{"id":"https://openalex.org/W2148062657","doi":"https://doi.org/10.1109/tip.2008.2008420","title":"Efficient Minimization Method for a Generalized Total Variation Functional","display_name":"Efficient Minimization Method for a Generalized Total Variation Functional","publication_year":2009,"publication_date":"2009-01-05","ids":{"openalex":"https://openalex.org/W2148062657","doi":"https://doi.org/10.1109/tip.2008.2008420","mag":"2148062657","pmid":"https://pubmed.ncbi.nlm.nih.gov/19116200"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2008.2008420","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2008.2008420","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5077092609","display_name":"Paul Rodr\u00edguez","orcid":"https://orcid.org/0000-0002-8501-0907"},"institutions":[{"id":"https://openalex.org/I65285256","display_name":"Pontificia Universidad Cat\u00f3lica del Per\u00fa","ror":"https://ror.org/00013q465","country_code":"PE","type":"education","lineage":["https://openalex.org/I65285256"]}],"countries":["PE"],"is_corresponding":false,"raw_author_name":"P. Rodriguez","raw_affiliation_strings":["Digital Signal Processing Group, Pontificia Universidad Cat\u00f3lica del Per\u00fa, Lima, Peru. prodrig@pucp.edu.pe","Digital Signal Processing Group, Pontificia Universidad, Lima, Peru"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Digital Signal Processing Group, Pontificia Universidad Cat\u00f3lica del Per\u00fa, Lima, Peru. prodrig@pucp.edu.pe","institution_ids":["https://openalex.org/I65285256"]},{"raw_affiliation_string":"Digital Signal Processing Group, Pontificia Universidad, Lima, Peru","institution_ids":["https://openalex.org/I65285256"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015244709","display_name":"Brendt Wohlberg","orcid":"https://orcid.org/0000-0002-4767-1843"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. Wohlberg","raw_affiliation_strings":["T 7 Mathematical Modeling and Analysis, Los Alamos National Laboratory, Los Alamos, NM, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"T 7 Mathematical Modeling and Analysis, Los Alamos National Laboratory, Los Alamos, NM, USA","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":18.1526,"has_fulltext":false,"cited_by_count":243,"citation_normalized_percentile":{"value":0.99616086,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"18","issue":"2","first_page":"322","last_page":"332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9980999827384949,"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":0.9980999827384949,"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":0.9945999979972839,"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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/noise-reduction","display_name":"Noise reduction","score":0.6321315765380859},{"id":"https://openalex.org/keywords/deconvolution","display_name":"Deconvolution","score":0.5722839832305908},{"id":"https://openalex.org/keywords/total-variation-denoising","display_name":"Total variation denoising","score":0.5411890745162964},{"id":"https://openalex.org/keywords/fidelity","display_name":"Fidelity","score":0.5364329218864441},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5345849990844727},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5152221322059631},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5129053592681885},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4886954128742218},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4855475127696991},{"id":"https://openalex.org/keywords/blind-deconvolution","display_name":"Blind deconvolution","score":0.4813481271266937},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4717491567134857},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4000590443611145},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3890749216079712},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3140760660171509},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.25779831409454346}],"concepts":[{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.6321315765380859},{"id":"https://openalex.org/C174576160","wikidata":"https://www.wikidata.org/wiki/Q1183700","display_name":"Deconvolution","level":2,"score":0.5722839832305908},{"id":"https://openalex.org/C207282899","wikidata":"https://www.wikidata.org/wiki/Q7828156","display_name":"Total variation denoising","level":3,"score":0.5411890745162964},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.5364329218864441},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5345849990844727},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5152221322059631},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5129053592681885},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4886954128742218},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4855475127696991},{"id":"https://openalex.org/C30044814","wikidata":"https://www.wikidata.org/wiki/Q11334452","display_name":"Blind