{"id":"https://openalex.org/W2749075270","doi":"https://doi.org/10.1137/16m1080781","title":"Nonlocal Means and Optimal Weights for Noise Removal","display_name":"Nonlocal Means and Optimal Weights for Noise Removal","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2749075270","doi":"https://doi.org/10.1137/16m1080781","mag":"2749075270"},"language":"en","primary_location":{"id":"doi:10.1137/16m1080781","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1080781","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://inria.hal.science/hal-01575918","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056596552","display_name":"Qiyu Jin","orcid":"https://orcid.org/0000-0001-8639-233X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Qiyu Jin","raw_affiliation_strings":["School of Mathematical Sciences"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051797730","display_name":"Ion Grama","orcid":"https://orcid.org/0000-0003-4957-4454"},"institutions":[{"id":"https://openalex.org/I4210119023","display_name":"Laboratoire de Math\u00e9matiques de Bretagne Atlantique","ror":"https://ror.org/02ght4n58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2802204017","https://openalex.org/I4210119023","https://openalex.org/I4210141950","https://openalex.org/I4412460332"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Ion Grama","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques de Bretagne Atlantique"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques de Bretagne Atlantique","institution_ids":["https://openalex.org/I4210119023"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033807512","display_name":"Charles Kervrann","orcid":"https://orcid.org/0000-0001-6263-0452"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Charles Kervrann","raw_affiliation_strings":["Space-timE RePresentation, Imaging and cellular dynamics of molecular COmplexes"],"affiliations":[{"raw_affiliation_string":"Space-timE RePresentation, Imaging and cellular dynamics of molecular COmplexes","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108581173","display_name":"Quansheng Liu","orcid":"https://orcid.org/0000-0002-3094-7006"},"institutions":[{"id":"https://openalex.org/I4210119023","display_name":"Laboratoire de Math\u00e9matiques de Bretagne Atlantique","ror":"https://ror.org/02ght4n58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2802204017","https://openalex.org/I4210119023","https://openalex.org/I4210141950","https://openalex.org/I4412460332"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Quansheng Liu","raw_affiliation_strings":["School of Computer and Software [Nanjing University]","Laboratoire de Math\u00e9matiques de Bretagne Atlantique"],"affiliations":[{"raw_affiliation_string":"School of Computer and Software [Nanjing University]","institution_ids":[]},{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques de Bretagne Atlantique","institution_ids":["https://openalex.org/I4210119023"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5056596552"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1257,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.92823766,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"10","issue":"4","first_page":"1878","last_page":"1920"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998999834060669,"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":0.9998999834060669,"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/T11659","display_name":"Advanced Image Fusion Techniques","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.9923999905586243,"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/pointwise","display_name":"Pointwise","score":0.8205701112747192},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6651282906532288},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.662747859954834},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.6228198409080505},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.574216365814209},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.551175057888031},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5398257970809937},{"id":"https://openalex.org/keywords/additive-white-gaussian-noise","display_name":"Additive white Gaussian noise","score":0.4878127872943878},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.48532480001449585},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.46669867634773254},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.46642380952835083},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4291931390762329},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.4126341640949249},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3503764271736145},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.34756243228912354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2790496349334717},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.20945170521736145},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.13330286741256714},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1103493869304657},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.10425642132759094},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08483177423477173}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8205701112747192},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6651282906532288},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.662747859954834},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.6228198409080505},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.574216365814209},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.551175057888031},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5398257970809937},{"id":"https://openalex.org/C169334058","wikidata":"https://www.wikidata.org/wiki/Q353292","display_name":"Additive