{"id":"https://openalex.org/W2020461703","doi":"https://doi.org/10.1137/090767558","title":"Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models","display_name":"Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2020461703","doi":"https://doi.org/10.1137/090767558","mag":"2020461703"},"language":"en","primary_location":{"id":"doi:10.1137/090767558","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090767558","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","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/A5010997999","display_name":"Chunlin Wu","orcid":"https://orcid.org/0000-0003-1932-7997"},"institutions":[{"id":"https://openalex.org/I4210123532","display_name":"Nordic Transport Development","ror":"https://ror.org/0295ktr04","country_code":"DK","type":"company","lineage":["https://openalex.org/I4210123532"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"Chunlin Wu","raw_affiliation_strings":["clwu@ntu.edu.sg and xctai@ntu.edu.sg#TAB#"],"affiliations":[{"raw_affiliation_string":"clwu@ntu.edu.sg and xctai@ntu.edu.sg#TAB#","institution_ids":["https://openalex.org/I4210123532"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101951979","display_name":"Xue\u2010Cheng Tai","orcid":"https://orcid.org/0000-0003-3359-9104"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xue-Cheng Tai","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010997999"],"corresponding_institution_ids":["https://openalex.org/I4210123532"],"apc_list":null,"apc_paid":null,"fwci":41.7519,"has_fulltext":false,"cited_by_count":611,"citation_normalized_percentile":{"value":0.99962388,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"3","issue":"3","first_page":"300","last_page":"339"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976999759674072,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9902999997138977,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.9423836469650269},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6084372997283936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5984559059143066},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5794217586517334},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5775516629219055},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5509976148605347},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5495067834854126},{"id":"https://openalex.org/keywords/bregman-divergence","display_name":"Bregman divergence","score":0.5303543210029602},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4423692524433136},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4357507526874542},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4084756076335907},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32079991698265076},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.30598992109298706},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23369884490966797},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10861366987228394}],"concepts":[{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.9423836469650269},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6084372997283936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5984559059143066},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5794217586517334},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5775516629219055},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5509976148605347},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5495067834854126},{"id":"https://openalex.org/C149073432","wikidata":"https://www.wikidata.org/wiki/Q4960382","display_name":"Bregman divergence","level":2,"score":0.5303543210029602},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4423692524433136},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4357507526874542},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4084756076335907},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32079991698265076},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30598992109298706},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23369884490966797},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10861366987228394},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090767558","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090767558","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.212.6028","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.212.6028","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://kowon.dongseo.ac.kr/~lbg/cagd/kmmcs/201001/cam09-76.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W19793066","https://openalex.org/W74071737","https://openalex.org/W368078881","https://openalex.org/W1480546554","https://openalex.org/W1508867082","https://openalex.org/W1653619892","https://openalex.org/W1850000976","https://openalex.org/W1972406935","https://openalex.org/W1978333359","https://openalex.org/W1978859603","https://openalex.org/W1985588167","https://openalex.org/W1995276029","https://openalex.org/W1996287810","https://openalex.org/W2005082281","https://openalex.org/W2005089986","https://openalex.org/W2011181254","https://openalex.org/W2014823423","https://openalex.org/W2016187631","https://openalex.org/W2026912579","https://openalex.org/W2027401313","https://openalex.org/W2033468335","https://openalex.org/W2033736734","https://openalex.org/W2035128422","https://openalex.org/W2037981501","https://openalex.org/W2039939700","https://openalex.org/W2049643151","https://openalex.org/W2057624533","https://openalex.org/W2058532290","https://openalex.org/W2072378378","https://openalex.org/W2080883550","https://openalex.org/W2084478514","https://openalex.org/W2086670019","https://openalex.org/W2091494211","https://openalex.org/W2096448861","https://openalex.org/W2103559027","https://openalex.org/W2119159934","https://openalex.org/W2122275806","https://openalex.org/W2122287830","https://openalex.org/W2122752532","https://openalex.org/W2122890444","https://openalex.org/W2135036909","https://openalex.org/W2137113506","https://openalex.org/W2142058898","https://openalex.org/W2146842127","https://openalex.org/W2151958211","https://openalex.org/W2169288322","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2315802443","https://openalex.org/W2525212141","https://openalex.org/W4300083746","https://openalex.org/W2809494150","https://openalex.org/W2955809168","https://openalex.org/W3006403843","https://openalex.org/W102932032","https://openalex.org/W2376104286","https://openalex.org/W2082353735","https://openalex.org/W2097845889"],"abstract_inverted_index":{"E.":[0],"Fatemi,":[1],"Physica":[2],"D,":[3],"60(1992),":[4],"pp.":[5,67],"259\u2013268]":[6],"based":[7],"on":[8],"total":[9],"variation":[10],"(TV)":[11],"minimization":[12],"has":[13],"proven":[14],"to":[15,26,40],"be":[16,41],"very":[17],"useful.":[18],"A":[19],"lot":[20],"of":[21,35,52],"efforts":[22],"have":[23],"been":[24],"devoted":[25],"obtain":[27],"fast":[28],"numerical":[29],"schemes":[30],"and":[31,59,69],"overcome":[32],"the":[33,36,45,49],"non-differentiability":[34],"model.":[37],"Methods":[38],"considered":[39],"particularly":[42],"efficient":[43],"for":[44],"ROF":[46],"model":[47],"include":[48],"dual":[50],"methods":[51],"Chan-Golub-Mulet":[53],"(CGM)":[54],"[T.F.":[55],"Chan,":[56],"G.H.":[57],"Golub,":[58],"P.":[60],"Mulet,":[61],"SIAM":[62],"J.":[63,73],"Sci.":[64],"Comput.,":[65],"20(1999),":[66],"1964\u20131977]":[68],"Chambolle":[70],"[A.":[71],"Chambolle,":[72],"Math.":[74],"Imaging":[75]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":24},{"year":2023,"cited_by_count":35},{"year":2022,"cited_by_count":42},{"year":2021,"cited_by_count":41},{"year":2020,"cited_by_count":56},{"year":2019,"cited_by_count":77},{"year":2018,"cited_by_count":46},{"year":2017,"cited_by_count":48},{"year":2016,"cited_by_count":40},{"year":2015,"cited_by_count":37},{"year":2014,"cited_by_count":44},{"year":2013,"cited_by_count":50},{"year":2012,"cited_by_count":29}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
