{"id":"https://openalex.org/W2083059319","doi":"https://doi.org/10.1109/tip.2015.2409562","title":"Adaptive Regularization With the Structure Tensor","display_name":"Adaptive Regularization With the Structure Tensor","publication_year":2015,"publication_date":"2015-03-06","ids":{"openalex":"https://openalex.org/W2083059319","doi":"https://doi.org/10.1109/tip.2015.2409562","mag":"2083059319","pmid":"https://pubmed.ncbi.nlm.nih.gov/25769155"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2015.2409562","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2015.2409562","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,"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"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5026933333","display_name":"Virginia Estellers","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Virginia Estellers","raw_affiliation_strings":["Department of Computer Science, University of California at Los Angeles, Los Angeles, CA, USA","[Department of Computer Science, University of California at Los Angeles, Los Angeles, CA, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of California at Los Angeles, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"[Department of Computer Science, University of California at Los Angeles, Los Angeles, CA, USA]","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038328783","display_name":"Stefano Soatto","orcid":"https://orcid.org/0000-0003-2902-6362"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stefano Soatto","raw_affiliation_strings":["Department of Computer Science, Electrical Engineering, University of California at Los Angeles, CA, USA","Department of Computer Science, Electrical Engineering, University of California at Los Angeles, Los Angeles, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Electrical Engineering, University of California at Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Computer Science, Electrical Engineering, University of California at Los Angeles, Los Angeles, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031210396","display_name":"Xavier Bresson","orcid":"https://orcid.org/0000-0002-7109-461X"},"institutions":[{"id":"https://openalex.org/I97565354","display_name":"University of Lausanne","ror":"https://ror.org/019whta54","country_code":"CH","type":"education","lineage":["https://openalex.org/I97565354"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Xavier Bresson","raw_affiliation_strings":["Medical Image Laboratory, Universite de Lausanne, Lausanne, Switzerland","[Medical Image Laboratory, Universite de Lausanne, Lausanne, Switzerland]"],"affiliations":[{"raw_affiliation_string":"Medical Image Laboratory, Universite de Lausanne, Lausanne, Switzerland","institution_ids":["https://openalex.org/I97565354"]},{"raw_affiliation_string":"[Medical Image Laboratory, Universite de Lausanne, Lausanne, Switzerland]","institution_ids":["https://openalex.org/I97565354"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026933333"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":10.7213,"has_fulltext":false,"cited_by_count":80,"citation_normalized_percentile":{"value":0.98914553,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"24","issue":"6","first_page":"1777","last_page":"1790"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9962000250816345,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9962000250816345,"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"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9890999794006348,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9890999794006348,"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/deblurring","display_name":"Deblurring","score":0.8493028879165649},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6569869518280029},{"id":"https://openalex.org/keywords/structure-tensor","display_name":"Structure tensor","score":0.6465155482292175},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.5599934458732605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5342214703559875},{"id":"https://openalex.org/keywords/anisotropic-diffusion","display_name":"Anisotropic diffusion","score":0.5258772373199463},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.48759832978248596},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.47017067670822144},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4492642879486084},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4322358965873718},{"id":"https://openalex.org/keywords/image-restoration","display_name":"Image restoration","score":0.4211086630821228},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4156067669391632},{"id":"https://openalex.org/keywords/total-variation-denoising","display_name":"Total variation denoising","score":0.41342049837112427},{"id":"https://openalex.org/keywords/geometry-processing","display_name":"Geometry processing","score":0.41101253032684326},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3505696654319763},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.34778672456741333},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.3131135106086731},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.29074347019195557},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.20436236262321472},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15644216537475586},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12346041202545166}],"concepts":[{"id":"https://openalex.org/C2777693668","wikidata":"https://www.wikidata.org/wiki/Q25053743","display_name":"Deblurring","level":5,"score":0.8493028879165649},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6569869518280029},{"id":"https://openalex.org/C113315163","wikidata":"https://www.wikidata.org/wiki/Q7625159","display_name":"Structure tensor","level":3,"score":0.6465155482292175},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.5599934458732605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5342214703559875},{"id":"https://openalex.org/C203504353","wikidata":"https://www.wikidata.org/wiki/Q4765461","display_name":"Anisotropic diffusion","level":3,"score":0.5258772373199463},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.48759832978248596},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.47017067670822144},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4492642879486084},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4322358965873718},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.4211086630821228},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4156067669391632},{"id":"https://openalex.org/C207282899","wikidata":"https://www.wikidata.org/wiki/Q7828156","display_name":"Total variation