white Gaussian noise","level":3,"score":0.4878127872943878},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.48532480001449585},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.46669867634773254},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.46642380952835083},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4291931390762329},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.4126341640949249},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3503764271736145},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.34756243228912354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2790496349334717},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.20945170521736145},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.13330286741256714},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1103493869304657},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.10425642132759094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08483177423477173},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1080781","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1080781","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:HAL:hal-01575918v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01575918","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, 2017","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01575918v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01575918","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, 2017","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5517430953","display_name":null,"funder_award_id":"11571052","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6828996767","display_name":null,"funder_award_id":"11401590","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7870678852","display_name":null,"funder_award_id":"61661039","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1965102920","https://openalex.org/W1972499291","https://openalex.org/W1972860294","https://openalex.org/W1973207753","https://openalex.org/W1986360843","https://openalex.org/W1986490170","https://openalex.org/W1988175255","https://openalex.org/W1993296994","https://openalex.org/W1997147589","https://openalex.org/W1998419211","https://openalex.org/W1998587681","https://openalex.org/W2000953144","https://openalex.org/W2009265594","https://openalex.org/W2012910518","https://openalex.org/W2023926794","https://openalex.org/W2031314447","https://openalex.org/W2038649727","https://openalex.org/W2039487641","https://openalex.org/W2041625018","https://openalex.org/W2042220165","https://openalex.org/W2056370875","https://openalex.org/W2061800457","https://openalex.org/W2062560607","https://openalex.org/W2067098972","https://openalex.org/W2101984093","https://openalex.org/W2103559027","https://openalex.org/W2108382860","https://openalex.org/W2112575052","https://openalex.org/W2116857329","https://openalex.org/W2117214938","https://openalex.org/W2118071128","https://openalex.org/W2130184048","https://openalex.org/W2136396015","https://openalex.org/W2141195893","https://openalex.org/W2142113560","https://openalex.org/W2142592339","https://openalex.org/W2143131425","https://openalex.org/W2144851790","https://openalex.org/W2146279621","https://openalex.org/W2153663612","https://openalex.org/W2157803030","https://openalex.org/W2158940042","https://openalex.org/W2166879250","https://openalex.org/W2172656675","https://openalex.org/W2963190952","https://openalex.org/W4248893591"],"related_works":["https://openalex.org/W1974392290","https://openalex.org/W1911817635","https://openalex.org/W2074565401","https://openalex.org/W2810224748","https://openalex.org/W2011915004","https://openalex.org/W2353656796","https://openalex.org/W1967187784","https://openalex.org/W2130974430","https://openalex.org/W3103566292","https://openalex.org/W1607924090"],"abstract_inverted_index":{"In":[0,67],"this":[1],"paper,":[2],"a":[3,38,96],"new":[4],"denoising":[5],"algorithm":[6,128,138],"to":[7,52,98,150],"deal":[8],"with":[9,40],"the":[10,19,31,44,63,68,76,88,101,114,119,126,133,141,151],"additive":[11],"white":[12],"Gaussian":[13,91],"noise":[14],"model":[15],"is":[16,51,129,146],"described.":[17],"Following":[18],"nonlocal":[20],"(NL)":[21],"means":[22,144,155],"approach,":[23],"we":[24,73,82,94],"propose":[25,95],"an":[26,59],"adaptive":[27,54,71,107],"estimator":[28,116],"based":[29],"on":[30,43],"weighted":[32],"average":[33],"of":[34,46,62,70,87,125,160],"observations":[35],"taken":[36],"in":[37,158],"neighborhood":[39],"weights":[41,55,78],"depending":[42],"similarity":[45],"local":[47],"patches.":[48],"The":[49,123],"idea":[50],"compute":[53],"that":[56,75,136],"best":[57],"minimize":[58],"upper":[60],"bound":[61],"pointwise":[64],"$L_2$":[65],"risk.":[66],"framework":[69],"estimation,":[72],"show":[74,135],"\u201coracle\u201d":[77],"are":[79],"optimal":[80,121],"if":[81],"consider":[83],"triangular":[84],"kernels":[85],"instead":[86],"commonly":[89],"used":[90],"kernel.":[92],"Furthermore,":[93],"way":[97],"automatically":[99],"choose":[100],"spatially":[102],"varying":[103],"smoothing":[104],"parameter":[105],"for":[106],"denoising.":[108],"Under":[109],"conventional":[110],"minimal":[111],"regularity":[112],"conditions,":[113],"obtained":[115],"converges":[117],"at":[118],"usual":[120],"rate.":[122],"implementation":[124],"proposed":[127],"also":[130],"straightforward":[131],"and":[132,145,165],"simulations":[134],"our":[137],"significantly":[139],"improves":[140],"classical":[142],"NL":[143,154],"competitive":[147],"when":[148],"compared":[149],"more":[152],"sophisticated":[153],"filters,":[156],"both":[157],"terms":[159],"peak":[161],"signal-to-noise":[162],"ratio":[163],"values":[164],"visual":[166],"quality.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}