{"id":"https://openalex.org/W2143466876","doi":"https://doi.org/10.1109/allerton.2012.6483297","title":"Compressive sensing off the grid","display_name":"Compressive sensing off the grid","publication_year":2012,"publication_date":"2012-10-01","ids":{"openalex":"https://openalex.org/W2143466876","doi":"https://doi.org/10.1109/allerton.2012.6483297","mag":"2143466876"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2012.6483297","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2012.6483297","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","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/A5101848896","display_name":"Gongguo Tang","orcid":"https://orcid.org/0000-0002-7879-1338"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Gongguo Tang","raw_affiliation_strings":["University of Wisconsin-Madison, USA","University of Wisconsin, Madison"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin, Madison","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016309034","display_name":"Badri Narayan Bhaskar","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Badri Narayan Bhaskar","raw_affiliation_strings":["University of Wisconsin-Madison, USA","University of Wisconsin, Madison"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin, Madison","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103253365","display_name":"Parikshit Shah","orcid":"https://orcid.org/0009-0000-3019-2144"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Parikshit Shah","raw_affiliation_strings":["University of Wisconsin-Madison, USA","University of Wisconsin, Madison"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin, Madison","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012870568","display_name":"Benjamin Recht","orcid":"https://orcid.org/0000-0002-0293-593X"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Benjamin Recht","raw_affiliation_strings":["University of Wisconsin-Madison, USA","University of Wisconsin, Madison"],"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison, USA","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin, Madison","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101848896"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":9.6005,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.98662117,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"1","issue":null,"first_page":"778","last_page":"785"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.8437495231628418},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6692919731140137},{"id":"https://openalex.org/keywords/basis-pursuit","display_name":"Basis pursuit","score":0.6435369253158569},{"id":"https://openalex.org/keywords/nyquist\u2013shannon-sampling-theorem","display_name":"Nyquist\u2013Shannon sampling theorem","score":0.579101026058197},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5354976654052734},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.4743282198905945},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.45400193333625793},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.45196446776390076},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4372766613960266},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.43695706129074097},{"id":"https://openalex.org/keywords/undersampling","display_name":"Undersampling","score":0.4263169467449188},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39187514781951904},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37176254391670227},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36462754011154175},{"id":"https://openalex.org/keywords/matching-pursuit","display_name":"Matching pursuit","score":0.24399110674858093},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19788473844528198},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10367697477340698},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.08774891495704651}],"concepts":[{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.8437495231628418},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6692919731140137},{"id":"https://openalex.org/C99217422","wikidata":"https://www.wikidata.org/wiki/Q4867576","display_name":"Basis pursuit","level":4,"score":0.6435369253158569},{"id":"https://openalex.org/C288623","wikidata":"https://www.wikidata.org/wiki/Q679800","display_name":"Nyquist\u2013Shannon sampling theorem","level":2,"score":0.579101026058197},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5354976654052734},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.4743282198905945},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.45400193333625793},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.45196446776390076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4372766613960266},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.43695706129074097},{"id":"https://openalex.org/C136536468","wikidata":"https://www.wikidata.org/wiki/Q1225894","display_name":"Undersampling","level":2,"score":0.4263169467449188},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39187514781951904},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37176254391670227},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36462754011154175},{"id":"https://openalex.org/C156872377","wikidata":"https://www.wikidata.org/wiki/Q6786281","display_name":"Matching