{"id":"https://openalex.org/W4392110286","doi":"https://doi.org/10.1137/22m1536996","title":"Learnable Nonlocal Self-Similarity of Deep Features for Image Denoising","display_name":"Learnable Nonlocal Self-Similarity of Deep Features for Image Denoising","publication_year":2024,"publication_date":"2024-02-23","ids":{"openalex":"https://openalex.org/W4392110286","doi":"https://doi.org/10.1137/22m1536996"},"language":"en","primary_location":{"id":"doi:10.1137/22m1536996","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1536996","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003483747","display_name":"Junying Meng","orcid":"https://orcid.org/0009-0003-3143-8857"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junying Meng","raw_affiliation_strings":["Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China"],"raw_orcid":"https://orcid.org/0009-0003-3143-8857","affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101903127","display_name":"Faqiang Wang","orcid":"https://orcid.org/0000-0001-5317-562X"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Faqiang Wang","raw_affiliation_strings":["Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100361699","display_name":"Jun Liu","orcid":"https://orcid.org/0000-0001-8697-3089"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Liu","raw_affiliation_strings":["Corresponding author. Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China","Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China"],"raw_orcid":"https://orcid.org/0000-0001-8697-3089","affiliations":[{"raw_affiliation_string":"Corresponding author. Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China","institution_ids":["https://openalex.org/I25254941"]},{"raw_affiliation_string":"Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I25254941"],"apc_list":null,"apc_paid":null,"fwci":1.0818,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.74917891,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"17","issue":"1","first_page":"441","last_page":"475"},"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":0.9979000091552734,"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/T11105","display_name":"Advanced Image Processing Techniques","score":0.9970999956130981,"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":0.6892149448394775},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.643807053565979},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.631536602973938},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.6236940622329712},{"id":"https://openalex.org/keywords/self-similarity","display_name":"Self-similarity","score":0.6165614128112793},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.5943357944488525},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5601314306259155},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46331122517585754},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4488893449306488},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.43748435378074646},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36490485072135925},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1314595341682434}],"concepts":[{"id":"https://openalex.org/C2983327147","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Image denoising","level":3,"score":0.6892149448394775},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.643807053565979},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.631536602973938},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.6236940622329712},{"id":"https://openalex.org/C119453123","wikidata":"https://www.wikidata.org/wiki/Q262372","display_name":"Self-similarity","level":2,"score":0.6165614128112793},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.5943357944488525},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5601314306259155},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46331122517585754},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4488893449306488},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.43748435378074646},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36490485072135925},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1314595341682434}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1536996","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1536996","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5199999809265137,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1070981533","display_name":null,"funder_award_id":"42293272","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1185775842","display_name":null,"funder_award_id":"1232011","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"},{"id":"https://openalex.org/G6735975849","display_name":null,"funder_award_id":"12371527","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6791881041","display_name":null,"funder_award_id":"12101058","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"},{"id":"https://openalex.org/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1906770428","https://openalex.org/W1912194039","https://openalex.org/W2014268383","https://openalex.org/W2056370875","https://openalex.org/W2060945009","https://openalex.org/W2103559027","https://openalex.org/W2110158442","https://openalex.org/W2116064496","https://openalex.org/W2118020555","https://openalex.org/W2130184048","https://openalex.org/W2507211415","https://openalex.org/W2508457857","https://openalex.org/W2556068545","https://openalex.org/W2692635131","https://openalex.org/W2764207251","https://openalex.org/W2793775504","https://openalex.org/W2999653953","https://openalex.org/W3000775737","https://openalex.org/W3048092834","https://openalex.org/W3104467360","https://openalex.org/W3171760114","https://openalex.org/W3185385692","https://openalex.org/W3193659426","https://openalex.org/W3211066356","https://openalex.org/W4378218572"],"related_works":["https://openalex.org/W2895947835","https://openalex.org/W2087258800","https://openalex.org/W2810018092","https://openalex.org/W2387428419","https://openalex.org/W2098237619","https://openalex.org/W1974034585","https://openalex.org/W2386722878","https://openalex.org/W2379232404","https://openalex.org/W2353444452","https://openalex.org/W2001438600"],"abstract_inverted_index":{"Abstract.":[0],"High-dimensional":[1],"deep":[2,18,21,41,57,90],"features":[3,19,58],"extracted":[4],"by":[5,51,79,105,201],"convolutional":[6],"neural":[7],"networks":[8],"have":[9],"nonlocal":[10,15,39,75,94,114,131,155,177],"self-similarity.":[11],"However,":[12],"incorporating":[13],"this":[14,33,202],"prior":[16,87],"of":[17,84,88,154,161,222],"into":[20],"network":[22,43,179,191],"architectures":[23],"with":[24,73,210],"an":[25],"interpretable":[26],"variational":[27,127,169],"framework":[28],"is":[29,49,77],"rarely":[30],"explored.":[31],"In":[32],"paper,":[34],"we":[35,147],"propose":[36],"a":[37,60,71,124,175,186],"learnable":[38,74,176],"self-similarity":[40,178,195],"feature":[42],"for":[44,129,180,189],"image":[45,181,227],"denoising.":[46,182,228],"Our":[47,121],"method":[48,122,203,225],"motivated":[50],"the":[52,55,66,81,85,89,93,107,130,151,162,167,216,220,223],"fact":[53],"that":[54,101,193],"high-dimensional":[56],"obey":[59],"mixture":[61],"probability":[62],"distribution":[63],"based":[64],"on":[65],"Parzen\u2013Rosenblatt":[67],"window":[68,142],"method.":[69],"Then":[70],"regularizer":[72],"weights":[76,95],"proposed":[78,168,224],"considering":[80],"dual":[82,99],"representation":[83],"log-probability":[86],"features.":[91],"Specifically,":[92],"are":[96,204],"introduced":[97],"as":[98,174],"variables":[100],"can":[102,148,171],"be":[103,172],"learned":[104],"unrolling":[106],"associated":[108],"numerical":[109],"scheme.":[110],"This":[111,183],"leads":[112],"to":[113,166],"modules":[115],"(NLMs)":[116],"in":[117,136,226],"newly":[118],"designed":[119],"networks.":[120,138],"provides":[123],"statistical":[125],"and":[126,143,196,206],"interpretation":[128],"self-attention":[132],"mechanism":[133],"widely":[134],"used":[135],"various":[137],"By":[139],"adopting":[140],"nonoverlapping":[141],"region":[144],"decomposition":[145],"techniques,":[146],"significantly":[149],"reduce":[150],"computational":[152],"complexity":[153],"self-similarity,":[156],"thus":[157],"enabling":[158],"parallel":[159],"computation":[160],"NLM.":[163],"The":[164,198],"solution":[165],"problem":[170],"formulated":[173],"work":[184],"offers":[185],"novel":[187],"approach":[188],"constructing":[190],"structures":[192],"consider":[194],"nonlocality.":[197],"improvements":[199],"achieved":[200],"predictable":[205],"partially":[207],"controllable.":[208],"Compared":[209],"several":[211],"closely":[212],"related":[213],"denoising":[214],"methods,":[215],"experimental":[217],"results":[218],"show":[219],"effectiveness":[221]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-08-22T07:34:49.880490","created_date":"2025-10-10T00:00:00"}