{"id":"https://openalex.org/W1511118377","doi":"https://doi.org/10.1137/07068881x","title":"Image Processing with Nonlocal Spectral Bases","display_name":"Image Processing with Nonlocal Spectral Bases","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1511118377","doi":"https://doi.org/10.1137/07068881x","mag":"1511118377"},"language":"en","primary_location":{"id":"doi:10.1137/07068881x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07068881x","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 & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"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":["CEntre de REcherches en MAth\u00e9matiques de la DEcision"],"affiliations":[{"raw_affiliation_string":"CEntre de REcherches en MAth\u00e9matiques de la DEcision","institution_ids":["https://openalex.org/I171048554"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058651667"],"corresponding_institution_ids":["https://openalex.org/I171048554"],"apc_list":null,"apc_paid":null,"fwci":5.9702,"has_fulltext":false,"cited_by_count":87,"citation_normalized_percentile":{"value":0.96377048,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"7","issue":"2","first_page":"703","last_page":"730"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9976999759674072,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6400694251060486},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.6215171217918396},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5362052321434021},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5284450054168701},{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.5196070075035095},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4969539940357208},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.4835081398487091},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.4595865309238434},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4585554003715515},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4536449909210205},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.41237810254096985},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.3856785297393799},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38023698329925537},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3551812171936035},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2652183175086975},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16235879063606262}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6400694251060486},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.6215171217918396},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5362052321434021},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5284450054168701},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.5196070075035095},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4969539940357208},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4835081398487091},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.4595865309238434},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4585554003715515},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4536449909210205},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.41237810254096985},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.3856785297393799},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38023698329925537},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3551812171936035},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2652183175086975},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16235879063606262},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/07068881x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/07068881x","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 & Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8999999761581421}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W127809959","https://openalex.org/W1486280163","https://openalex.org/W1506777192","https://openalex.org/W1578099820","https://openalex.org/W1579238192","https://openalex.org/W1587541211","https://openalex.org/W1604668941","https://openalex.org/W1608578576","https://openalex.org/W1652206149","https://openalex.org/W1673090216","https://openalex.org/W1967277558","https://openalex.org/W1984032850","https://openalex.org/W1994154911","https://openalex.org/W2000214666","https://openalex.org/W2005089986","https://openalex.org/W2006554089","https://openalex.org/W2019248995","https://openalex.org/W2024221621","https://openalex.org/W2024738905","https://openalex.org/W2025779824","https://openalex.org/W2027772247","https://openalex.org/W2038649727","https://openalex.org/W2056370875","https://openalex.org/W2064702003","https://openalex.org/W2067191022","https://openalex.org/W2069912449","https://openalex.org/W2097308346","https://openalex.org/W2099046646","https://openalex.org/W2099244020","https://openalex.org/W2102443333","https://openalex.org/W2103559027","https://openalex.org/W2103829273","https://openalex.org/W2104290444","https://openalex.org/W2104339857","https://openalex.org/W2109504624","https://openalex.org/W2109991658","https://openalex.org/W2115755118","https://openalex.org/W2116013899","https://openalex.org/W2120023453","https://openalex.org/W2122890444","https://openalex.org/W2126922884","https://openalex.org/W2135073078","https://openalex.org/W2136396015","https://openalex.org/W2136622531","https://openalex.org/W2140947779","https://openalex.org/W2149287117","https://openalex.org/W2150134853","https://openalex.org/W2155540403","https://openalex.org/W2156447271","https://openalex.org/W2158252006","https://openalex.org/W2158940042","https://openalex.org/W2162547327","https://openalex.org/W2164270936","https://openalex.org/W2168896212","https://openalex.org/W2951489751","https://openalex.org/W3165903168"],"related_works":["https://openalex.org/W2953058328","https://openalex.org/W1542224353","https://openalex.org/W1661087619","https://openalex.org/W2750730210","https://openalex.org/W2799167307","https://openalex.org/W4361272408","https://openalex.org/W2147467385","https://openalex.org/W4238278477","https://openalex.org/W2091205541","https://openalex.org/W2035143246"],"abstract_inverted_index":{"This":[0,104],"article":[1],"studies":[2],"regularization":[3],"schemes":[4,60],"that":[5,64,90],"are":[6,119],"defined":[7],"using":[8],"a":[9,16,34,98,101,126],"lifting":[10],"of":[11,23,29,40,58,69,78,121,132,140,155,164],"the":[12,66,70,75,79,122,130,133,138,148,156,162],"image":[13],"pixels":[14],"in":[15,113,147,167],"high-dimensional":[17],"space.":[18],"For":[19],"some":[20],"specific":[21,76],"classes":[22],"geometric":[24],"images,":[25],"this":[26,44],"discrete":[27,123],"set":[28],"points":[30],"is":[31,159],"sampled":[32],"along":[33],"low-dimensional":[35],"smooth":[36],"manifold.":[37,103],"The":[38,153],"construction":[39],"differential":[41],"operators":[42,112],"on":[43,74,125],"lifted":[45,71],"space":[46],"allows":[47,107],"one":[48,81,108],"to":[49,62,109,129],"compute":[50],"PDE":[51,141],"flows":[52],"and":[53,86,145,150],"perform":[54],"variational":[55],"optimizations.":[56],"All":[57],"these":[59],"lead":[61],"regularizations":[63],"exploit":[65],"manifold":[67,127],"structure":[68],"image.":[72,134],"Depending":[73],"definition":[77],"lifting,":[80],"recovers":[82],"several":[83],"well-known":[84],"semilocal":[85,99,149],"nonlocal":[87,102,151,157],"denoising":[88],"algorithms":[89],"can":[91],"be":[92],"interpreted":[93],"as":[94],"local":[95],"estimators":[96],"over":[97],"or":[100],"framework":[105],"also":[106],"define":[110],"thresholding":[111],"adapted":[114,128],"orthogonal":[115,168],"bases.":[116,169],"These":[117],"bases":[118],"eigenvectors":[120],"Laplacian":[124],"geometry":[131],"Numerical":[135],"results":[136],"compare":[137],"efficiency":[139],"flows,":[142],"energy":[143],"minimizations,":[144],"thresholdings":[146],"settings.":[152],"superiority":[154],"computations":[158],"studied":[160],"through":[161],"performance":[163],"nonlinear":[165],"approximation":[166]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}