{"id":"https://openalex.org/W2002857344","doi":"https://doi.org/10.1137/110829209","title":"An Iterative Lagrange Multiplier Method for Constrained Total-Variation-Based Image Denoising","display_name":"An Iterative Lagrange Multiplier Method for Constrained Total-Variation-Based Image Denoising","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2002857344","doi":"https://doi.org/10.1137/110829209","mag":"2002857344"},"language":"en","primary_location":{"id":"doi:10.1137/110829209","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110829209","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5100390066","display_name":"Jianping Zhang","orcid":"https://orcid.org/0000-0001-7141-9464"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jianping Zhang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100452006","display_name":"Ke Chen","orcid":"https://orcid.org/0000-0002-6093-6623"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ke Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5070938702","display_name":"Bo Yu","orcid":"https://orcid.org/0000-0002-0898-8493"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bo Yu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100390066"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3201,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.92924189,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"3","first_page":"983","last_page":"1003"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.8604022860527039},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.8293464183807373},{"id":"https://openalex.org/keywords/total-variation-denoising","display_name":"Total variation denoising","score":0.6942338347434998},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6828897595405579},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6530264019966125},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5857744216918945},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5111363530158997},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4991495609283447},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.4774937331676483},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.4716448187828064},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46654653549194336},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.44632551074028015},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.43148335814476013},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.43057963252067566},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3532503843307495},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2850033640861511},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.111554354429245}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.8604022860527039},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.8293464183807373},{"id":"https://openalex.org/C207282899","wikidata":"https://www.wikidata.org/wiki/Q7828156","display_name":"Total variation denoising","level":3,"score":0.6942338347434998},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6828897595405579},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6530264019966125},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5857744216918945},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5111363530158997},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4991495609283447},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.4774937331676483},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.4716448187828064},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46654653549194336},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44632551074028015},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.43148335814476013},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.43057963252067566},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3532503843307495},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2850033640861511},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.111554354429245},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110829209","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110829209","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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":35,"referenced_works":["https://openalex.org/W105397765","https://openalex.org/W1964535604","https://openalex.org/W1972406935","https://openalex.org/W1985588167","https://openalex.org/W1985741394","https://openalex.org/W1986151195","https://openalex.org/W1989893875","https://openalex.org/W1990274520","https://openalex.org/W1998252084","https://openalex.org/W1998999283","https://openalex.org/W1999424151","https://openalex.org/W2011181254","https://openalex.org/W2013388817","https://openalex.org/W2017848200","https://openalex.org/W2018816711","https://openalex.org/W2020461703","https://openalex.org/W2020999234","https://openalex.org/W2022737993","https://openalex.org/W2034192630","https://openalex.org/W2039939700","https://openalex.org/W2044407864","https://openalex.org/W2061565858","https://openalex.org/W2074918423","https://openalex.org/W2079724595","https://openalex.org/W2080385522","https://openalex.org/W2087882684","https://openalex.org/W2092018092","https://openalex.org/W2093622097","https://openalex.org/W2103559027","https://openalex.org/W2112589491","https://openalex.org/W2119658486","https://openalex.org/W2122890444","https://openalex.org/W2132236849","https://openalex.org/W2167400582","https://openalex.org/W2333813520"],"related_works":["https://openalex.org/W2615021531","https://openalex.org/W2078035581","https://openalex.org/W2182841669","https://openalex.org/W2039078354","https://openalex.org/W2115007255","https://openalex.org/W2491081908","https://openalex.org/W2358522314","https://openalex.org/W2890366747","https://openalex.org/W2002857344","https://openalex.org/W2474851184"],"abstract_inverted_index":{"Various":[0],"effective":[1],"algorithms":[2,30],"have":[3],"been":[4,149],"proposed":[5,172],"in":[6,202],"the":[7,16,23,47,54,86,98,105,115,119,131,137,167],"past":[8],"two":[9],"decades":[10],"for":[11,114,161],"nonlinear":[12],"PDEs":[13],"arising":[14],"from":[15,136],"unconstrained":[17],"total-variation-based":[18],"image":[19,205],"denoising":[20],"problem":[21],"regularizing":[22],"total":[24,139],"variation":[25,140],"constrained":[26,138],"minimization":[27],"model.":[28],"Such":[29],"can":[31,77,174,190],"be":[32,78],"used":[33],"to":[34,53,67,129,165],"obtain":[35,68],"a":[36,42,50,57,69,101,124,162,193],"satisfactory":[37],"result":[38],"as":[39,41],"long":[40],"suitable":[43,70],"regularization":[44,71,116],"parameter":[45,72,117],"balancing":[46],"trade-off":[48],"between":[49],"good":[51],"fit":[52],"data":[55],"and":[56,170,197],"regular":[58],"solution":[59,88,99,196],"is":[60,64,82,89,100,122,128],"given.":[61],"However,":[62],"it":[63,81],"generally":[65],"difficult":[66],"without":[73],"which":[74],"restored":[75],"images":[76,179],"unsatisfactory:":[79],"if":[80,95],"too":[83,96],"large,":[84],"then":[85],"resulting":[87],"still":[90],"contaminated":[91],"by":[92],"noise,":[93],"while":[94],"small,":[97],"poor":[102],"approximation":[103],"of":[104,204],"true":[106],"noise-free":[107],"solution.":[108],"To":[109],"provide":[110],"an":[111,157],"automatic":[112],"method":[113,173],"when":[118],"noise":[120],"level":[121],"known":[123],"priori,":[125],"one":[126],"way":[127],"address":[130],"coupled":[132],"Karush\u2013Kuhn\u2013Tucker":[133],"(KKT)":[134],"systems":[135],"optimization":[141],"problem.":[142,153],"So":[143],"far":[144],"much":[145],"less":[146],"work":[147],"has":[148],"done":[150],"on":[151],"this":[152],"This":[154],"paper":[155],"presents":[156],"iterative":[158],"update":[159],"algorithm":[160],"Lagrange":[163],"multiplier":[164],"solve":[166],"KKT":[168],"conditions,":[169],"our":[171,188],"adaptively":[175],"deal":[176],"with":[177,180],"noisy":[178],"different":[181],"variances":[182],"$\\sigma^2$.":[183],"Numerical":[184],"experiments":[185],"show":[186],"that":[187],"model":[189],"effectively":[191],"find":[192],"highly":[194],"accurate":[195],"produce":[198],"excellent":[199],"restoration":[200],"results":[201],"terms":[203],"quality.":[206]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
