{"id":"https://openalex.org/W4223964342","doi":"https://doi.org/10.1137/21m143786x","title":"Selecting Regularization Parameters for Nuclear Norm--Type Minimization Problems","display_name":"Selecting Regularization Parameters for Nuclear Norm--Type Minimization Problems","publication_year":2022,"publication_date":"2022-08-01","ids":{"openalex":"https://openalex.org/W4223964342","doi":"https://doi.org/10.1137/21m143786x"},"language":"en","primary_location":{"id":"doi:10.1137/21m143786x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m143786x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://scholars.cityu.edu.hk/en/publications/selecting-regularization-parameters-for-nuclear-norm-type-minimiz","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100329682","display_name":"Kexin Li","orcid":"https://orcid.org/0009-0001-5344-3636"},"institutions":[{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kexin Li","raw_affiliation_strings":["Key Laboratory of Computing and Stochastic Mathematics (LCSM), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics (LCSM), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, China","institution_ids":["https://openalex.org/I173759888"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100325323","display_name":"Hongwei Li","orcid":"https://orcid.org/0000-0001-6809-7097"},"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"]},{"id":"https://openalex.org/I4210165198","display_name":"Beijing Advanced Sciences and Innovation Center","ror":"https://ror.org/05qm21180","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165198"]},{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongwei Li","raw_affiliation_strings":["Beijing Advanced Innovation Center for Imaging Theory and Technology Capital Normal Uni-versity, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Advanced Innovation Center for Imaging Theory and Technology Capital Normal Uni-versity, Beijing, China","institution_ids":["https://openalex.org/I25254941","https://openalex.org/I4210165198","https://openalex.org/I96852419"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004126693","display_name":"Raymond H. Chan","orcid":"https://orcid.org/0000-0003-0910-4685"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raymond H. Chan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5033802995","display_name":"You\u2010Wei Wen","orcid":"https://orcid.org/0000-0002-9892-3668"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]},{"id":"https://openalex.org/I173759888","display_name":"Hunan Normal University","ror":"https://ror.org/053w1zy07","country_code":"CN","type":"education","lineage":["https://openalex.org/I173759888"]}],"countries":["CN","HK"],"is_corresponding":true,"raw_author_name":"Youwei Wen","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong SAR, China; Hong Kong Centre for Cerebro-Cardiovascular Health Engineering","Key Laboratory of Computing and Stochastic Mathematics (LCSM), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, China"],"raw_orcid":"https://orcid.org/0000-0002-9892-3668","affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong, Hong Kong SAR, China; Hong Kong Centre for Cerebro-Cardiovascular Health Engineering","institution_ids":["https://openalex.org/I168719708"]},{"raw_affiliation_string":"Key Laboratory of Computing and Stochastic Mathematics (LCSM), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, China","institution_ids":["https://openalex.org/I173759888"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5033802995"],"corresponding_institution_ids":["https://openalex.org/I168719708","https://openalex.org/I173759888"],"apc_list":null,"apc_paid":null,"fwci":0.4196,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.46827627,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"44","issue":"4","first_page":"A2204","last_page":"A2225"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13487","display_name":"Statistical and numerical algorithms","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7695542573928833},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6466487050056458},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5865700244903564},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5566467046737671},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.522326648235321},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.49344101548194885},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.48583170771598816},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4636707305908203},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.4469963312149048},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4291324019432068},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14191386103630066},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.09245124459266663},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08640694618225098}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7695542573928833},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6466487050056458},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5865700244903564},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5566467046737671},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.522326648235321},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.49344101548194885},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.48583170771598816},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4636707305908203},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.4469963312149048},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4291324019432068},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14191386103630066},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.09245124459266663},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08640694618225098},{"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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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":3,"locations":[{"id":"doi:10.1137/21m143786x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m143786x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/selecting-regularization-parameters-for-nuclear-norm-type-minimiz","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/44245174-88c1-4e12-b871-29fd8dd4882e","is_oa":true,"landing_page_url":"https://hdl.handle.net/2031/44245174-88c1-4e12-b871-29fd8dd4882e","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"LI, K, LI, H, CHAN, R