{"id":"https://openalex.org/W2083042020","doi":"https://doi.org/10.1137/080714488","title":"Probing the Pareto Frontier for Basis Pursuit Solutions","display_name":"Probing the Pareto Frontier for Basis Pursuit Solutions","publication_year":2008,"publication_date":"2008-11-26","ids":{"openalex":"https://openalex.org/W2083042020","doi":"https://doi.org/10.1137/080714488","mag":"2083042020"},"language":"en","primary_location":{"id":"doi:10.1137/080714488","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080714488","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5091640094","display_name":"E. van den Berg","orcid":"https://orcid.org/0000-0002-0991-3397"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ewout van den Berg","raw_affiliation_strings":["ewout@cs.ubc.ca and mpf@cs.ubc.ca#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ewout@cs.ubc.ca and mpf@cs.ubc.ca#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054518852","display_name":"Michael P. Friedlander","orcid":"https://orcid.org/0000-0003-0222-5222"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael P. Friedlander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":96.0719,"has_fulltext":false,"cited_by_count":1983,"citation_normalized_percentile":{"value":0.99975959,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"31","issue":"2","first_page":"890","last_page":"912"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9988999962806702,"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":0.9988999962806702,"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/T10988","display_name":"Advanced Fiber Laser Technologies","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8160651922225952},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5961381196975708},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.48806655406951904},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.47208306193351746},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.46735337376594543},{"id":"https://openalex.org/keywords/underdetermined-system","display_name":"Underdetermined system","score":0.46715277433395386},{"id":"https://openalex.org/keywords/basis-pursuit","display_name":"Basis pursuit","score":0.43857407569885254},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4330505132675171},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.42926231026649475},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2734874188899994},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.23814907670021057},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18488141894340515}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8160651922225952},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5961381196975708},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.48806655406951904},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.47208306193351746},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.46735337376594543},{"id":"https://openalex.org/C179690561","wikidata":"https://www.wikidata.org/wiki/Q4316110","display_name":"Underdetermined system","level":2,"score":0.46715277433395386},{"id":"https://openalex.org/C99217422","wikidata":"https://www.wikidata.org/wiki/Q4867576","display_name":"Basis pursuit","level":4,"score":0.43857407569885254},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4330505132675171},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.42926231026649475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2734874188899994},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.23814907670021057},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18488141894340515},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C156872377","wikidata":"https://www.wikidata.org/wiki/Q6786281","display_name":"Matching pursuit","level":3,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/080714488","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080714488","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.129.2337","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.129.2337","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ubc.ca/~mpf/downloads/BergFried08.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.161.9332","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.9332","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.ubc.ca/~mpf/downloads/BergFriedlander08.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.168.1724","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.168.1724","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2008/01/1889.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1583497301","https://openalex.org/W1594234351","https://openalex.org/W1967073510","https://openalex.org/W1968735445","https://openalex.org/W1971293584","https://openalex.org/W1973734200","https://openalex.org/W1984568490","https://openalex.org/W1986931325","https://openalex.org/W1999997491","https://openalex.org/W2000218110","https://openalex.org/W2010315317","https://openalex.org/W2011307855","https://openalex.org/W2023562215","https://openalex.org/W2029816571","https://openalex.org/W2050826786","https://openalex.org/W2050834445","https://openalex.org/W2058192020","https://openalex.org/W2062102668","https://openalex.org/W2063978378","https://openalex.org/W2076605490","https://openalex.org/W2078204800","https://openalex.org/W2098012923","https://openalex.org/W2101675075","https://openalex.org/W2107501462","https://openalex.org/W2109449402","https://openalex.org/W2118075667","https://openalex.org/W2129638195","https://openalex.org/W2135046866","https://openalex.org/W2144331407","https://openalex.org/W2145096794","https://openalex.org/W2147656689","https://openalex.org/W2149846618","https://openalex.org/W2153686064","https://openalex.org/W2158252006","https://openalex.org/W2164452299","https://openalex.org/W2296319761","https://openalex.org/W2296616510","https://openalex.org/W2798766386","https://openalex.org/W3022380717","https://openalex.org/W3029645440","https://openalex.org/W3105135706","https://openalex.org/W4231139742","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W2206593303","https://openalex.org/W2067878805","https://openalex.org/W2158149279","https://openalex.org/W2796146443","https://openalex.org/W2101657445","https://openalex.org/W2963765059","https://openalex.org/W2045049118","https://openalex.org/W2964246754","https://openalex.org/W2138863404","https://openalex.org/W2106440213"],"abstract_inverted_index":{"The":[0,131],"basis":[1],"pursuit":[2,15],"problem":[3,21,120,136],"seeks":[4],"a":[5,25,29,80,112,118,150],"minimum":[6],"one-norm":[7,42,124],"solution":[8,133],"of":[9,43,59,134,153],"an":[10,66,122],"underdetermined":[11],"least-squares":[12,20,38,119],"problem.":[13],"Basis":[14],"denoise":[16],"(BPDN)":[17],"fits":[18],"the":[19,33,37,41,44,90,106,144,158],"only":[22],"approximately,":[23],"and":[24,40,53,61,100,139],"single":[26],"parameter":[27],"determines":[28],"curve":[30,50],"that":[31,48,63,96,103,157],"traces":[32],"optimal":[34],"trade-off":[35],"between":[36],"fit":[39],"solution.":[45],"We":[46,78],"prove":[47],"this":[49,88,135],"is":[51,92],"convex":[52],"continuously":[54],"differentiable":[55],"over":[56],"all":[57],"points":[58,86],"interest,":[60],"show":[62],"it":[64],"gives":[65,137],"explicit":[67,123],"relationship":[68],"to":[69,76,162],"two":[70],"other":[71],"optimization":[72],"problems":[73,95,155],"closely":[74],"related":[75],"BPDN.":[77],"describe":[79],"root-finding":[81,145],"algorithm":[82,91],"for":[83,94,101,143],"finding":[84],"arbitrary":[85],"on":[87,149],"curve;":[89],"suitable":[93],"are":[97,104,129],"large":[98,163],"scale":[99],"those":[102],"in":[105],"complex":[107],"domain.":[108],"At":[109],"each":[110],"iteration,":[111],"spectral":[113],"gradient-projection":[114],"method":[115,159],"approximately":[116],"minimizes":[117],"with":[121],"constraint.":[125],"Only":[126],"matrix-vector":[127],"operations":[128],"required.":[130],"primal-dual":[132],"function":[138],"derivative":[140],"information":[141],"needed":[142],"method.":[146],"Numerical":[147],"experiments":[148],"comprehensive":[151],"set":[152],"test":[154],"demonstrate":[156],"scales":[160],"well":[161],"problems.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":16},{"year":2025,"cited_by_count":54},{"year":2024,"cited_by_count":64},{"year":2023,"cited_by_count":65},{"year":2022,"cited_by_count":75},{"year":2021,"cited_by_count":139},{"year":2020,"cited_by_count":101},{"year":2019,"cited_by_count":124},{"year":2018,"cited_by_count":134},{"year":2017,"cited_by_count":160},{"year":2016,"cited_by_count":186},{"year":2015,"cited_by_count":142},{"year":2014,"cited_by_count":161},{"year":2013,"cited_by_count":166},{"year":2012,"cited_by_count":145}],"updated_date":"2026-06-19T17:40:00.097472","created_date":"2025-10-10T00:00:00"}
