{"id":"https://openalex.org/W2000594266","doi":"https://doi.org/10.1137/090769521","title":"Total Generalized Variation","display_name":"Total Generalized Variation","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2000594266","doi":"https://doi.org/10.1137/090769521","mag":"2000594266"},"language":"en","primary_location":{"id":"doi:10.1137/090769521","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090769521","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/A5060778033","display_name":"Kristian Bredies","orcid":"https://orcid.org/0000-0001-7140-043X"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Kristian Bredies","raw_affiliation_strings":["kristian.bredies@uni-graz.at and karl.kunisch@uni-graz.at#TAB#"],"affiliations":[{"raw_affiliation_string":"kristian.bredies@uni-graz.at and karl.kunisch@uni-graz.at#TAB#","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074607617","display_name":"Karl Kunisch","orcid":"https://orcid.org/0000-0003-1113-7355"},"institutions":[{"id":"https://openalex.org/I15766117","display_name":"University of Graz","ror":"https://ror.org/01faaaf77","country_code":"AT","type":"education","lineage":["https://openalex.org/I15766117"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Karl Kunisch","raw_affiliation_strings":["University of Graz"],"affiliations":[{"raw_affiliation_string":"University of Graz","institution_ids":["https://openalex.org/I15766117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032205387","display_name":"Thomas Pock","orcid":"https://orcid.org/0000-0001-6120-1058"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas Pock","raw_affiliation_strings":["pock@icg.tugraz.at#TAB#"],"affiliations":[{"raw_affiliation_string":"pock@icg.tugraz.at#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060778033"],"corresponding_institution_ids":["https://openalex.org/I15766117"],"apc_list":null,"apc_paid":null,"fwci":42.5503,"has_fulltext":false,"cited_by_count":1509,"citation_normalized_percentile":{"value":0.99971786,"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":"492","last_page":"526"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9994000196456909,"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":0.9994000196456909,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9868000149726868,"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/bounded-variation","display_name":"Bounded variation","score":0.8453637361526489},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.7859943509101868},{"id":"https://openalex.org/keywords/variation","display_name":"Variation (astronomy)","score":0.7715593576431274},{"id":"https://openalex.org/keywords/total-variation-denoising","display_name":"Total variation denoising","score":0.7128797173500061},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7008517980575562},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.596012532711029},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5346642732620239},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44405311346054077},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.44220104813575745},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3480013608932495},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3127948045730591},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28642433881759644},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26512598991394043},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.22692999243736267},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.21879959106445312},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06746557354927063}],"concepts":[{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.8453637361526489},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7859943509101868},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.7715593576431274},{"id":"https://openalex.org/C207282899","wikidata":"https://www.wikidata.org/wiki/Q7828156","display_name":"Total variation denoising","level":3,"score":0.7128797173500061},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7008517980575562},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.596012532711029},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5346642732620239},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44405311346054077},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.44220104813575745},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3480013608932495},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3127948045730591},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28642433881759644},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26512598991394043},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.22692999243736267},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.21879959106445312},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06746557354927063},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090769521","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090769521","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:10.1.1.378.6330","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.378.6330","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://gpu4vision.icg.tugraz.at/papers/2009/pock_tgv.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":22,"referenced_works":["https://openalex.org/W182881619","https://openalex.org/W1480714962","https://openalex.org/W1509697219","https://openalex.org/W1511424556","https://openalex.org/W1544177383","https://openalex.org/W1978859603","https://openalex.org/W1985588167","https://openalex.org/W1992276332","https://openalex.org/W2005089986","https://openalex.org/W2025977958","https://openalex.org/W2037981501","https://openalex.org/W2039939700","https://openalex.org/W2042703116","https://openalex.org/W2050872129","https://openalex.org/W2067736594","https://openalex.org/W2069947795","https://openalex.org/W2100533333","https://openalex.org/W2100556411","https://openalex.org/W2103559027","https://openalex.org/W2122890444","https://openalex.org/W2126829454","https://openalex.org/W2142308565"],"related_works":["https://openalex.org/W2350325755","https://openalex.org/W2356614471","https://openalex.org/W2588406281","https://openalex.org/W4300576100","https://openalex.org/W2389758888","https://openalex.org/W2344001031","https://openalex.org/W1485170658","https://openalex.org/W2000661607","https://openalex.org/W1605636162","https://openalex.org/W2756378021"],"abstract_inverted_index":{"The":[0],"novel":[1],"concept":[2,29],"of":[3,7,15,34,42],"total":[4],"generalized":[5],"variation":[6,25],"a":[8,46,65,72],"function":[9],"u":[10],"is":[11],"introduced":[12],"and":[13],"some":[14],"its":[16],"essential":[17],"properties":[18],"are":[19],"proved.":[20],"Differently":[21],"from":[22],"the":[23,27,39],"bounded":[24],"semi-norm,":[26],"new":[28],"involves":[30],"higher":[31],"order":[32],"derivatives":[33],"u.":[35],"Numerical":[36],"examples":[37],"illustrate":[38],"high":[40],"quality":[41],"this":[43,55],"functional":[44,56],"as":[45,64],"regularization":[47],"term":[48],"for":[49],"mathematical":[50],"imaging":[51],"problems.":[52],"In":[53],"particular":[54],"selectively":[57],"regularizes":[58],"on":[59],"different":[60],"regularity":[61],"levels":[62],"and,":[63],"side":[66],"effect,":[67],"does":[68],"not":[69],"lead":[70],"to":[71],"staircasing":[73],"effect.":[74]},"counts_by_year":[{"year":2026,"cited_by_count":16},{"year":2025,"cited_by_count":69},{"year":2024,"cited_by_count":81},{"year":2023,"cited_by_count":112},{"year":2022,"cited_by_count":121},{"year":2021,"cited_by_count":172},{"year":2020,"cited_by_count":122},{"year":2019,"cited_by_count":145},{"year":2018,"cited_by_count":147},{"year":2017,"cited_by_count":113},{"year":2016,"cited_by_count":122},{"year":2015,"cited_by_count":111},{"year":2014,"cited_by_count":70},{"year":2013,"cited_by_count":61},{"year":2012,"cited_by_count":30}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