pursuit","level":3,"score":0.24399110674858093},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19788473844528198},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10367697477340698},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.08774891495704651},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/allerton.2012.6483297","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2012.6483297","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W134544389","https://openalex.org/W171072194","https://openalex.org/W210359992","https://openalex.org/W622930292","https://openalex.org/W1529624360","https://openalex.org/W1542648917","https://openalex.org/W1573820523","https://openalex.org/W1588330761","https://openalex.org/W1680593177","https://openalex.org/W1974718273","https://openalex.org/W1977327182","https://openalex.org/W1980300788","https://openalex.org/W1980610004","https://openalex.org/W1983127118","https://openalex.org/W1986195997","https://openalex.org/W1988828143","https://openalex.org/W2008287878","https://openalex.org/W2008797802","https://openalex.org/W2017154474","https://openalex.org/W2018962290","https://openalex.org/W2025617394","https://openalex.org/W2039479881","https://openalex.org/W2041227508","https://openalex.org/W2065656021","https://openalex.org/W2067161429","https://openalex.org/W2067718036","https://openalex.org/W2068242608","https://openalex.org/W2069798394","https://openalex.org/W2074471762","https://openalex.org/W2078524554","https://openalex.org/W2080855151","https://openalex.org/W2091256848","https://openalex.org/W2103519107","https://openalex.org/W2104266187","https://openalex.org/W2107411554","https://openalex.org/W2109357213","https://openalex.org/W2115366189","https://openalex.org/W2116613037","https://openalex.org/W2118550318","https://openalex.org/W2119667497","https://openalex.org/W2119826715","https://openalex.org/W2120872934","https://openalex.org/W2123457453","https://openalex.org/W2123629701","https://openalex.org/W2133285942","https://openalex.org/W2137540169","https://openalex.org/W2137628444","https://openalex.org/W2140122025","https://openalex.org/W2141116650","https://openalex.org/W2143148420","https://openalex.org/W2145096794","https://openalex.org/W2146678402","https://openalex.org/W2149213383","https://openalex.org/W2149454052","https://openalex.org/W2156377127","https://openalex.org/W2160396672","https://openalex.org/W2163916252","https://openalex.org/W2169811219","https://openalex.org/W2296319761","https://openalex.org/W2296616510","https://openalex.org/W2610857016","https://openalex.org/W2611328865","https://openalex.org/W2951457851","https://openalex.org/W2963087994","https://openalex.org/W2964325628","https://openalex.org/W3098045837","https://openalex.org/W3104501706","https://openalex.org/W3124617746","https://openalex.org/W4243182635","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W3011226087","https://openalex.org/W2212041357","https://openalex.org/W2895530314","https://openalex.org/W3214931932","https://openalex.org/W1959447026","https://openalex.org/W2052082011","https://openalex.org/W2903019797","https://openalex.org/W2218273114","https://openalex.org/W2497512603","https://openalex.org/W2806748726"],"abstract_inverted_index":{"We":[0,53,80],"consider":[1],"the":[2,6,31,47,63,77,82,115,123,135,138,144,155],"problem":[3],"of":[4,9,12,20,137],"estimating":[5],"frequency":[7,49,78,117],"components":[8],"a":[10,17,39,93],"mixture":[11],"s":[13,104,106],"complex":[14],"sinusoids":[15],"from":[16,149],"random":[18,98,109],"subset":[19],"n":[21,108],"regularly":[22],"spaced":[23],"samples.":[24],"Unlike":[25],"previous":[26],"work":[27],"in":[28,46,169,172],"compressive":[29,163],"sensing,":[30],"frequencies":[32,124],"are":[33,111,125,131,177],"not":[34],"assumed":[35],"to":[36,60,75,113,133],"lie":[37],"on":[38,154,161],"grid,":[40],"but":[41],"can":[42],"assume":[43],"any":[44,71],"values":[45],"normalized":[48],"domain":[50],"[0,":[51],"1].":[52],"propose":[54],"an":[55,87],"atomic":[56,83],"norm":[57,84],"minimization":[58,85],"approach":[59,142],"exactly":[61],"recover":[62],"unobserved":[64],"samples,":[65],"which":[66],"is":[67],"then":[68],"followed":[69],"by":[70,151],"linear":[72],"prediction":[73],"method":[74],"identify":[76],"components.":[79],"reformulate":[81],"as":[86],"exact":[88,116],"semidefinite":[89],"program.":[90],"By":[91],"constructing":[92],"dual":[94],"certificate":[95],"polynomial":[96],"using":[97],"kernels,":[99],"we":[100],"show":[101],"that":[102],"roughly":[103],"log":[105,107],"samples":[110],"sufficient":[112],"guarantee":[114],"estimation":[118],"with":[119],"high":[120],"probability,":[121],"provided":[122],"well":[126],"separated.":[127],"Extensive":[128],"numerical":[129],"experiments":[130],"performed":[132],"illustrate":[134],"effectiveness":[136],"proposed":[139],"method.":[140],"Our":[141],"avoids":[143],"basis":[145],"mismatch":[146],"issue":[147],"arising":[148],"discretization":[150],"working":[152],"directly":[153],"continuous":[156],"parameter":[157],"space.":[158],"Potential":[159],"impact":[160],"both":[162],"sensing":[164],"and":[165,175],"line":[166],"spectral":[167],"estimation,":[168],"particular":[170],"implications":[171],"sub-Nyquist":[173],"sampling":[174],"superresolution,":[176],"discussed.":[178]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}