{"id":"https://openalex.org/W2012910518","doi":"https://doi.org/10.1137/120902276","title":"Posterior Expectation of the Total Variation Model: Properties and Experiments","display_name":"Posterior Expectation of the Total Variation Model: Properties and Experiments","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2012910518","doi":"https://doi.org/10.1137/120902276","mag":"2012910518"},"language":"en","primary_location":{"id":"doi:10.1137/120902276","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120902276","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-00764175","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052084530","display_name":"C\u00e9cile Louchet","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131315","display_name":"Laboratoire de Math\u00e9matiques Analyse, Probabilit\u00e9s, Mod\u00e9lisation Orl\u00e9ans","ror":"https://ror.org/03d6rdf69","country_code":"FR","type":"facility","lineage":["https://openalex.org/I12449238","https://openalex.org/I1294671590","https://openalex.org/I4210131315","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"C\u00e9cile Louchet","raw_affiliation_strings":["Math\u00e9matiques - Analyse, Probabilit\u00e9s, Mod\u00e9lisation - Orl\u00e9ans"],"affiliations":[{"raw_affiliation_string":"Math\u00e9matiques - Analyse, Probabilit\u00e9s, Mod\u00e9lisation - Orl\u00e9ans","institution_ids":["https://openalex.org/I4210131315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090845509","display_name":"Lionel Moisan","orcid":"https://orcid.org/0000-0001-6019-2698"},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Lionel Moisan","raw_affiliation_strings":["Math\u00e9matiques Appliqu\u00e9es Paris 5"],"affiliations":[{"raw_affiliation_string":"Math\u00e9matiques Appliqu\u00e9es Paris 5","institution_ids":["https://openalex.org/I204730241"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052084530"],"corresponding_institution_ids":["https://openalex.org/I4210131315"],"apc_list":null,"apc_paid":null,"fwci":2.4879,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.90463597,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"6","issue":"4","first_page":"2640","last_page":"2684"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9970999956130981,"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":0.9970999956130981,"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9909999966621399,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.972599983215332,"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/maximum-a-posteriori-estimation","display_name":"Maximum a posteriori estimation","score":0.8843708038330078},{"id":"https://openalex.org/keywords/posterior-probability","display_name":"Posterior probability","score":0.7568575143814087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6563694477081299},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6147039532661438},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5212650895118713},{"id":"https://openalex.org/keywords/expectation\u2013maximization-algorithm","display_name":"Expectation\u2013maximization algorithm","score":0.5085469484329224},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.4789220094680786},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4757123589515686},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.46243131160736084},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4471936523914337},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44563180208206177},{"id":"https://openalex.org/keywords/bayes-estimator","display_name":"Bayes estimator","score":0.4381486177444458},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43775755167007446},{"id":"https://openalex.org/keywords/point-distribution-model","display_name":"Point distribution model","score":0.43222978711128235},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4231807589530945},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.42010581493377686},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4017432928085327},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.33956751227378845},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2504892945289612},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24268978834152222},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18982306122779846},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16380301117897034},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10649251937866211}],"concepts":[{"id":"https://openalex.org/C9810830","wikidata":"https://www.wikidata.org/wiki/Q635384","display_name":"Maximum a posteriori estimation","level":3,"score":0.8843708038330078},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.7568575143814087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6563694477081299},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6147039532661438},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5212650895118713},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.5085469484329224},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.4789220094680786},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4757123589515686},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.46243131160736084},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4471936523914337},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44563180208206177},{"id":"https://openalex.org/C68022304","wikidata":"https://www.wikidata.org/wiki/Q842217","display_name":"Bayes estimator","level":3,"score":0.4381486177444458},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43775755167007446},{"id":"https://openalex.org/C118317068","wikidata":"https://www.wikidata.org/wiki/Q2100760","display_name":"Point distribution model","level":2,"score":0.43222978711128235},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4231807589530945},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.42010581493377686},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4017432928085327},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.33956751227378845},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2504892945289612},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24268978834152222},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18982306122779846},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16380301117897034},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10649251937866211},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/120902276","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120902276","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:10.1.1.370.1862","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.370.1862","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/76/41/75/PDF/paper1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.411.1524","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.411.1524","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.inria.fr/docs/00/85/84/64/PDF/paper1.