{"id":"https://openalex.org/W2007203285","doi":"https://doi.org/10.1109/tip.2007.891064","title":"A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding","display_name":"A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding","publication_year":2007,"publication_date":"2007-02-28","ids":{"openalex":"https://openalex.org/W2007203285","doi":"https://doi.org/10.1109/tip.2007.891064","mag":"2007203285","pmid":"https://pubmed.ncbi.nlm.nih.gov/17357721"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2007.891064","doi":"https://doi.org/10.1109/tip.2007.891064","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2007.891064","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-a","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-2","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://infoscience.epfl.ch/bitstreams/1a06a770-004e-49b2-9753-83d11dbe0491/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055577533","display_name":"Florian Luisier A","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Florian Luisier","raw_affiliation_strings":["Biomedical Imaging Group, Swiss Federal Institute of Technology (EPFL), CH-1015 Lausanne, Switzerland. florian.luisier@epfl.ch"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group, Swiss Federal Institute of Technology (EPFL), CH-1015 Lausanne, Switzerland. florian.luisier@epfl.ch","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111724730","display_name":"Thierry Blu","orcid":"https://orcid.org/0000-0001-5759-0011","observed_orcids":["https://orcid.org/0000-0001-5759-0011"]},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Thierry Blu","raw_affiliation_strings":["Biomedical Imaging Group (BIG), Swiss Federal Institute of Technology, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group (BIG), Swiss Federal Institute of Technology, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027830035","display_name":"Michael A. Unser","orcid":"https://orcid.org/0000-0003-1248-2513","observed_orcids":["https://orcid.org/0000-0003-1248-2513"]},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Michael Unser","raw_affiliation_strings":["Biomedical Imaging Group (BIG), Swiss Federal Institute of Technology, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Biomedical Imaging Group (BIG), Swiss Federal Institute of Technology, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":44.6653,"has_fulltext":true,"cited_by_count":615,"citation_normalized_percentile":{"value":0.99864098,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"16","issue":"3","first_page":"593","last_page":"606"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":1.0,"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":1.0,"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/T11019","display_name":"Image Enhancement Techniques","score":0.0,"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.0,"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/image-denoising","display_name":"image denoising","score":0.9940000176429749},{"id":"https://openalex.org/keywords/stein-s-unbiased-risk-estimate","display_name":"Stein's unbiased risk estimate","score":0.9089999794960022},{"id":"https://openalex.org/keywords/mean-squared-error-estimation","display_name":"mean squared error estimation","score":0.7200000286102295},{"id":"https://openalex.org/keywords/wavelet-coefficient-modeling","display_name":"wavelet coefficient modeling","score":0.7120000123977661}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.74948650598526},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.6407660245895386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6136540174484253},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.6024152040481567},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.5679001212120056},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.5338571667671204},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.45107007026672363},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44520869851112366},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.43629974126815796},{"id":"https://openalex.org/C88829872","wikidata":"https://www.wikidata.org/wiki/Q5048176","display_name":"Cascade algorithm","level":5,"score":0.42610377073287964},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4202979803085327},{"id":"https://openalex.org/C155777637","wikidata":"https://www.wikidata.org/wiki/Q2736187","display_name":"Wavelet packet decomposition","level":4,"score":0.39025208353996277},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.3641948103904724},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3502967953681946},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2963145077228546},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17948588728904724},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D007089","descriptor_name":"Image Enhancement","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D007090","descriptor_name":"Image Interpretation, Computer-Assisted","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":true},{"descriptor_ui":"D012680","descriptor_name":"Sensitivity and Specificity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D015203","descriptor_name":"Reproducibility of Results","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016247","descriptor_name":"Information Storage and Retrieval","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D016477","descriptor_name":"Artifacts","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":5,"locations":[{"id":"doi:10.1109/tip.2007.891064","doi":"https://doi.org/10.1109/tip.2007.891064","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2007.891064","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","ccf-a","cwts-core","dongbi-a","doyens","jufo-3","ki-jl-2","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},{"id":"pmid:17357721","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/17357721","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":"Evaluation