Calderbank","orcid":null},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Robert Calderbank","raw_affiliation_strings":["Department of Computer Science, Duke University, Durham, NC, USA","Dept. of Comput. Sci., Duke Univ., Durham, NC, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Duke University, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]},{"raw_affiliation_string":"Dept. of Comput. Sci., Duke Univ., Durham, NC, USA#TAB#","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5053809095"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":55.2808,"has_fulltext":false,"cited_by_count":907,"citation_normalized_percentile":{"value":0.99956899,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"59","issue":"5","first_page":"2182","last_page":"2195"},"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9976000189781189,"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/compressed-sensing","display_name":"Compressed sensing","score":0.7401869893074036},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.7154561877250671},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.555975615978241},{"id":"https://openalex.org/keywords/basis-pursuit","display_name":"Basis pursuit","score":0.5248113870620728},{"id":"https://openalex.org/keywords/radar","display_name":"Radar","score":0.49571311473846436},{"id":"https://openalex.org/keywords/sonar","display_name":"Sonar","score":0.4799090325832367},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4535055160522461},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.4444027543067932},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4383164942264557},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4139976501464844},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.34747225046157837},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30890583992004395},{"id":"https://openalex.org/keywords/matching-pursuit","display_name":"Matching pursuit","score":0.2705267071723938},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13625669479370117},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.11274805665016174},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10844665765762329}],"concepts":[{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.7401869893074036},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.7154561877250671},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.555975615978241},{"id":"https://openalex.org/C99217422","wikidata":"https://www.wikidata.org/wiki/Q4867576","display_name":"Basis pursuit","level":4,"score":0.5248113870620728},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.49571311473846436},{"id":"https://openalex.org/C555745239","wikidata":"https://www.wikidata.org/wiki/Q133220","display_name":"Sonar","level":2,"score":0.4799090325832367},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4535055160522461},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4444027543067932},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4383164942264557},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4139976501464844},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.34747225046157837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30890583992004395},{"id":"https://openalex.org/C156872377","wikidata":"https://www.wikidata.org/wiki/Q6786281","display_name":"Matching pursuit","level":3,"score":0.2705267071723938},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13625669479370117},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.11274805665016174},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10844665765762329},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2011.2112650","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2011.2112650","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W126755431","https://openalex.org/W653761051","https://openalex.org/W1618478980","https://openalex.org/W1981745143","https://openalex.org/W1983749341","https://openalex.org/W1988828143","https://openalex.org/W1991091427","https://openalex.org/W1999955334","https://openalex.org/W2015418199","https://openalex.org/W2026276849","https://openalex.org/W2030449718","https://openalex.org/W2033332370","https://openalex.org/W2050994160","https://openalex.org/W2089957712","https://openalex.org/W2091256848","https://openalex.org/W2095978736","https://openalex.org/W2096650463","https://openalex.org/W2097816293","https://openalex.org/W2104266187","https://openalex.org/W2110140246","https://openalex.org/W2114832444","https://openalex.org/W2116148865","https://openalex.org/W2119667497","https://openalex.org/W2120991191","https://openalex.org/W2121194215","https://openalex.org/W2128131274","https://openalex.org/W2129131372","https://openalex.org/W2129638195","https://openalex.org/W2133285942","https://openalex.org/W2134033146","https://openalex.org/W2137628444","https://openalex.org/W2138857456","https://openalex.org/W2140122025","https://openalex.org/W2140466267","https://openalex.org/W2145096794","https://openalex.org/W2148469899","https://openalex.org/W2154332973","https://openalex.org/W2156377127","https://openalex.org/W2162654459","https://openalex.org/W2169411722","https://openalex.org/W2170929819","https://openalex.org/W2289917018","https://openalex.org/W2296616510","https://openalex.org/W2477424298","https://openalex.org/W2538726670","https://openalex.org/W3112177775","https://openalex.org/W3147705998","https://openalex.org/W4246841922","https://openalex.org/W4250955649","https://openalex.org/W4252734343","https://openalex.org/W6648381281","https://openalex.org/W6656846733","https://openalex.org/W6677362584","https://openalex.org/W6679865946"],"related_works":["https://openalex.org/W2199748221","https://openalex.org/W3088606048","https://openalex.org/W2169904627","https://openalex.org/W2436826437","https://openalex.org/W2952153915","https://openalex.org/W4289259997","https://openalex.org/W2330143608","https://openalex.org/W4300448317","https://openalex.org/W2562633204","https://openalex.org/W2388133936"],"abstract_inverted_index":{"The":[0],"theory":[1],"of":[2,9,12,58,130,155,174,208,273,284,300,317,361],"compressed":[3,156,355],"sensing":[4,157,356],"suggests":[5],"that":[6,64,218,262,295,345],"successful":[7],"inversion":[8,353],"an":[10,70,334],"image":[11,66,225,352],"the":[13,55,65,104,119,122,128,131,140,143,153,161,164,172,178,200,209,224,230,234,250,263,271,282,298,314,359],"physical":[14,99],"world":[15],"(broadly":[16],"defined":[17],"to":[18,90,158,189,290,368],"include":[19],"speech":[20],"signals,":[21],"radar/sonar":[22],"returns,":[23],"vibration":[24],"records,":[25],"sensor":[26],"array":[27],"snapshot":[28],"vectors,":[29],"2-D":[30],"images,":[31],"and":[32,39,80,82,134,142,163,216,229,236,370],"so":[33],"on)":[34],"for":[35,146,199,239,249,307,351,364],"its":[36,308],"source":[37],"modes":[38],"amplitudes":[40],"can":[41],"be":[42,52,91],"achieved":[43],"at":[44],"measurement":[45],"dimensions":[46],"far":[47],"lower":[48],"than":[49],"what":[50],"might":[51],"expected":[53],"from":[54,325,354],"classical":[56],"theories":[57],"spectrum":[59,78],"or":[60,107],"modal":[61],"analysis,":[62,79],"provided":[63],"is":[67,87,101,137,187],"sparse":[68,102,192,264,292,331],"in":[69,77,96,103,108,127,270,281,320,358],"apriori":[71,110],"known":[72,111],"basis.":[73,94,112],"For":[74],"imaging":[75],"problems":[76],"passive":[81],"active":[83],"radar/sonar,":[84],"this":[85,149],"basis":[86,106,175,251,274,285,318,362],"usually":[88],"taken":[89],"a":[92,330,347],"DFT":[93,105,327],"However,":[95],"reality":[97],"no":[98],"field":[100],"any":[109,291],"No":[113],"matter":[114],"how":[115],"finely":[116],"we":[117,151,277],"grid":[118,132],"parameter":[120],"space":[121],"sources":[123],"may":[124,266],"not":[125],"lie":[126],"center":[129],"cells":[133],"consequently":[135],"there":[136],"mismatch":[138,159,176,231,319],"between":[139,160,233],"assumed":[141,162,235],"actual":[144,165,237],"bases":[145,238],"sparsity.":[147,240],"In":[148],"paper,":[150],"study":[152],"sensitivity":[154],"sparsity":[166],"bases.":[167],"We":[168,195,241,311,337],"start":[169],"by":[170,342],"analyzing":[171],"effect":[173],"on":[177,297],"best":[179,210,301],"<i":[180,201,211,253,302],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[181,202,205,212,254,257,303],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">k</i>":[182,213,304],"-term":[183,214,305],"approximation":[184,215],"error,":[185,260],"which":[186],"central":[188],"providing":[190],"exact":[191],"recovery":[193,259,265,293],"guarantees.":[194,310],"establish":[196],"achievable":[197],"bounds":[198,220],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">l</i>":[203,255],"<sub":[204,256],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[206,258],"error":[207],"show":[217],"these":[219],"grow":[221],"linearly":[222],"with":[223,245],"(or":[226],"grid)":[227],"dimension":[228],"level":[232],"then":[242],"derive":[243],"bounds,":[244],"similar":[246],"growth":[247],"behavior,":[248],"pursuit":[252],"indicating":[261],"suffer":[267],"large":[268],"errors":[269],"presence":[272,360],"mismatch.":[275],"Although,":[276],"present":[278],"our":[279,287,339],"results":[280],"context":[283],"pursuit,":[286],"analysis":[288,341],"applies":[289],"principle":[294],"relies":[296],"accuracy":[299],"approximations":[306],"performance":[309,349],"particularly":[312],"highlight":[313],"problematic":[315],"nature":[316],"Fourier":[321],"imaging,":[322],"where":[323],"spillage":[324],"off-grid":[326],"components":[328],"turns":[329],"representation":[332],"into":[333],"incompressible":[335],"one.":[336],"substantiate":[338],"mathematical":[340],"numerical":[343],"examples":[344],"demonstrate":[346],"considerable":[348],"degradation":[350],"measurements":[357],"mismatch,":[363],"problem":[365],"sizes":[366],"common":[367],"radar":[369],"sonar.":[371]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":46},{"year":2024,"cited_by_count":52},{"year":2023,"cited_by_count":44},{"year":2022,"cited_by_count":38},{"year":2021,"cited_by_count":101},{"year":2020,"cited_by_count":68},{"year":2019,"cited_by_count":88},{"year":2018,"cited_by_count":72},{"year":2017,"cited_by_count":81},{"year":2016,"cited_by_count":77},{"year":2015,"cited_by_count":78},{"year":2014,"cited_by_count":65},{"year":2013,"cited_by_count":56},{"year":2012,"cited_by_count":28}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}