{"id":"https://openalex.org/W2338117771","doi":"https://doi.org/10.1109/tcsvt.2016.2556498","title":"Nonlocal Gradient Sparsity Regularization for Image Restoration","display_name":"Nonlocal Gradient Sparsity Regularization for Image Restoration","publication_year":2016,"publication_date":"2016-04-20","ids":{"openalex":"https://openalex.org/W2338117771","doi":"https://doi.org/10.1109/tcsvt.2016.2556498","mag":"2338117771"},"language":"en","primary_location":{"id":"doi:10.1109/tcsvt.2016.2556498","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsvt.2016.2556498","pdf_url":null,"source":{"id":"https://openalex.org/S115173108","display_name":"IEEE Transactions on Circuits and Systems for Video Technology","issn_l":"1051-8215","issn":["1051-8215","1558-2205"],"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 Circuits and Systems for Video Technology","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/A5079154623","display_name":"Hangfan Liu","orcid":"https://orcid.org/0000-0002-1207-7713"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hangfan Liu","raw_affiliation_strings":["Institute of Digital Media, School of Electronic Engineering and Computer Science, and National Engineering Laboratory for Video Technology (NELVT), Peking University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Digital Media, School of Electronic Engineering and Computer Science, and National Engineering Laboratory for Video Technology (NELVT), Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013727612","display_name":"Ruiqin Xiong","orcid":"https://orcid.org/0000-0001-9796-0478"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ruiqin Xiong","raw_affiliation_strings":["Institute of Digital Media, School of Electronic Engineering and Computer Science, and National Engineering Laboratory for Video Technology (NELVT), Peking University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Digital Media, School of Electronic Engineering and Computer Science, and National Engineering Laboratory for Video Technology (NELVT), Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055937409","display_name":"Xinfeng Zhang","orcid":"https://orcid.org/0000-0002-7517-3868"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Xinfeng Zhang","raw_affiliation_strings":["Rapid-Rich Object Search (ROSE) Laboratory, Nanyang Technological University, Singapore"],"affiliations":[{"raw_affiliation_string":"Rapid-Rich Object Search (ROSE) Laboratory, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101653272","display_name":"Yongbing Zhang","orcid":"https://orcid.org/0009-0008-1568-3728"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]},{"id":"https://openalex.org/I3131625388","display_name":"University Town of Shenzhen","ror":"https://ror.org/05f5j6225","country_code":"CN","type":"education","lineage":["https://openalex.org/I3131625388"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yongbing Zhang","raw_affiliation_strings":["Shenzhen Key Laboratory of Broadband Network and Multimedia, Graduate School at Shenzhen, Tsinghua University, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Shenzhen Key Laboratory of Broadband Network and Multimedia, Graduate School at Shenzhen, Tsinghua University, Shenzhen, China","institution_ids":["https://openalex.org/I3131625388","https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039832462","display_name":"Siwei Ma","orcid":"https://orcid.org/0000-0002-2731-5403"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Siwei Ma","raw_affiliation_strings":["Institute of Digital Media, School of Electronic Engineering and Computer Science, and National Engineering Laboratory for Video Technology (NELVT), Peking University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Digital Media, School of Electronic Engineering and Computer Science, and National Engineering Laboratory for Video Technology (NELVT), Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018478553","display_name":"Wen Gao","orcid":"https://orcid.org/0000-0002-8070-802X"},"institutions":[{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wen Gao","raw_affiliation_strings":["Institute of Digital Media, School of Electronic Engineering and Computer Science, and National Engineering Laboratory for Video Technology (NELVT), Peking University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Digital Media, School of Electronic Engineering and Computer Science, and National Engineering Laboratory for Video Technology (NELVT), Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5079154623"],"corresponding_institution_ids":["https://openalex.org/I20231570"],"apc_list":null,"apc_paid":null,"fwci":4.1751,"has_fulltext":false,"cited_by_count":78,"citation_normalized_percentile":{"value":0.96177018,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"27","issue":"9","first_page":"1909","last_page":"1921"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9997000098228455,"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":0.9997000098228455,"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/T11105","display_name":"Advanced Image Processing Techniques","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/T13114","display_name":"Image Processing Techniques and Applications","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.741242527961731},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6881318092346191},{"id":"https://openalex.org/keywords/image-restoration","display_name":"Image restoration","score":0.593921422958374},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5708839297294617},{"id":"https://openalex.org/keywords/morphological-gradient","display_name":"Morphological gradient","score":0.5467471480369568},{"id":"https://openalex.org/keywords/image-gradient","display_name":"Image gradient","score":0.5440889596939087},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.5256444215774536},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5087476372718811},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.4983189105987549},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4386175274848938},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43202877044677734},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.39195629954338074},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39031538367271423},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.3518489599227905},{"id":"https://openalex.org/keywords/image-texture","display_name":"Image texture","score":0.3232032060623169},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09900093078613281}],"concepts":[{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.741242527961731},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6881318092346191},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.593921422958374},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5708839297294617},{"id":"https://openalex.org/C96133863","wikidata":"https://www.wikidata.org/wiki/Q6913458","display_name":"Morphological gradient","level":5,"score":0.5467471480369568},{"id":"https://openalex.org/C182037307","wikidata":"https://www.wikidata.org/wiki/Q17039097","display_name":"Image gradient","level":5,"score":0.5440889596939087},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.5256444215774536},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5087476372718811},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.4983189105987549},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4386175274848938},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43202877044677734},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.39195629954338074},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39031538367271423},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.3518489599227905},{"id":"https://openalex.org/C63099799","wikidata":"https://www.wikidata.org/wiki/Q17147001","display_name":"Image texture","level":4,"score":0.3232032060623169},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09900093078613281}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsvt.2016.2556498","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsvt.2016.2556498","pdf_url":null,"source":{"id":"https://openalex.org/S115173108","display_name":"IEEE Transactions on Circuits and Systems for Video Technology","issn_l":"1051-8215","issn":["1051-8215","1558-2205"],"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 Circuits and Systems for Video Technology","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G109436452","display_name":null,"funder_award_id":"2015CB351800","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G2401495373","display_name":null,"funder_award_id":"61421062","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5868647121","display_name":null,"funder_award_id":"61370114","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7012924746","display_name":null,"funder_award_id":"61425026","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8408667715","display_name":null,"funder_award_id":"4132039","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":75,"referenced_works":["https://openalex.org/W19793066","https://openalex.org/W1522271611","https://openalex.org/W1605636162","https://openalex.org/W1915372217","https://openalex.org/W1946766895","https://openalex.org/W1978333359","https://openalex.org/W1981624870","https://openalex.org/W1983041613","https://openalex.org/W1984077106","https://openalex.org/W1985023924","https