{"id":"https://openalex.org/W2160824952","doi":"https://doi.org/10.1109/tit.2011.2104512","title":"Thresholded Basis Pursuit: LP Algorithm for Order-Wise Optimal Support Recovery for Sparse and Approximately Sparse Signals From Noisy Random Measurements","display_name":"Thresholded Basis Pursuit: LP Algorithm for Order-Wise Optimal Support Recovery for Sparse and Approximately Sparse Signals From Noisy Random Measurements","publication_year":2011,"publication_date":"2011-02-18","ids":{"openalex":"https://openalex.org/W2160824952","doi":"https://doi.org/10.1109/tit.2011.2104512","mag":"2160824952"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2104512","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2104512","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":["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/A5048704387","display_name":"Venkatesh Saligrama","orcid":"https://orcid.org/0000-0002-0675-2268"},"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":"Venkatesh Saligrama","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA","Dept. of Electr. & Comput. Eng., Boston Univ., Boston, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA","institution_ids":["https://openalex.org/I111088046"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Boston Univ., Boston, MA, USA","institution_ids":["https://openalex.org/I111088046"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101551661","display_name":"Manqi Zhao","orcid":"https://orcid.org/0000-0002-5953-0079"},"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","Dept. of Electr. & Comput. Eng., Boston Univ., Boston, MA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Boston University, Boston, MA, USA","institution_ids":["https://openalex.org/I111088046"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Boston Univ., Boston, MA, USA","institution_ids":["https://openalex.org/I111088046"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048704387"],"corresponding_institution_ids":["https://openalex.org/I111088046"],"apc_list":null,"apc_paid":null,"fwci":2.1133,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.87319241,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"57","issue":"3","first_page":"1567","last_page":"1586"},"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":0.9979000091552734,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.6415166854858398},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6008598208427429},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.6005308628082275},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.5679176449775696},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5461477041244507},{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.5083579421043396},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5079630017280579},{"id":"https://openalex.org/keywords/basis-pursuit","display_name":"Basis pursuit","score":0.48902663588523865},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.479796439409256},{"id":"https://openalex.org/keywords/signal-to-noise-ratio","display_name":"Signal-to-noise ratio (imaging)","score":0.47839462757110596},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.43888336420059204},{"id":"https://openalex.org/keywords/signal-reconstruction","display_name":"Signal reconstruction","score":0.4152947962284088},{"id":"https://openalex.org/keywords/contrast","display_name":"Contrast (vision)","score":0.4112662672996521},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.3664688467979431},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.33718010783195496},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31059393286705017},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24590802192687988},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18611544370651245},{"id":"https://openalex.org/keywords/matching-pursuit","display_name":"Matching pursuit","score":0.1499689817428589},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09524181485176086},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.08214700222015381}],"concepts":[{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6415166854858398},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6008598208427429},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.6005308628082275},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.5679176449775696},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5461477041244507},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.5083579421043396},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5079630017280579},{"id":"https://openalex.org/C99217422","wikidata":"https://www.wikidata.org/wiki/Q4867576","display_name":"Basis pursuit","level":4,"score":0.48902663588523865},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.479796439409256},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.47839462757110596},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.43888336420059204},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.4152947962284088},{"id":"https://openalex.org/C2776502983","wikidata":"https://www.wikidata.org/wiki/Q690182","display_name":"Contrast (vision)","level":2,"score":0.4112662672996521},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.3664688467979431},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.33718010783195496},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31059393286705017},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24590802192687988},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18611544370651245},{"id":"https://openalex.org/C156872377","wikidata":"https://www.wikidata.org/wiki/Q6786281","display_name":"Matching pursuit","level":3,"score":0.1499689817428589},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09524181485176086},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.08214700222015381},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2011.2104512","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2104512","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1495421100","https://openalex.org/W1674742109","https://openalex.org/W1762430620","https://openalex.org/W2015418199","https://openalex.org/W2029458236","https://openalex.org/W2030449718","https://openalex.org/W2044199623","https://openalex.org/W2050834445","https://openalex.org/W2068546229","https://openalex.org/W2072184935","https://openalex.org/W2085000883","https://openalex.org/W2109379066","https://openalex.org/W2115139597","https://openalex.org/W2115275122","https://openalex.org/W2115447612","https://openalex.org/W2122548617","https://openalex.org/W2127300249","https://openalex.org/W2129131372","https://openalex.org/W2129638195","https://openalex.org/W2137427562","https://openalex.org/W2145096794","https://openalex.org/W2147656689","https://openalex.org/W2164452299","https://openalex.org/W2289917018","https://openalex.org/W2296616510","https://openalex.org/W2610857016","https://openalex.org/W2963607629","https://openalex.org/W3101762025","https://openalex.org/W3101990100","https://openalex.org/W4229746864","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W2537887767","https://openalex.org/W2388133936","https://openalex.org/W2330143608","https://openalex.org/W2199748221","https://openalex.org/W2436826437","https://openalex.org/W3104324607","https://openalex.org/W2340242818","https://openalex.org/W4317698318","https://openalex.org/W1987102304","https://openalex.org/W3090413343"],"abstract_inverted_index":{"In":[0,189],"this":[1,164],"paper,":[2],"we":[3,114,234],"present":[4],"a":[5,14,61,109,156,158],"linear":[6],"programming":[7],"solution":[8,102],"for":[9,144],"sign":[10,58,106,118,242],"pattern":[11,52,59,107,119,243],"recovery":[12,53,244],"of":[13,22,29,57,60,108,120,174,179,224],"sparse":[15,62,111],"signal,":[16],"x,":[17],"from":[18],"noisy":[19,222],"random":[20,39,49],"projections":[21],"the":[23,38,48,55,75,94,100,105,117,167,225,236],"signal.":[24,63,112],"We":[25,97],"consider":[26],"two":[27],"types":[28],"noise":[30,35,45,71,239],"models:":[31],"input":[32],"noise,":[33,43],"where":[34,44,155],"enters":[36,46],"before":[37,241],"projection,":[40],"and":[41,73,92,135,181,199],"output":[42],"after":[47],"projection.":[50],"Sign":[51],"involves":[54],"estimation":[56],"Our":[64,216],"idea":[65],"is":[66,157,219],"to":[67,191],"pretend":[68],"that":[69,99,116],"no":[70],"exists":[72],"solve":[74],"noiseless":[76,226],"\u2113":[77,227],"<sub":[78,85,228],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[79,86,229],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[80,87,230],"problem,":[81,231],"namely,":[82],"min":[83],"||\u03b2||":[84],"s.t.":[88],"y":[89],"-":[90,132],"G\u03b2":[91],"quantizing":[93],"resulting":[95],"solution.":[96],"show":[98,115],"quantized":[101],"perfectly":[103],"reconstructs":[104],"sufficiently":[110,159],"Specifically,":[113],"an":[121,186],"arbitrary":[122],"k-sparse,":[123],"n-dimensional":[124],"signal":[125,214],"x":[126],"can":[127],"be":[128],"recovered":[129],"with":[130],"SNR":[131],"\u03a9(log":[133],"n)":[134],"measurements":[136],"scaling":[137],"as":[138],"m":[139],"=":[140],"\u038f,(log":[141],"n":[142],"/k)":[143],"all":[145],"sparsity":[146,183,208],"levels":[147,209],"k":[148,152],"satisfying":[149],"0":[150],"<;":[151],"\u2264":[153],"an,":[154],"small":[160],"positive":[161],"constant.":[162],"Surprisingly,":[163],"bound":[165],"matches":[166],"optimal":[168],"Max-Likelihood":[169],"performance":[170],"bounds":[171],"in":[172,185,232],"terms":[173],"SNR,":[175,206],"re":[176],"quired":[177],"number":[178],"measurements,":[180],"admissible":[182,238],"level":[184,240],"order-wise":[187],"sense.":[188],"contrast":[190],"our":[192],"results,":[193],"previous":[194],"results":[195],"based":[196,220],"on":[197,213,221],"LASSO":[198],"Max-Correlation":[200],"techniques":[201],"either":[202],"assume":[203],"significantly":[204],"larger":[205],"sub-linear":[207],"or":[210],"restrictive":[211],"assumptions":[212],"sets.":[215],"proof":[217],"technique":[218],"perturbation":[223],"that,":[233],"estimate":[235],"maximum":[237],"fails.":[245]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}