{"id":"https://openalex.org/W2067736594","doi":"https://doi.org/10.1137/s0036139903422784","title":"Total Bounded Variation Regularization as a Bilaterally Constrained Optimization Problem","display_name":"Total Bounded Variation Regularization as a Bilaterally Constrained Optimization Problem","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2067736594","doi":"https://doi.org/10.1137/s0036139903422784","mag":"2067736594"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139903422784","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139903422784","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/Total_bounded_variation_regularization_as_a_bilaterally_constrained_optimization_problem/23345987","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074607617","display_name":"Karl Kunisch","orcid":"https://orcid.org/0000-0003-1113-7355"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K. Kunisch","raw_affiliation_strings":["**Rice University;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"**Rice University;","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062202097","display_name":"Michael Hinterm\u00fcller","orcid":"https://orcid.org/0000-0001-9471-2479"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Hinterm\u00fcller","raw_affiliation_strings":["**Rice University;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"**Rice University;","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.3635,"has_fulltext":false,"cited_by_count":146,"citation_normalized_percentile":{"value":0.97657993,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"64","issue":"4","first_page":"1311","last_page":"1333"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9987000226974487,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9926000237464905,"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/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.754361629486084},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7020896077156067},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6819342374801636},{"id":"https://openalex.org/keywords/bounded-variation","display_name":"Bounded variation","score":0.6567685604095459},{"id":"https://openalex.org/keywords/total-variation-denoising","display_name":"Total variation denoising","score":0.6056726574897766},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5848948359489441},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5631449818611145},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5533058643341064},{"id":"https://openalex.org/keywords/constrained-optimization-problem","display_name":"Constrained optimization problem","score":0.4387779235839844},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3258357644081116},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24785709381103516},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.20666754245758057},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11480993032455444},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10800591111183167}],"concepts":[{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.754361629486084},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7020896077156067},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6819342374801636},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.6567685604095459},{"id":"https://openalex.org/C207282899","wikidata":"https://www.wikidata.org/wiki/Q7828156","display_name":"Total variation denoising","level":3,"score":0.6056726574897766},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5848948359489441},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5631449818611145},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5533058643341064},{"id":"https://openalex.org/C2989514635","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization problem","level":3,"score":0.4387779235839844},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3258357644081116},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24785709381103516},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.20666754245758057},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11480993032455444},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10800591111183167}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036139903422784","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139903422784","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:figshare.com:article/23345987","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Total_bounded_variation_regularization_as_a_bilaterally_constrained_optimization_problem/23345987","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/23345987","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Total_bounded_variation_regularization_as_a_bilaterally_constrained_optimization_problem/23345987","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1489458628","https://openalex.org/W1571840955","https://openalex.org/W1653619892","https://openalex.org/W1674659126","https://openalex.org/W1972419797","https://openalex.org/W1972596295","https://openalex.org/W1985588167","https://openalex.org/W1986938753","https://openalex.org/W1992688650","https://openalex.org/W1996726072","https://openalex.org/W2002597165","https://openalex.org/W2012118748","https://openalex.org/W2017848200","https://openalex.org/W2026365342","https://openalex.org/W2039939700","https://openalex.org/W2070584352","https://openalex.org/W2072081687","https://openalex.org/W2087499062","https://openalex.org/W2089312400","https://openalex.org/W2103559027","https://openalex.org/W2105910985","https://openalex.org/W2107604145","https://openalex.org/W2114424556","https://openalex.org/W2146052399","https://openalex.org/W2162894628","https://openalex.org/W2530256364","https://openalex.org/W3011612142","https://openalex.org/W3042562017","https://openalex.org/W4213046749","https://openalex.org/W4237027898","https://openalex.org/W4252104256","https://openalex.org/W4301021743"],"related_works":["https://openalex.org/W2588406281","https://openalex.org/W2344001031","https://openalex.org/W1605636162","https://openalex.org/W2756378021","https://openalex.org/W2000594266","https://openalex.org/W4292601995","https://openalex.org/W2890366747","https://openalex.org/W2080883550","https://openalex.org/W4297923868","https://openalex.org/W3042163361"],"abstract_inverted_index":{"It":[0],"is":[1,69,74],"demonstrated":[2],"that":[3,81],"the":[4,49,58,82,87,103,106],"predual":[5],"for":[6,43,97],"problems":[7,44],"with":[8,45,86],"total":[9],"bounded":[10,52],"variation":[11,53],"regularization":[12],"terms":[13],"can":[14],"be":[15],"expressed":[16],"as":[17,64,91],"a":[18,25,65,77],"bilaterally":[19],"constrained":[20],"optimization":[21,40],"problem.":[22],"Existence":[23],"of":[24,51,105],"Lagrange":[26,83],"multiplier":[27,84],"and":[28,71,100],"an":[29,92],"optimality":[30],"system":[31],"are":[32],"established.":[33],"This":[34],"allows":[35],"us":[36],"to":[37],"utilize":[38],"efficient":[39],"methods":[41],"developed":[42],"box":[46,88],"constraints":[47,89],"in":[48,56],"context":[50],"formulations.":[54],"Here,":[55],"particular,":[57],"primal-dual":[59],"active":[60],"set":[61],"method,":[62,68],"considered":[63],"semismooth":[66],"Newton":[67],"analyzed,":[70],"superlinear":[72],"convergence":[73],"proved.":[75],"As":[76],"by-product":[78],"we":[79],"obtain":[80],"associated":[85],"acts":[90],"edge":[93],"detector.":[94],"Numerical":[95],"results":[96],"image":[98],"denoising":[99],"zooming/resizing":[101],"show":[102],"efficiency":[104],"new":[107],"approach.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":10}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