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00764175v3","is_oa":true,"landing_page_url":"https://hal.science/hal-00764175","pdf_url":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://epubs.siam.org/toc/sjisbi/6/4","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00764175v3","is_oa":true,"landing_page_url":"https://hal.science/hal-00764175","pdf_url":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://epubs.siam.org/toc/sjisbi/6/4","raw_type":"Journal articles"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":81,"referenced_works":["https://openalex.org/W161217653","https://openalex.org/W372212883","https://openalex.org/W392228186","https://openalex.org/W1256797459","https://openalex.org/W1480714962","https://openalex.org/W1496099826","https://openalex.org/W1500583293","https://openalex.org/W1508867082","https://openalex.org/W1573820523","https://openalex.org/W1578985305","https://openalex.org/W1604521381","https://openalex.org/W1606276843","https://openalex.org/W1654451837","https://openalex.org/W1953936588","https://openalex.org/W1978859603","https://openalex.org/W1986938753","https://openalex.org/W1987394250","https://openalex.org/W1992276332","https://openalex.org/W1996771141","https://openalex.org/W1997063559","https://openalex.org/W2000594266","https://openalex.org/W2003884262","https://openalex.org/W2004449346","https://openalex.org/W2008454012","https://openalex.org/W2009265594","https://openalex.org/W2012118748","https://openalex.org/W2018237299","https://openalex.org/W2021345239","https://openalex.org/W2031832209","https://openalex.org/W2033603511","https://openalex.org/W2038495454","https://openalex.org/W2038649727","https://openalex.org/W2040378863","https://openalex.org/W2042261731","https://openalex.org/W2048511268","https://openalex.org/W2048971218","https://openalex.org/W2050872129","https://openalex.org/W2054640142","https://openalex.org/W2055834582","https://openalex.org/W2061133334","https://openalex.org/W2075254304","https://openalex.org/W2075457552","https://openalex.org/W2075674485","https://openalex.org/W2081930078","https://openalex.org/W2092231222","https://openalex.org/W2092663520","https://openalex.org/W2093109539","https://openalex.org/W2093371713","https://openalex.org/W2097335885","https://openalex.org/W2100533333","https://openalex.org/W2103559027","https://openalex.org/W2105880637","https://openalex.org/W2122192562","https://openalex.org/W2122275806","https://openalex.org/W2130184048","https://openalex.org/W2135479785","https://openalex.org/W2136423906","https://openalex.org/W2137666346","https://openalex.org/W2138448055","https://openalex.org/W2139643804","https://openalex.org/W2141006018","https://openalex.org/W2143131425","https://openalex.org/W2147656689","https://openalex.org/W2162980292","https://openalex.org/W2166887721","https://openalex.org/W2272584315","https://openalex.org/W2320459610","https://openalex.org/W2324239163","https://openalex.org/W2523352299","https://openalex.org/W2545464558","https://openalex.org/W2602441275","https://openalex.org/W2785061205","https://openalex.org/W2898734996","https://openalex.org/W2963777151","https://openalex.org/W3101933250","https://openalex.org/W4237080436","https://openalex.org/W4246709859","https://openalex.org/W4252713891","https://openalex.org/W4253250161","https://openalex.org/W4285719527","https://openalex.org/W4299862321"],"related_works":["https://openalex.org/W2114899076","https://openalex.org/W1783992599","https://openalex.org/W2124697778","https://openalex.org/W2135468550","https://openalex.org/W2133422797","https://openalex.org/W2045588782","https://openalex.org/W2181917637","https://openalex.org/W4284711868","https://openalex.org/W2070699059","https://openalex.org/W2012910518"],"abstract_inverted_index":{"The":[0],"total":[1],"variation":[2],"image":[3],"(or":[4],"signal)":[5],"denoising":[6],"model":[7,73,123],"is":[8,38],"a":[9,17,21,32,42,69],"variational":[10],"approach":[11],"that":[12,49,74,114,118],"can":[13],"be":[14],"interpreted,":[15],"in":[16,60,116],"Bayesian":[18],"framework,":[19],"as":[20],"search":[22],"for":[23,41,100],"the":[24,28,46,51,61,76,79,89,101,105,128],"maximum":[25,85],"point":[26],"of":[27,53,71,78,83,104],"posterior":[29,80,106],"density":[30],"(maximum":[31],"posteriori":[33],"estimator).":[34],"This":[35],"maximization":[36],"aspect":[37],"partly":[39],"responsible":[40],"restoration":[43],"bias":[44],"called":[45],"\u201cstaircasing":[47],"effect,\u201d":[48],"is,":[50],"outbreak":[52],"quasi-constant":[54],"regions":[55],"separated":[56],"by":[57],"sharp":[58],"edges":[59],"intensity":[62],"map.":[63],"In":[64],"this":[65,72,94,122],"paper":[66],"we":[67],"study":[68],"variant":[70,95],"considers":[75],"expectation":[77],"distribution":[81],"instead":[82],"its":[84],"point.":[86],"Apart":[87],"from":[88,127],"least":[90],"square":[91],"error":[92],"optimality,":[93],"seems":[96],"to":[97],"better":[98],"account":[99],"global":[102],"properties":[103],"distribution.":[107],"We":[108],"present":[109],"theoretical":[110],"and":[111],"numerical":[112],"results":[113],"demonstrate":[115],"particular":[117],"images":[119],"denoised":[120],"with":[121],"do":[124],"not":[125],"suffer":[126],"staircasing":[129],"effect.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}