://openalex.org/W1985588167","https://openalex.org/W2002969407","https://openalex.org/W2005089986","https://openalex.org/W2006262236","https://openalex.org/W2011181254","https://openalex.org/W2017620942","https://openalex.org/W2017848200","https://openalex.org/W2028349405","https://openalex.org/W2029684123","https://openalex.org/W2038834876","https://openalex.org/W2039939700","https://openalex.org/W2041982225","https://openalex.org/W2042220165","https://openalex.org/W2042984553","https://openalex.org/W2044157931","https://openalex.org/W2045079989","https://openalex.org/W2045737896","https://openalex.org/W2056370875","https://openalex.org/W2060676175","https://openalex.org/W2060945009","https://openalex.org/W2074406023","https://openalex.org/W2075858322","https://openalex.org/W2085899807","https://openalex.org/W2086729767","https://openalex.org/W2091494211","https://openalex.org/W2095106682","https://openalex.org/W2097073572","https://openalex.org/W2099233802","https://openalex.org/W2100705753","https://openalex.org/W2101409571","https://openalex.org/W2103559027","https://openalex.org/W2112009428","https://openalex.org/W2115706991","https://openalex.org/W2124584309","https://openalex.org/W2133665775","https://openalex.org/W2135065661","https://openalex.org/W2137113506","https://openalex.org/W2142058898","https://openalex.org/W2142224912","https://openalex.org/W2145962650","https://openalex.org/W2146842127","https://openalex.org/W2152920451","https://openalex.org/W2153663612","https://openalex.org/W2158252006","https://openalex.org/W2163398148","https://openalex.org/W2165939075","https://openalex.org/W2169253121","https://openalex.org/W2169288322","https://openalex.org/W2169899245","https://openalex.org/W2170885533","https://openalex.org/W2171783193","https://openalex.org/W2244252827","https://openalex.org/W2288002998","https://openalex.org/W2342838199","https://openalex.org/W2536599074","https://openalex.org/W2543013670","https://openalex.org/W2962727219","https://openalex.org/W3005708632","https://openalex.org/W3098154762","https://openalex.org/W4301014524","https://openalex.org/W6600792419","https://openalex.org/W6668902313","https://openalex.org/W6671975367","https://openalex.org/W6677581936","https://openalex.org/W7073876970"],"related_works":["https://openalex.org/W2352200706","https://openalex.org/W2959508763","https://openalex.org/W1991896712","https://openalex.org/W2383665989","https://openalex.org/W2369107151","https://openalex.org/W2378258130","https://openalex.org/W4210660906","https://openalex.org/W2392840155","https://openalex.org/W2362181716","https://openalex.org/W2781860599"],"abstract_inverted_index":{"Total":[0],"variation":[1],"(TV)":[2],"regularization":[3],"is":[4,155],"widely":[5],"used":[6],"in":[7,38,130],"image":[8,16,75,86,102,179],"restoration":[9],"to":[10,119,144],"exploit":[11],"the":[12,19,28,41,71,74,82,91,97,101,120,124,138,141,161,165],"local":[13],"smoothness":[14],"of":[15,44,66,73,85,90,94,112,140,153],"content.":[17],"Essentially,":[18],"TV":[20,67,167],"model":[21],"assumes":[22],"a":[23,62,106,110],"zero-mean":[24,42],"Laplacian":[25],"distribution":[26,143],"for":[27,51],"gradient":[29,46,76,103,128,142,154],"at":[30,105,123],"all":[31],"pixels.":[32],"However,":[33],"real-world":[34],"images":[35],"are":[36,117,135],"nonstationary":[37,83],"general,":[39],"and":[40,168,173,177],"assumption":[43],"pixel":[45,108],"might":[47],"be":[48,145],"invalid,":[49],"especially":[50],"regions":[52],"with":[53,77],"strong":[54],"edges":[55],"or":[56],"rich":[57],"textures.":[58],"This":[59],"paper":[60],"introduces":[61],"nonlocal":[63],"(NL)":[64],"extension":[65],"regularization,":[68],"which":[69,116],"models":[70],"sparsity":[72],"pixelwise":[78],"content-adaptive":[79],"distributions,":[80],"reflecting":[81],"nature":[84],"statistics.":[87],"Taking":[88],"advantage":[89],"NL":[92,132],"similarity":[93],"natural":[95],"images,":[96],"proposed":[98,162],"approach":[99],"estimates":[100],"statistics":[104],"particular":[107],"from":[109],"group":[111],"nonlocally":[113],"searched":[114],"patches,":[115],"similar":[118,133],"patch":[121],"located":[122],"current":[125],"pixel.":[126],"The":[127],"data":[129],"these":[131],"patches":[134],"regarded":[136],"as":[137],"samples":[139],"learned.":[146],"In":[147],"this":[148],"way,":[149],"more":[150],"accurate":[151],"estimation":[152],"achieved.":[156],"Experimental":[157],"results":[158],"demonstrate":[159],"that":[160],"method":[163],"outperforms":[164],"conventional":[166],"several":[169],"other":[170],"anchors":[171],"remarkably":[172],"produces":[174],"better":[175],"objective":[176],"subjective":[178],"qualities.":[180]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}