denoising","level":3,"score":0.41342049837112427},{"id":"https://openalex.org/C2779521785","wikidata":"https://www.wikidata.org/wiki/Q5535529","display_name":"Geometry processing","level":3,"score":0.41101253032684326},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3505696654319763},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.34778672456741333},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.3131135106086731},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.29074347019195557},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.20436236262321472},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15644216537475586},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12346041202545166}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tip.2015.2409562","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2015.2409562","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,"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:25769155","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25769155","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,"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":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.697.2639","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.697.2639","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://vision.ucla.edu/papers/estellersSB15.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.7699999809265137,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G8223824799","display_name":null,"funder_award_id":"FA9550-12-1-0364","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G977783228","display_name":null,"funder_award_id":"P2ELP2_148890","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W1480546554","https://openalex.org/W1486280163","https://openalex.org/W1499695691","https://openalex.org/W1508901342","https://openalex.org/W1523201499","https://openalex.org/W1593352143","https://openalex.org/W1605636162","https://openalex.org/W1822716517","https://openalex.org/W1895520453","https://openalex.org/W1916830916","https://openalex.org/W1947239887","https://openalex.org/W1978333359","https://openalex.org/W1985588167","https://openalex.org/W1996287810","https://openalex.org/W1997221482","https://openalex.org/W1998252084","https://openalex.org/W1998991750","https://openalex.org/W2000594266","https://openalex.org/W2008025478","https://openalex.org/W2019248995","https://openalex.org/W2020461703","https://openalex.org/W2021904562","https://openalex.org/W2032236594","https://openalex.org/W2046033161","https://openalex.org/W2047884269","https://openalex.org/W2048192550","https://openalex.org/W2053951212","https://openalex.org/W2056370875","https://openalex.org/W2060945009","https://openalex.org/W2061649600","https://openalex.org/W2082473969","https://openalex.org/W2091494211","https://openalex.org/W2092663520","https://openalex.org/W2103559027","https://openalex.org/W2104404402","https://openalex.org/W2117406282","https://openalex.org/W2122752532","https://openalex.org/W2126922884","https://openalex.org/W2136396015","https://openalex.org/W2140178321","https://openalex.org/W2141498692","https://openalex.org/W2142058898","https://openalex.org/W2144854819","https://openalex.org/W2148791483","https://openalex.org/W2150134853","https://openalex.org/W2152920451","https://openalex.org/W2164822588","https://openalex.org/W2170836521","https://openalex.org/W2171408098","https://openalex.org/W2401491153","https://openalex.org/W2556398415","https://openalex.org/W2732771853","https://openalex.org/W3100489614","https://openalex.org/W3101805643","https://openalex.org/W3121742466","https://openalex.org/W4210770595","https://openalex.org/W4229650096","https://openalex.org/W4285719527","https://openalex.org/W4292069163","https://openalex.org/W6685204951"],"related_works":["https://openalex.org/W2077051484","https://openalex.org/W2084920026","https://openalex.org/W2262332166","https://openalex.org/W2373529328","https://openalex.org/W2319782925","https://openalex.org/W1539611277","https://openalex.org/W2355754289","https://openalex.org/W2386523173","https://openalex.org/W2024636891","https://openalex.org/W1767254247"],"abstract_inverted_index":{"Natural":[0],"images":[1,202],"exhibit":[2],"geometric":[3],"structures":[4,66],"that":[5,25,111],"are":[6],"informative":[7],"of":[8,11,29,42,64,78,89,96,121,125,138,149,200],"the":[9,12,27,38,43,53,60,85,90,118,139,150,170,197],"properties":[10],"underlying":[13],"scene.":[14],"Modern":[15],"image":[16,91,109,122,151,181],"processing":[17],"algorithms":[18,179],"respect":[19],"such":[20],"characteristics":[21],"by":[22,46,123],"employing":[23],"regularizers":[24],"capture":[26,59],"statistics":[28],"natural":[30,68,201],"images.":[31,69],"For":[32],"instance,":[33],"total":[34],"variation":[35],"(TV)":[36],"respects":[37],"highly":[39],"kurtotic":[40],"distribution":[41],"pointwise":[44],"gradient":[45,54,79],"allowing":[47],"for":[48,108,180],"large":[49],"magnitude":[50,55],"outlayers.":[51],"However,":[52],"alone":[56],"does":[57],"not":[58],"directionality":[61],"and":[62,87,146,173,177,184,207],"scale":[63],"local":[65,119,198],"in":[67,93],"The":[70],"structure":[71,127,140],"tensor":[72,141],"provides":[73],"a":[74,94,105,113,143,213],"more":[75],"meaningful":[76],"description":[77],"information":[80],"as":[81,142],"it":[82,195],"describes":[83],"both":[84],"size":[86],"orientation":[88],"gradients":[92],"neighborhood":[95],"each":[97],"point.":[98],"Based":[99],"on":[100],"this":[101,158],"observation,":[102],"we":[103],"propose":[104],"variational":[106],"model":[107],"reconstruction":[110,148],"employs":[112],"regularization":[114],"functional":[115],"adapted":[116],"to":[117,165,191,203],"geometry":[120],"means":[124],"its":[126],"tensor.":[128,159],"Our":[129,187,210],"method":[130,188],"alternates":[131],"two":[132],"minimization":[133],"steps:":[134],"1)":[135],"robust":[136],"estimation":[137],"semidefinite":[144],"program":[145],"2)":[147],"with":[152],"an":[153],"adaptive":[154],"regularizer":[155],"defined":[156],"from":[157],"This":[160],"two-step":[161],"procedure":[162],"allows":[163],"us":[164],"extend":[166],"anisotropic":[167],"diffusion":[168,208],"into":[169],"convex":[171],"setting":[172],"develop":[174],"robust,":[175],"efficient,":[176],"easy-to-code":[178],"denoising,":[182],"deblurring,":[183],"compressed":[185],"sensing.":[186],"extends":[189],"naturally":[190],"nonlocal":[192,205],"regularization,":[193],"where":[194],"exploits":[196],"self-similarity":[199],"improve":[204],"TV":[206],"operators.":[209],"experiments":[211],"show":[212],"consistent":[214],"accuracy":[215],"improvement":[216],"over":[217],"classic":[218],"regularization.":[219]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}