{"id":"https://openalex.org/W2970893197","doi":"https://doi.org/10.1109/icip.2019.8803145","title":"A Comparative Study for the Nuclear Norms Minimization Methods","display_name":"A Comparative Study for the Nuclear Norms Minimization Methods","publication_year":2019,"publication_date":"2019-08-26","ids":{"openalex":"https://openalex.org/W2970893197","doi":"https://doi.org/10.1109/icip.2019.8803145","mag":"2970893197"},"language":"en","primary_location":{"id":"doi:10.1109/icip.2019.8803145","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2019.8803145","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Conference on Image Processing (ICIP)","raw_type":"proceedings-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/A5032774989","display_name":"Zhiyuan Zha","orcid":"https://orcid.org/0000-0002-5515-5339"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhiyuan Zha","raw_affiliation_strings":["University of Electronic Science and Technology of China, Chengdu, China"],"affiliations":[{"raw_affiliation_string":"University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024709593","display_name":"Bihan Wen","orcid":"https://orcid.org/0000-0002-6874-6453"},"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":"Bihan Wen","raw_affiliation_strings":["Nanyang Technological University, Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"Nanyang Technological University, Singapore, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102020945","display_name":"Jiachao Zhang","orcid":"https://orcid.org/0000-0002-3124-9461"},"institutions":[{"id":"https://openalex.org/I2799736854","display_name":"Nanjing Institute of Technology","ror":"https://ror.org/00n6txq60","country_code":"CN","type":"education","lineage":["https://openalex.org/I2799736854"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiachao Zhang","raw_affiliation_strings":["Nanjing Institute of Technology, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"Nanjing Institute of Technology, Nanjing, China","institution_ids":["https://openalex.org/I2799736854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037979193","display_name":"Jiantao Zhou","orcid":"https://orcid.org/0000-0002-6015-2618"},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Jiantao Zhou","raw_affiliation_strings":["University of Macau, Macau, China"],"affiliations":[{"raw_affiliation_string":"University of Macau, Macau, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034427070","display_name":"Ce Zhu","orcid":"https://orcid.org/0000-0001-7607-707X"},"institutions":[{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ce Zhu","raw_affiliation_strings":["University of Electronic Science and Technology of China, Chengdu, China"],"affiliations":[{"raw_affiliation_string":"University of Electronic Science and Technology of China, Chengdu, China","institution_ids":["https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5032774989"],"corresponding_institution_ids":["https://openalex.org/I150229711"],"apc_list":null,"apc_paid":null,"fwci":1.3242,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.7896308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"2050","last_page":"2054"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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/T10057","display_name":"Face and Expression Recognition","score":0.9972000122070312,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/minification","display_name":"Minification","score":0.7056452035903931},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6017992496490479},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5697892904281616},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.5343666672706604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4802189767360687},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4143190383911133},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.405964732170105},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3403320908546448},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2756071984767914},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.26517820358276367}],"concepts":[{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.7056452035903931},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6017992496490479},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5697892904281616},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.5343666672706604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4802189767360687},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4143190383911133},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.405964732170105},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3403320908546448},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2756071984767914},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26517820358276367},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icip.2019.8803145","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icip.2019.8803145","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE International Conference on Image Processing (ICIP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1482071412","https://openalex.org/W1486694121","https://openalex.org/W1969698720","https://openalex.org/W1970833585","https://openalex.org/W1974042113","https://openalex.org/W1978749115","https://openalex.org/W1994040806","https://openalex.org/W1997201895","https://openalex.org/W2014311222","https://openalex.org/W2040895929","https://openalex.org/W2045737896","https://openalex.org/W2048695508","https://openalex.org/W2056370875","https://openalex.org/W2075157914","https://openalex.org/W2076430826","https://openalex.org/W2097073572","https://openalex.org/W2103972604","https://openalex.org/W2107861471","https://openalex.org/W2109240917","https://openalex.org/W2116857329","https://openalex.org/W2125527601","https://openalex.org/W2131628350","https://openalex.org/W2153663612","https://openalex.org/W2160547390","https://openalex.org/W2172275395","https://openalex.org/W2175634846","https://openalex.org/W2207282238","https://openalex.org/W2505029951","https://openalex.org/W2536599074","https://openalex.org/W2571662414","https://openalex.org/W2606594217","https://openalex.org/W2963218026","https://openalex.org/W3104099693","https://openalex.org/W6628883312","https://openalex.org/W6662532501","https://openalex.org/W6679973066"],"related_works":["https://openalex.org/W4366831400","https://openalex.org/W2158044763","https://openalex.org/W4298234822","https://openalex.org/W2782047334","https://openalex.org/W3017414697","https://openalex.org/W3206304544","https://openalex.org/W1554365047","https://openalex.org/W3174042135","https://openalex.org/W2006601391","https://openalex.org/W2962791795"],"abstract_inverted_index":{"The":[0],"nuclear":[1,57],"norm":[2,58,181],"minimization":[3,59,125,148,157,173,182],"(NNM)":[4],"is":[5,89,119,191,223],"commonly":[6],"used":[7],"to":[8,37,76,121,142,212],"approximate":[9,39],"the":[10,20,40,45,55,72,77,106,123,131,150,166,198,205,214],"matrix":[11,41],"rank":[12,65,124],"by":[13,162],"shrinking":[14],"all":[15],"singular":[16,21,78],"values":[17,22],"equally.":[18],"However,":[19,80],"have":[23,52],"clear":[24],"physical":[25],"meanings":[26],"in":[27,94,158,174,183,233],"many":[28],"practical":[29],"problems,":[30],"and":[31,103,126,138,149,228,236],"NNM":[32,102,137,227],"may":[33],"not":[34],"be":[35],"able":[36],"faithfully":[38],"rank.":[42],"To":[43],"alleviate":[44],"above-mentioned":[46],"limitation":[47],"of":[48,108,165],"NNM,":[49,68],"recent":[50],"studies":[51],"suggested":[53],"that":[54,136,189,221],"weighted":[56,151,167],"(WNNM)":[60],"can":[61],"achieve":[62],"a":[63,84],"better":[64],"estimation":[66],"than":[67,92,194,226],"which":[69],"heuristically":[70],"set":[71],"weight":[73],"being":[74],"inverse":[75],"values.":[79],"it":[81,211],"still":[82],"lacks":[83],"rigorous":[85],"explanation":[86],"why":[87],"WNNM":[88,104,139,190,206,222],"more":[90,192,224],"effective":[91,193,225],"NMM":[93],"various":[95],"applications.":[96],"In":[97],"this":[98],"paper,":[99],"we":[100,134,186,208],"analyze":[101],"from":[105],"perspective":[107],"group":[109],"sparse":[110,184],"representation":[111],"(GSR).":[112],"Concretely,":[113],"an":[114],"adaptive":[115],"dictionary":[116],"learning":[117],"method":[118],"devised":[120],"connect":[122],"GSR":[127],"models.":[128],"Based":[129],"on":[130],"proposed":[132],"dictionary,":[133],"prove":[135],"are":[140],"equivalent":[141],"\u2113":[143,152,168,177],"<sub":[144,153,169,178],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[145,154,170,179],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[146,155,171],"-norm":[147,156,172],"GSR,":[159],"respectively.":[160],"Inspired":[161],"enhancing":[163],"sparsity":[164],"comparison":[175],"with":[176,204],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1-</sub>":[180],"representation,":[185],"thus":[187],"explain":[188],"NMM.":[195],"By":[196],"integrating":[197],"image":[199,215],"nonlocal":[200],"self-similarity":[201],"(NSS)":[202],"prior":[203],"model,":[207],"then":[209],"apply":[210],"solve":[213],"denoising":[216],"problem.":[217],"Experimental":[218],"results":[219],"demonstrate":[220],"outperforms":[229],"several":[230],"state-of-the-art":[231],"methods":[232],"both":[234],"objective":[235],"perceptual":[237],"quality.":[238]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
