{"id":"https://openalex.org/W2007093302","doi":"https://doi.org/10.1137/06065828x","title":"Denoising of Frame Coefficients Using $\\ell^1$ Data-Fidelity Term and Edge-Preserving Regularization","display_name":"Denoising of Frame Coefficients Using $\\ell^1$ Data-Fidelity Term and Edge-Preserving Regularization","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2007093302","doi":"https://doi.org/10.1137/06065828x","mag":"2007093302"},"language":"en","primary_location":{"id":"doi:10.1137/06065828x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06065828x","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00204984","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101487072","display_name":"Sylvain Durand","orcid":"https://orcid.org/0000-0003-1529-098X"},"institutions":[{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Sylvain Durand","raw_affiliation_strings":["[\u00c9cole Normale Sup\u00e9rieure Paris-Saclay]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[\u00c9cole Normale Sup\u00e9rieure Paris-Saclay]","institution_ids":["https://openalex.org/I29607241"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004818798","display_name":"Mila Nikolova","orcid":null},"institutions":[{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Mila Nikolova","raw_affiliation_strings":["[\u00c9cole Normale Sup\u00e9rieure Paris-Saclay]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[\u00c9cole Normale Sup\u00e9rieure Paris-Saclay]","institution_ids":["https://openalex.org/I29607241"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2775,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.9430009,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"6","issue":"2","first_page":"547","last_page":"576"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9980000257492065,"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":0.9980000257492065,"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9595000147819519,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6899904012680054},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6820337772369385},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.674002468585968},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.5861552953720093},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5691322684288025},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.53341144323349},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.49225226044654846},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47502025961875916},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4168446362018585},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3446360230445862},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2702610492706299},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2694905996322632},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2600764334201813},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08471187949180603}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6899904012680054},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6820337772369385},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.674002468585968},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.5861552953720093},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5691322684288025},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.53341144323349},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.49225226044654846},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47502025961875916},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4168446362018585},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3446360230445862},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2702610492706299},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2694905996322632},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2600764334201813},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08471187949180603},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/06065828x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/06065828x","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00204984v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00204984","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":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2007, 6 (2), pp.547-576. &#x27E8;10.1137/06065828X&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00204984v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00204984","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":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2007, 6 (2), pp.547-576. &#x27E8;10.1137/06065828X&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W59771946","https://openalex.org/W152228862","https://openalex.org/W633432057","https://openalex.org/W1507028917","https://openalex.org/W1553702074","https://openalex.org/W1554544485","https://openalex.org/W1972163814","https://openalex.org/W1972612537","https://openalex.org/W1984213606","https://openalex.org/W1985517056","https://openalex.org/W1992276332","https://openalex.org/W1992369383","https://openalex.org/W2006592653","https://openalex.org/W2008419427","https://openalex.org/W2015263936","https://openalex.org/W2017848200","https://openalex.org/W2020999234","https://openalex.org/W2033603511","https://openalex.org/W2045210749","https://openalex.org/W2050872129","https://openalex.org/W2066920141","https://openalex.org/W2079724595","https://openalex.org/W2088616581","https://openalex.org/W2091322926","https://openalex.org/W2091540466","https://openalex.org/W2099864919","https://openalex.org/W2103559027","https://openalex.org/W2105910985","https://openalex.org/W2107604145","https://openalex.org/W2111824420","https://openalex.org/W2111841405","https://openalex.org/W2115755118","https://openalex.org/W2124335859","https://openalex.org/W2129014341","https://openalex.org/W2133441707","https://openalex.org/W2145096794","https://openalex.org/W2149846618","https://openalex.org/W2151514667","https://openalex.org/W2156575092","https://openalex.org/W2158252006","https://openalex.org/W2158940042","https://openalex.org/W2165891581","https://openalex.org/W2166887721","https://openalex.org/W2167037342","https://openalex.org/W2167400582","https://openalex.org/W2168334281","https://openalex.org/W2168530812","https://openalex.org/W2168571615","https://openalex.org/W2320459610","https://openalex.org/W4285719527","https://openalex.org/W4299300834"],"related_works":["https://openalex.org/W3006513224","https://openalex.org/W2046456988","https://openalex.org/W2357409937","https://openalex.org/W2510582230","https://openalex.org/W2382174632","https://openalex.org/W2978674666","https://openalex.org/W2074430941","https://openalex.org/W2129959498","https://openalex.org/W2113096305","https://openalex.org/W3209466624"],"abstract_inverted_index":{"We":[0,35,79,112],"consider":[1],"the":[2,27,41,47,77,95,106,109,114,117],"denoising":[3],"of":[4,23,26,43,51,108,120],"a":[5,24,30,33,37,81],"function":[6,84],"containing":[7],"smooth":[8],"regions":[9],"and":[10,53,65,116],"edges.":[11],"Classical":[12],"ways":[13],"to":[14,57,63,70,73,89],"solve":[15],"this":[16,121],"problem":[17],"are":[18,99],"variational":[19],"methods":[20],"amd":[21],"shrinkage":[22,49],"representation":[25],"data":[28],"in":[29,76,105],"basis":[31],"or":[32],"frame.":[34],"propose":[36],"method":[38,50],"which":[39,98],"combines":[40],"advantages":[42],"both":[44],"approaches.":[45],"followinig":[46],"wavelet":[48],"Donoho":[52],"Johnstone,":[54],"we":[55],"set":[56,69],"zero":[58],"all":[59,86],"frame":[60],"coefficients":[61,88,97],"correponding":[62],"noise":[64],"some":[66],"coefficients,":[67],"erroneously":[68],"zero,":[71],"leading":[72],"Gibbs-lika":[74],"oscillations":[75],"estimate.":[78],"design":[80],"specialized":[82],"objective":[83,122],"allowing":[85],"these":[87],"be":[90],"selectively":[91],"restored,":[92],"without":[93],"modifying":[94],"other":[96],"well":[100],"nealy":[101],"faithful,":[102],"using":[103],"regularized":[104],"domain":[107],"restored":[110],"function.":[111,123],"analyse":[113],"well-posedness":[115],"main":[118],"properties":[119]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}
