{"id":"https://openalex.org/W1981337995","doi":"https://doi.org/10.1137/090770783","title":"Learning the Morphological Diversity","display_name":"Learning the Morphological Diversity","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1981337995","doi":"https://doi.org/10.1137/090770783","mag":"1981337995"},"language":"en","primary_location":{"id":"doi:10.1137/090770783","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090770783","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-00415782","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058651667","display_name":"Gabriel Peyr\u00e9","orcid":"https://orcid.org/0000-0002-4477-0387"},"institutions":[{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Gabriel Peyr\u00e9","raw_affiliation_strings":["gabriel.peyre@ceremade.dauphine.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"gabriel.peyre@ceremade.dauphine.fr#TAB#","institution_ids":["https://openalex.org/I171048554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008136365","display_name":"Jalal Fadili","orcid":"https://orcid.org/0000-0002-8165-7578"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jalal Fadili","raw_affiliation_strings":["jalal.fadili@greyc.ensicaen.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"jalal.fadili@greyc.ensicaen.fr#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008794792","display_name":"Jean\u2010Luc Starck","orcid":"https://orcid.org/0000-0003-2177-7794"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jean-Luc Starck","raw_affiliation_strings":["jstarck@cea.fr#TAB#"],"affiliations":[{"raw_affiliation_string":"jstarck@cea.fr#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058651667"],"corresponding_institution_ids":["https://openalex.org/I171048554"],"apc_list":null,"apc_paid":null,"fwci":5.8185,"has_fulltext":false,"cited_by_count":97,"citation_normalized_percentile":{"value":0.96467364,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"3","issue":"3","first_page":"646","last_page":"669"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9988999962806702,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9988999962806702,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9980999827384949,"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/inpainting","display_name":"Inpainting","score":0.9376777410507202},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.599553108215332},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.578737199306488},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5643339157104492},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5232031345367432},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4990959167480469},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.47341400384902954},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4437633156776428},{"id":"https://openalex.org/keywords/texture","display_name":"Texture (cosmology)","score":0.4418404698371887},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4317079782485962},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3604446351528168},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34143346548080444},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.10434022545814514}],"concepts":[{"id":"https://openalex.org/C11727466","wikidata":"https://www.wikidata.org/wiki/Q1628157","display_name":"Inpainting","level":3,"score":0.9376777410507202},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.599553108215332},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.578737199306488},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5643339157104492},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5232031345367432},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4990959167480469},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.47341400384902954},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4437633156776428},{"id":"https://openalex.org/C2781195486","wikidata":"https://www.wikidata.org/wiki/Q289436","display_name":"Texture (cosmology)","level":3,"score":0.4418404698371887},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4317079782485962},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3604446351528168},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34143346548080444},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.10434022545814514},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/090770783","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090770783","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:10.1.1.211.9638","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.211.9638","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/41/57/82/PDF/PeyreFadiliStarckSIIMS.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00415782v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00415782","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":"SIAM Journal on Imaging Sciences, 2010, 3 (3), pp.646-669. &#x27E8;10.1137/090770783&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00415782v2","is_oa":true,"landing_page_url":"https://hal.science/hal-00415782","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":"SIAM Journal on Imaging Sciences, 2010, 3 (3), pp.646-669. &#x27E8;10.1137/090770783&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"score":0.7099999785423279,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W207373900","https://openalex.org/W1488881187","https://openalex.org/W1540764732","https://openalex.org/W1560910787","https://openalex.org/W1951629768","https://openalex.org/W1986931325","https://openalex.org/W1999905919","https://openalex.org/W2005876975","https://openalex.org/W2006262045","https://openalex.org/W2008231398","https://openalex.org/W2016860730","https://openalex.org/W2024738905","https://openalex.org/W2034885738","https://openalex.org/W2059921811","https://openalex.org/W2062102668","https://openalex.org/W2063978378","https://openalex.org/W2064702003","https://openalex.org/W2069912449","https://openalex.org/W2082855665","https://openalex.org/W2088498643","https://openalex.org/W2092231222","https://openalex.org/W2100415658","https://openalex.org/W2101657089","https://openalex.org/W2102443333","https://openalex.org/W2103559027","https://openalex.org/W2105038642","https://openalex.org/W2105536051","https://openalex.org/W2107844156","https://openalex.org/W2108454251","https://openalex.org/W2109196586","https://openalex.org/W2109504624","https://openalex.org/W2110505738","https://openalex.org/W2112447569","https://openalex.org/W2113990625","https://openalex.org/W2114122776","https://openalex.org/W2115429828","https://openalex.org/W2115706991","https://openalex.org/W2115755118","https://openalex.org/W2115794584","https://openalex.org/W2116013899","https://openalex.org/W2121651107","https://openalex.org/W2125945051","https://openalex.org/W2128638419","https://openalex.org/W2130184048","https://openalex.org/W2137234026","https://openalex.org/W2140499889","https://openalex.org/W2140598595","https://openalex.org/W2142940228","https://openalex.org/W2145889472","https://openalex.org/W2146482778","https://openalex.org/W2152222383","https://openalex.org/W2153663612","https://openalex.org/W2154996879","https://openalex.org/W2157434051","https://openalex.org/W2158940042","https://openalex.org/W2160547390","https://openalex.org/W2161219071","https://openalex.org/W2162547327","https://openalex.org/W2167732364","https://openalex.org/W2295936755","https://openalex.org/W4213316114"],"related_works":["https://openalex.org/W3178025616","https://openalex.org/W2060947339","https://openalex.org/W2131831293","https://openalex.org/W2017457812","https://openalex.org/W1995073329","https://openalex.org/W2946160871","https://openalex.org/W3035059915","https://openalex.org/W425542480","https://openalex.org/W49967185","https://openalex.org/W2107727507"],"abstract_inverted_index":{"This":[0,70],"article":[1],"proposes":[2],"a":[3,10,55,64,95],"new":[4,85],"method":[5],"for":[6],"image":[7],"separation":[8,60],"into":[9],"linear":[11],"combination":[12],"of":[13,29,67,98],"morphological":[14,87],"components.":[15],"Sparsity":[16],"in":[17,45,126],"fixed":[18,49,115],"dictionaries":[19,41,103],"is":[20,61,73,91,123],"used":[21],"to":[22,75,93,109],"extract":[23],"the":[24,30,46,59,99],"cartoon":[25],"and":[26,50,58],"oscillating":[27],"content":[28],"image.":[31,47],"Complicated":[32],"texture":[33,129],"patterns":[34],"are":[35],"extracted":[36],"by":[37,114],"learning":[38],"adapted":[39,102],"local":[40],"that":[42,120],"sparsify":[43],"patches":[44],"These":[48],"learned":[51,104],"sparsity":[52],"priors":[53],"define":[54],"nonconvex":[56],"energy,":[57],"obtained":[62],"as":[63,82],"stationary":[65,96],"point":[66,97],"this":[68,121],"energy.":[69,100],"variational":[71],"optimization":[72],"extended":[74],"solve":[76],"more":[77],"general":[78],"inverse":[79],"problems":[80],"such":[81],"inpainting.":[83],"A":[84],"adaptive":[86],"component":[88],"analysis":[89],"algorithm":[90],"derived":[92],"find":[94],"Using":[101],"from":[105],"data":[106],"allows":[107],"one":[108],"circumvent":[110],"some":[111],"difficulties":[112],"faced":[113],"dictionaries.":[116],"Numerical":[117],"results":[118],"demonstrate":[119],"adaptivity":[122],"indeed":[124],"crucial":[125],"capturing":[127],"complex":[128],"patterns.":[130]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":42},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
