{"id":"https://openalex.org/W4313701453","doi":"https://doi.org/10.1109/icassp49357.2023.10095610","title":"On The Primal and Dual Formulations Of The Discrete Mumford-Shah Functional","display_name":"On The Primal and Dual Formulations Of The Discrete Mumford-Shah Functional","publication_year":2023,"publication_date":"2023-05-05","ids":{"openalex":"https://openalex.org/W4313701453","doi":"https://doi.org/10.1109/icassp49357.2023.10095610"},"language":"en","primary_location":{"id":"doi:10.1109/icassp49357.2023.10095610","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/icassp49357.2023.10095610","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-03912074v2/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074166239","display_name":"Nelly Pustelnik","orcid":"https://orcid.org/0000-0001-7310-1927"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210096929","display_name":"Laboratoire de Physique de l'ENS de Lyon","ror":"https://ror.org/00w5ay796","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I113428412","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210096929","https://openalex.org/I4405259976","https://openalex.org/I4405263940","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Nelly Pustelnik","raw_affiliation_strings":["Laboratoire de Physique,ENSL, CNRS,Lyon,France,F-69342"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique,ENSL, CNRS,Lyon,France,F-69342","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210096929"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074166239"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210096929"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.7109721302986145},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5444974899291992},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3707178235054016},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3333631157875061},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32844528555870056},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17193764448165894},{"id":"https://openalex.org/keywords/art","display_name":"Art","score":0.05051019787788391}],"concepts":[{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.7109721302986145},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5444974899291992},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3707178235054016},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3333631157875061},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32844528555870056},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17193764448165894},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.05051019787788391},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/icassp49357.2023.10095610","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/icassp49357.2023.10095610","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-03912074v2","is_oa":true,"landing_page_url":"https://hal.science/hal-03912074","pdf_url":"https://hal.science/hal-03912074v2/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE ICASSP, Jun 2023, Rhodes (Gr\u00e8ce), Greece. &#x27E8;10.1109/ICASSP49357.2023.10095610&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03912074v2","is_oa":true,"landing_page_url":"https://hal.science/hal-03912074","pdf_url":"https://hal.science/hal-03912074v2/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE ICASSP, Jun 2023, Rhodes (Gr\u00e8ce), Greece. &#x27E8;10.1109/ICASSP49357.2023.10095610&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.7300000190734863}],"awards":[{"id":"https://openalex.org/G7438514334","display_name":"Multiscale estimation and Interface detection","funder_award_id":"ANR-19-CE48-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8318455765","display_name":null,"funder_award_id":"ANR-19","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4313701453.pdf","grobid_xml":"https://content.openalex.org/works/W4313701453.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1969765423","https://openalex.org/W2008164950","https://openalex.org/W2020999234","https://openalex.org/W2043439856","https://openalex.org/W2078853581","https://openalex.org/W2080744942","https://openalex.org/W2105910985","https://openalex.org/W2114487471","https://openalex.org/W2123711313","https://openalex.org/W2129732816","https://openalex.org/W2171413647","https://openalex.org/W2806853070","https://openalex.org/W2884917220","https://openalex.org/W2928605992","https://openalex.org/W3106343576","https://openalex.org/W4214948769","https://openalex.org/W4244769743","https://openalex.org/W4293775970","https://openalex.org/W4312058677","https://openalex.org/W6652474128"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":{"This":[0,29],"work":[1],"focuses":[2],"on":[3,46,52,72],"the":[4,21,36,47,79,94,114],"discrete":[5],"Mumford-Shah":[6],"(D-MS)":[7],"functional":[8,30],"which":[9,67],"aims":[10],"to":[11,44,62,102,146],"perform":[12],"jointly":[13],"image":[14],"reconstruction":[15],"and":[16,87,111,124,149],"contour":[17],"detection":[18],"but":[19,38],"at":[20],"price":[22],"of":[23,32,116,130,140],"minimizing":[24],"a":[25,122,127],"non-convex":[26],"objective":[27,64],"function.":[28],"was":[31,39,107],"main":[33],"interest":[34],"during":[35],"90\u2019s":[37,80],"then":[40],"forsaken":[41],"in":[42,93],"order":[43],"focus":[45],"unique":[48],"restoration":[49],"task":[50],"relying":[51],"non-smooth":[53],"convex":[54],"minimization.":[55],"Recent":[56],"advances":[57],"about":[58,82],"D-MS":[59],"were":[60,90],"dedicated":[61,101],"alternative":[63],"functions":[65],"for":[66],"efficient":[68],"numerical":[69],"solution":[70],"based":[71],"proximal":[73],"iterations":[74],"can":[75,132],"be":[76,133],"designed.":[77],"In":[78],"literature":[81],"D-MS,":[83],"equivalences":[84],"between":[85],"primal":[86,123],"dual":[88,125],"formulations":[89],"derived.":[91],"However,":[92],"framework":[95],"obtained":[96],"by":[97],"more":[98],"recent":[99,136],"developments":[100],"DMS":[103],"such":[104,154],"an":[105],"equivalence":[106],"not":[108],"yet":[109],"derived":[110],"it":[112],"is":[113],"goal":[115],"this":[117],"work.":[118],"By":[119],"providing":[120],"both":[121],"formulation,":[126],"large":[128],"panel":[129],"algorithms":[131,138],"employed":[134],"including":[135],"proximal-based":[137],"benefiting":[139],"good":[141],"convergence":[142],"behavior,":[143],"especially":[144],"due":[145],"KL":[147],"properties":[148],"also":[150],"most":[151],"standard":[152],"methods":[153],"as":[155],"BFGS.":[156]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
