{"id":"https://openalex.org/W2082608952","doi":"https://doi.org/10.1137/090752754","title":"An Upwind Finite-Difference Method for Total Variation\u2013Based Image Smoothing","display_name":"An Upwind Finite-Difference Method for Total Variation\u2013Based Image Smoothing","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2082608952","doi":"https://doi.org/10.1137/090752754","mag":"2082608952"},"language":"en","primary_location":{"id":"doi:10.1137/090752754","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090752754","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/A5089573258","display_name":"Antonin Chambolle","orcid":"https://orcid.org/0000-0002-9465-4659"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Antonin Chambolle","raw_affiliation_strings":["antonin.chambolle@polytechnique.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"antonin.chambolle@polytechnique.fr#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018631987","display_name":"Stacey Levine","orcid":"https://orcid.org/0000-0001-6535-7535"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stacey E. Levine","raw_affiliation_strings":["sel@mathcs.duq.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"sel@mathcs.duq.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000961188","display_name":"Bradley J. Lucier","orcid":"https://orcid.org/0000-0003-3808-939X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bradley J. Lucier","raw_affiliation_strings":["lucier@math.purdue.edu#TAB#"],"affiliations":[{"raw_affiliation_string":"lucier@math.purdue.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089573258"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2008,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.9444038,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"4","issue":"1","first_page":"277","last_page":"299"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9959999918937683,"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/T11558","display_name":"Composite Material Mechanics","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematics","display_name":"Mathematics","score":0.7944914698600769},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.7657820582389832},{"id":"https://openalex.org/keywords/upwind-scheme","display_name":"Upwind scheme","score":0.6893399357795715},{"id":"https://openalex.org/keywords/bounded-variation","display_name":"Bounded variation","score":0.6476086378097534},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6021639108657837},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5998422503471375},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5929101705551147},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.5871899127960205},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5849779844284058},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5094240307807922},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49949097633361816},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.4749893248081207},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4051724374294281},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.16254860162734985},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0685863196849823}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7944914698600769},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.7657820582389832},{"id":"https://openalex.org/C94025248","wikidata":"https://www.wikidata.org/wiki/Q7899499","display_name":"Upwind scheme","level":3,"score":0.6893399357795715},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.6476086378097534},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6021639108657837},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5998422503471375},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5929101705551147},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.5871899127960205},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5849779844284058},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5094240307807922},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49949097633361816},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.4749893248081207},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4051724374294281},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.16254860162734985},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0685863196849823},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/090752754","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090752754","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:10.1.1.216.543","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.216.543","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.purdue.edu/%7Elucier/692/CLL09.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.224.6759","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.224.6759","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.purdue.edu/%7Elucier/pde-papers/75275.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W207373900","https://openalex.org/W649818166","https://openalex.org/W1500521460","https://openalex.org/W1533665822","https://openalex.org/W1653619892","https://openalex.org/W1976688370","https://openalex.org/W1991113069","https://openalex.org/W2002882465","https://openalex.org/W2005089986","https://openalex.org/W2006262045","https://openalex.org/W2011181254","https://openalex.org/W2014823423","https://openalex.org/W2039466093","https://openalex.org/W2039939700","https://openalex.org/W2043380148","https://openalex.org/W2050872129","https://openalex.org/W2053487511","https://openalex.org/W2061979078","https://openalex.org/W2074214991","https://openalex.org/W2080385522","https://openalex.org/W2089231054","https://openalex.org/W2089469793","https://openalex.org/W2092231222","https://openalex.org/W2100533333","https://openalex.org/W2103559027","https://openalex.org/W2122890444","https://openalex.org/W2144132602","https://openalex.org/W2163345036","https://openalex.org/W2166087152","https://openalex.org/W2726656315"],"related_works":["https://openalex.org/W2035359254","https://openalex.org/W2951708071","https://openalex.org/W2047537332","https://openalex.org/W2079953012","https://openalex.org/W2060612917","https://openalex.org/W2140291031","https://openalex.org/W2082608952","https://openalex.org/W1966016812","https://openalex.org/W2041227812","https://openalex.org/W1976419327"],"abstract_inverted_index":{"In":[0],"this":[1,45],"paper":[2],"we":[3,105],"study":[4],"finite-difference":[5,39,64],"approximations":[6],"to":[7,66],"the":[8,12,42,49,56,67,79,88,92,99,112,118,121],"variational":[9],"problem":[10],"using":[11],"bounded":[13],"variation":[14],"(BV)":[15],"smoothness":[16],"penalty":[17],"that":[18,98,109],"was":[19],"introduced":[20],"in":[21,48],"an":[22,37],"image":[23],"smoothing":[24],"context":[25],"by":[26,55],"Rudin,":[27],"Osher,":[28],"and":[29,86,104,114],"Fatemi.":[30],"We":[31,71,95],"give":[32],"a":[33,60,73],"dual":[34],"formulation":[35,46,90],"for":[36,41,59,76],"upwind":[38,93],"approximation":[40,65,80],"BV":[43,69],"seminorm;":[44],"is":[47,102],"same":[50],"spirit":[51],"as":[52],"one":[53],"popularized":[54],"first":[57],"author":[58],"simpler,":[61],"less":[62],"isotropic,":[63],"(isotropic)":[68],"seminorm.":[70],"introduce":[72],"multiscale":[74,100],"method":[75,85,101],"speeding":[77],"up":[78],"of":[81,87,91,117,120],"both":[82,111],"Chambolle's":[83],"original":[84],"new":[89],"scheme.":[94],"demonstrate":[96],"numerically":[97],"effective,":[103],"provide":[106],"numerical":[107,122],"examples":[108],"illustrate":[110],"qualitative":[113],"quantitative":[115],"behavior":[116],"solutions":[119],"formulations.":[123]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