H & WEN, Y 2022, 'SELECTING REGULARIZATION PARAMETERS FOR NUCLEAR NORM-TYPE MINIMIZATION PROBLEMS', SIAM Journal on Scientific Computing, vol. 44, no. 4, pp. A2204-A2225. https://doi.org/10.1137/21M143786X","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/selecting-regularization-parameters-for-nuclear-norm-type-minimiz","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1289935930","display_name":null,"funder_award_id":"9380101","funder_id":"https://openalex.org/F4320309893","funder_display_name":"City University of Hong Kong"},{"id":"https://openalex.org/G1486628861","display_name":null,"funder_award_id":"C1013-21GF","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1614035033","display_name":"CT\u6709\u9650\u89d2\u91cd\u5efa\u975e\u51f8\u4f18\u5316\u6a21\u578b\u4e0e\u76f8\u5bb9\u7b97\u6cd5\u7814\u7a76","funder_award_id":"61971292","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2011489027","display_name":null,"funder_award_id":"CUHK14301718","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3048301346","display_name":null,"funder_award_id":"CUHK14301718","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G3358759369","display_name":null,"funder_award_id":"CityU9380101","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G4514602524","display_name":"\u56fe\u50cfRetinex\u95ee\u9898\u7684\u6570\u503c\u7b97\u6cd5\u4e0e\u7406\u8bba\u7814\u7a76","funder_award_id":"11971215","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4716426265","display_name":null,"funder_award_id":"11871210","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5241975850","display_name":null,"funder_award_id":"CityU11301120","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G659521206","display_name":null,"funder_award_id":"CityU11301120","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G8276224932","display_name":null,"funder_award_id":"C1013-21GF","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320322942","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1482071412","https://openalex.org/W1570089119","https://openalex.org/W1578255497","https://openalex.org/W1950149046","https://openalex.org/W1968735445","https://openalex.org/W1969698720","https://openalex.org/W1972889810","https://openalex.org/W1974042113","https://openalex.org/W1976172121","https://openalex.org/W1990381576","https://openalex.org/W1992719146","https://openalex.org/W1998143450","https://openalex.org/W2004026774","https://openalex.org/W2011359124","https://openalex.org/W2014311222","https://openalex.org/W2031604650","https://openalex.org/W2034004195","https://openalex.org/W2035858287","https://openalex.org/W2048695508","https://openalex.org/W2052387674","https://openalex.org/W2053831664","https://openalex.org/W2056532343","https://openalex.org/W2057261601","https://openalex.org/W2063942101","https://openalex.org/W2064980127","https://openalex.org/W2101797518","https://openalex.org/W2103972604","https://openalex.org/W2108763700","https://openalex.org/W2112589491","https://openalex.org/W2115755118","https://openalex.org/W2116641053","https://openalex.org/W2117756735","https://openalex.org/W2151514667","https://openalex.org/W2156739854","https://openalex.org/W2158940042","https://openalex.org/W2189846329","https://openalex.org/W2266965707","https://openalex.org/W2462232592","https://openalex.org/W2505029951","https://openalex.org/W2611328865","https://openalex.org/W2766804299","https://openalex.org/W2896222781","https://openalex.org/W2916328532","https://openalex.org/W2962760844","https://openalex.org/W2962946304","https://openalex.org/W2963780177","https://openalex.org/W3013432954","https://openalex.org/W4241368925"],"related_works":["https://openalex.org/W102932032","https://openalex.org/W2152704622","https://openalex.org/W2951921877","https://openalex.org/W2039078354","https://openalex.org/W4288631859","https://openalex.org/W4307784304","https://openalex.org/W2157453464","https://openalex.org/W3102819058","https://openalex.org/W2785776846","https://openalex.org/W1690323570"],"abstract_inverted_index":{"The":[0,159],"reconstruction":[1],"of":[2,31,45,90,106,120,181],"a":[3,21,101,112,144],"low-rank":[4],"matrix":[5,99],"from":[6],"its":[7,11],"noisy":[8],"observation":[9],"finds":[10],"usage":[12],"in":[13,118],"many":[14],"applications.":[15],"It":[16],"can":[17,38,60,138,186],"be":[18,39,61,139,187],"reformulated":[19],"into":[20],"constrained":[22],"nuclear":[23,150],"norm":[24,89],"minimization":[25,153,184],"problem,":[26,135],"where":[27,69],"the":[28,32,42,46,49,56,58,64,70,77,87,91,94,97,125,128,132,149,156,179,183,206],"bound":[29],"$\\eta$":[30],"constraint":[33],"is":[34,52,74,100,124],"explicitly":[35],"given":[36],"or":[37],"estimated":[40],"by":[41,63,172,189],"probability":[43],"distribution":[44],"noise.":[47],"When":[48],"Lagrangian":[50,78],"method":[51],"applied":[53,140],"to":[54,76,141,165,204],"find":[55],"minimizer,":[57],"solution":[59,115],"obtained":[62,162,171],"singular":[65],"value":[66],"thresholding":[67,71],"operator,":[68],"parameter":[72,130,147],"$\\lambda$":[73,117,123],"related":[75],"multiplier.":[79],"In":[80],"this":[81],"paper,":[82],"we":[83,110],"first":[84],"show":[85],"that":[86,109],"Frobenius":[88],"discrepancy":[92,157],"between":[93],"minimizer":[95],"and":[96,198],"observed":[98],"strictly":[102],"monotonically":[103],"increasing":[104],"function":[105],"$\\lambda$.":[107],"From":[108],"derive":[111],"closed":[113],"form":[114],"for":[116,131,148],"terms":[119],"$\\eta$.":[121],"Since":[122],"same":[126],"as":[127],"regularization":[129,146,160],"unconstrained":[133],"regularized":[134,152],"our":[136],"results":[137],"automatically":[142],"choosing":[143],"suitable":[145],"norm--type":[151],"problems":[154],"using":[155],"principle.":[158],"parameters":[161],"are":[163,202],"comparable":[164],"(and":[166],"sometimes":[167],"better":[168],"than)":[169],"those":[170],"Stein's":[173],"unbiased":[174],"risk":[175],"estimator":[176],"approach,":[177],"while":[178],"cost":[180],"solving":[182],"problem":[185],"reduced":[188],"11--18":[190],"times.":[191],"Numerical":[192],"experiments":[193],"with":[194],"both":[195],"synthetic":[196],"data":[197,201],"real":[199],"MRI":[200],"performed":[203],"validate":[205],"proposed":[207],"approach.":[208]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