deconvolution","level":3,"score":0.4813481271266937},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4717491567134857},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4000590443611145},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3890749216079712},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3140760660171509},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25779831409454346},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2008.2008420","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2008.2008420","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},{"id":"pmid:19116200","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19116200","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.146.5764","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.146.5764","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.lanl.gov/~brendt/Publications/Docs/rodriguez-2009-efficient.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":55,"referenced_works":["https://openalex.org/W19793066","https://openalex.org/W250604557","https://openalex.org/W612879516","https://openalex.org/W1499695691","https://openalex.org/W1533665822","https://openalex.org/W1559687661","https://openalex.org/W1578722091","https://openalex.org/W1603910097","https://openalex.org/W1962625785","https://openalex.org/W1971563238","https://openalex.org/W1985588167","https://openalex.org/W1986931325","https://openalex.org/W1997542937","https://openalex.org/W1998999283","https://openalex.org/W2005089986","https://openalex.org/W2013347084","https://openalex.org/W2028349405","https://openalex.org/W2028496557","https://openalex.org/W2031832209","https://openalex.org/W2033603511","https://openalex.org/W2033894760","https://openalex.org/W2034619845","https://openalex.org/W2036513962","https://openalex.org/W2040378863","https://openalex.org/W2043394915","https://openalex.org/W2048245744","https://openalex.org/W2048369486","https://openalex.org/W2049633694","https://openalex.org/W2054113207","https://openalex.org/W2061979078","https://openalex.org/W2065742895","https://openalex.org/W2093133114","https://openalex.org/W2103559027","https://openalex.org/W2103913786","https://openalex.org/W2104064396","https://openalex.org/W2107501462","https://openalex.org/W2107604145","https://openalex.org/W2111841405","https://openalex.org/W2113075591","https://openalex.org/W2114424556","https://openalex.org/W2118427319","https://openalex.org/W2119159934","https://openalex.org/W2135367316","https://openalex.org/W2139738865","https://openalex.org/W2143163931","https://openalex.org/W2143476164","https://openalex.org/W2144275666","https://openalex.org/W2149414429","https://openalex.org/W2163779523","https://openalex.org/W2167400582","https://openalex.org/W2168334281","https://openalex.org/W2170984511","https://openalex.org/W2308181013","https://openalex.org/W2545067411","https://openalex.org/W4206097460"],"related_works":["https://openalex.org/W2034520358","https://openalex.org/W2028099218","https://openalex.org/W2059639161","https://openalex.org/W2586325539","https://openalex.org/W2058895457","https://openalex.org/W1538056422","https://openalex.org/W2023738877","https://openalex.org/W2147401053","https://openalex.org/W2029084792","https://openalex.org/W2589098082"],"abstract_inverted_index":{"Replacing":[0],"the":[1,7,45,56,96,100,105],"l(2)":[2],"data":[3,16],"fidelity":[4,17],"term":[5,18],"of":[6,26,47,81,108],"standard":[8],"Total":[9],"Variation":[10],"(TV)":[11],"functional":[12,37],"with":[13,95],"an":[14,61],"l(1)":[15],"has":[19],"been":[20],"found":[21],"to":[22,42,55],"offer":[23],"a":[24,66,118],"number":[25],"theoretical":[27],"and":[28,52,73,78,103],"practical":[29],"benefits.":[30],"Efficient":[31],"algorithms":[32],"for":[33,113],"minimizing":[34],"this":[35],"l(1)-TV":[36,74],"have":[38],"only":[39],"recently":[40],"begun":[41],"be":[43],"developed,":[44],"fastest":[46,106],"which":[48,109],"exploit":[49],"graph":[50],"representations,":[51],"are":[53,111],"restricted":[54],"denoising":[57,88,101],"problem.":[58],"We":[59],"describe":[60],"alternative":[62],"approach":[63],"that":[64],"minimizes":[65],"generalized":[67],"TV":[68],"functional,":[69],"including":[70],"both":[71],"l(2)-TV":[72],"as":[75],"special":[76],"cases,":[77],"is":[79,93,104],"capable":[80],"solving":[82],"more":[83],"general":[84,114],"inverse":[85,115],"problems":[86,116],"than":[87],"(e.g.,":[89],"deconvolution).":[90],"This":[91],"algorithm":[92,107],"competitive":[94],"graph-based":[97],"methods":[98],"in":[99],"case,":[102],"we":[110],"aware":[112],"involving":[117],"nontrivial":[119],"forward":[120],"linear":[121],"operator.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":21},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":25},{"year":2014,"cited_by_count":22},{"year":2013,"cited_by_count":21},{"year":2012,"cited_by_count":14}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}