Study"},{"id":"pmh:oai:infoscience.tind.io:130329","doi":null,"is_oa":true,"landing_page_url":"http://bigwww.epfl.ch/publications/luisier0701.html","pdf_url":"https://infoscience.epfl.ch/bitstreams/1a06a770-004e-49b2-9753-83d11dbe0491/download","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"research article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.71.2820","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.71.2820","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://bigwww.epfl.ch/publications/luisier0701.pdf","raw_type":"text"},{"id":"pmh:oai:infoscience.epfl.ch:130329","doi":null,"is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/130329","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:infoscience.tind.io:130329","doi":null,"is_oa":true,"landing_page_url":"http://bigwww.epfl.ch/publications/luisier0701.html","pdf_url":"https://infoscience.epfl.ch/bitstreams/1a06a770-004e-49b2-9753-83d11dbe0491/download","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"research article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5599649393","display_name":null,"funder_award_id":"200020","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6278475803","display_name":"Spline methods for the continuous/discrete processing of images","funder_award_id":"109415","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G628552264","display_name":null,"funder_award_id":"200020","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320323832","display_name":"Centre d'Imagerie BioM\u00e9dicale","ror":"https://ror.org/03fw2bn12"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2007203285.pdf","grobid_xml":"https://content.openalex.org/works/W2007203285.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1584444527","https://openalex.org/W1775729916","https://openalex.org/W2009532511","https://openalex.org/W2043022774","https://openalex.org/W2054640142","https://openalex.org/W2062024414","https://openalex.org/W2065391104","https://openalex.org/W2070094080","https://openalex.org/W2079724595","https://openalex.org/W2082076175","https://openalex.org/W2104763670","https://openalex.org/W2113945798","https://openalex.org/W2119445186","https://openalex.org/W2125527601","https://openalex.org/W2129276048","https://openalex.org/W2132680427","https://openalex.org/W2134929491","https://openalex.org/W2135209903","https://openalex.org/W2140667604","https://openalex.org/W2143304716","https://openalex.org/W2144451417","https://openalex.org/W2152047336","https://openalex.org/W2154688547","https://openalex.org/W2158940042","https://openalex.org/W2163612361","https://openalex.org/W2163761533","https://openalex.org/W2170885533","https://openalex.org/W4255272544","https://openalex.org/W4295332281","https://openalex.org/W6634927326"],"related_works":["https://openalex.org/W7095589646","https://openalex.org/W2323264583","https://openalex.org/W2170688758","https://openalex.org/W2055453762","https://openalex.org/W2142371824","https://openalex.org/W2243744091","https://openalex.org/W2181652920","https://openalex.org/W2145984041","https://openalex.org/W2120084591","https://openalex.org/W1987641800"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3,14,28,65,103,112,120,179,195,201],"new":[4,155],"approach":[5,156],"to":[6,101,118,131],"orthonormal":[7,148],"wavelet":[8,19,126,149,202],"image":[9,50,79],"denoising.":[10],"Instead":[11],"of":[12,30,42,106,110,172,182,188,194],"postulating":[13],"statistical":[15,122],"model":[16,123],"for":[17,124],"the":[18,24,43,48,52,77,83,87,94,125,132,135,170,192],"coefficients,":[20],"we":[21,60],"directly":[22],"parametrize":[23],"denoising":[25,176],"process":[26],"as":[27],"sum":[29],"elementary":[31],"nonlinear":[32],"processes":[33],"with":[34,169],"unknown":[35,95],"weights.":[36],"We":[37,144],"then":[38],"minimize":[39],"an":[40,146],"estimate":[41,90,114],"mean":[44],"square":[45],"error":[46],"between":[47],"clean":[49,84],"and":[51,97,129,157,164],"denoised":[53],"one.":[54,85],"The":[55,108],"key":[56],"point":[57],"is":[58,91,191],"that":[59],"have":[61],"at":[62],"our":[63],"disposal":[64],"very":[66],"accurate,":[67],"statistically":[68],"unbiased,":[69],"MSE":[70],"estimate--Stein's":[71],"unbiased":[72],"risk":[73],"estimate--that":[74],"depends":[75],"on":[76,82,153,178],"noisy":[78],"alone,":[80],"not":[81,140],"Like":[86],"MSE,":[88],"this":[89,111,154,189],"quadratic":[92],"in":[93,134,200],"weights,":[96],"its":[98,159],"minimization":[99],"amounts":[100],"solving":[102],"linear":[104],"system":[105],"equations.":[107],"existence":[109],"priori":[113],"makes":[115],"it":[116,168],"unnecessary":[117],"devise":[119],"specific":[121],"coefficients.":[127],"Instead,":[128],"contrary":[130],"custom":[133],"literature,":[136],"these":[137],"coefficients":[138],"are":[139],"considered":[141],"random":[142],"anymore.":[143],"describe":[145],"interscale":[147],"thresholding":[150],"algorithm":[151],"based":[152],"show":[158],"near-optimal":[160],"performance--both":[161],"regarding":[162],"quality":[163],"CPU":[165],"requirement--by":[166],"comparing":[167],"results":[171],"three":[173],"state-of-the-art":[174],"nonredundant":[175],"algorithms":[177],"large":[180],"set":[181],"test":[183],"images.":[184],"An":[185],"interesting":[186],"fallout":[187],"study":[190],"development":[193],"new,":[196],"group-delay-based,":[197],"parent-child":[198],"prediction":[199],"dyadic":[203],"tree.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":17},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":17},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":37},{"year":2018,"cited_by_count":39},{"year":2017,"cited_by_count":42},{"year":2016,"cited_by_count":46},{"year":2015,"cited_by_count":48},{"year":2014,"cited_by_count":62},{"year":2013,"cited_by_count":37},{"year":2012,"cited_by_count":46}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
