{"id":"https://openalex.org/W2921396149","doi":"https://doi.org/10.1109/tnnls.2019.2900572","title":"Efficient Recovery of Low-Rank Matrix via Double Nonconvex Nonsmooth Rank Minimization","display_name":"Efficient Recovery of Low-Rank Matrix via Double Nonconvex Nonsmooth Rank Minimization","publication_year":2019,"publication_date":"2019-03-18","ids":{"openalex":"https://openalex.org/W2921396149","doi":"https://doi.org/10.1109/tnnls.2019.2900572","mag":"2921396149","pmid":"https://pubmed.ncbi.nlm.nih.gov/30892254"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2019.2900572","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2019.2900572","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","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/A5066566618","display_name":"Hengmin Zhang","orcid":"https://orcid.org/0000-0002-2472-6637"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hengmin Zhang","raw_affiliation_strings":["[PCA Laboratory, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing, China]"],"raw_orcid":"https://orcid.org/0000-0002-2472-6637","affiliations":[{"raw_affiliation_string":"[PCA Laboratory, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing, China]","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030222911","display_name":"Chen Gong","orcid":"https://orcid.org/0000-0002-4092-9856"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen Gong","raw_affiliation_strings":["[PCA Laboratory, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing, China]"],"raw_orcid":"https://orcid.org/0000-0002-4092-9856","affiliations":[{"raw_affiliation_string":"[PCA Laboratory, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing, China]","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064363522","display_name":"Jianjun Qian","orcid":"https://orcid.org/0000-0002-0968-8556"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianjun Qian","raw_affiliation_strings":["[PCA Laboratory, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing, China]"],"raw_orcid":"https://orcid.org/0000-0002-0968-8556","affiliations":[{"raw_affiliation_string":"[PCA Laboratory, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information of Ministry of Education, Nanjing University of Science and Technology, Nanjing, China]","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048088901","display_name":"Bob Zhang","orcid":"https://orcid.org/0000-0003-2497-9519"},"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":"Bob Zhang","raw_affiliation_strings":["Dept. of Comput. & Inf. Sci., Univ. of Macau, Macau, China"],"raw_orcid":"https://orcid.org/0000-0003-2497-9519","affiliations":[{"raw_affiliation_string":"Dept. of Comput. & Inf. Sci., Univ. of Macau, Macau, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054364063","display_name":"Chunyan Xu","orcid":"https://orcid.org/0000-0002-0814-4362"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunyan Xu","raw_affiliation_strings":["[PCA Laboratory, Jiangsu Key Laboratory of Image and Video Understanding for Social Security, School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China]"],"raw_orcid":"https://orcid.org/0000-0002-0814-4362","affiliations":[{"raw_affiliation_string":"[PCA Laboratory, Jiangsu Key Laboratory of Image and Video Understanding for Social Security, School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China]","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100726984","display_name":"Jian Yang","orcid":"https://orcid.org/0000-0003-4800-832X"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Yang","raw_affiliation_strings":["[PCA Laboratory, Jiangsu Key Laboratory of Image and Video Understanding for Social Security, School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China]"],"raw_orcid":"https://orcid.org/0000-0003-4800-832X","affiliations":[{"raw_affiliation_string":"[PCA Laboratory, Jiangsu Key Laboratory of Image and Video Understanding for Social Security, School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China]","institution_ids":["https://openalex.org/I36399199"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5066566618"],"corresponding_institution_ids":["https://openalex.org/I36399199"],"apc_list":null,"apc_paid":null,"fwci":4.6591,"has_fulltext":false,"cited_by_count":56,"citation_normalized_percentile":{"value":0.96047096,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"30","issue":"10","first_page":"2916","last_page":"2925"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":1.0,"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":0.9865999817848206,"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":0.982200026512146,"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/rank","display_name":"Rank (graph theory)","score":0.6477708220481873},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.6087737083435059},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5876443386077881},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.5726576447486877},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5442245006561279},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.5183292627334595},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5080935955047607},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.50571608543396},{"id":"https://openalex.org/keywords/robust-principal-component-analysis","display_name":"Robust principal component analysis","score":0.5048492550849915},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.499220609664917},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.4829946756362915},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.45656734704971313},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4557769298553467},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.44509774446487427},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.4356009364128113},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43211299180984497},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3877510130405426},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.32360512018203735},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18343499302864075},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11927524209022522},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.10669338703155518},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.10387983918190002},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07982268929481506}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6477708220481873},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.6087737083435059},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5876443386077881},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.5726576447486877},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5442245006561279},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.5183292627334595},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5080935955047607},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.50571608543396},{"id":"https://openalex.org/C2777749129","wikidata":"https://www.wikidata.org/wiki/Q17148469","display_name":"Robust principal component analysis","level":3,"score":0.5048492550849915},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.499220609664917},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.4829946756362915},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.45656734704971313},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4557769298553467},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.44509774446487427},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.4356009364128113},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43211299180984497},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3877510130405426},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.32360512018203735},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18343499302864075},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11927524209022522},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.10669338703155518},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.10387983918190002},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07982268929481506},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2019.2900572","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2019.2900572","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:30892254","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30892254","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 neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W195665135","https://openalex.org/W1482071412","https://openalex.org/W1486694121","https://openalex.org/W1507780841","https://openalex.org/W1736339626","https://openalex.org/W1906374873","https://openalex.org/W1943431218","https://openalex.org/W1965125844","https://openalex.org/W1967138577","https://openalex.org/W1969698720","https://openalex.org/W1980500788","https://openalex.org/W1992603145","https://openalex.org/W1997201895","https://openalex.org/W2012285303","https://openalex.org/W2013854956","https://openalex.org/W2021770241","https://openalex.org/W2022451443","https://openalex.org/W2023271934","https://openalex.org/W2027982384","https://openalex.org/W2039284087","https://openalex.org/W2060204507","https://openalex.org/W2063715296","https://openalex.org/W2074682976","https://openalex.org/W2075547019","https://openalex.org/W2079775628","https://openalex.org/W2084983808","https://openalex.org/W2092841641","https://openalex.org/W2100556411","https://openalex.org/W2103972604","https://openalex.org/W2107861471","https://openalex.org/W2110531331","https://openalex.org/W2111854674","https://openalex.org/W2118550318","https://openalex.org/W2129732816","https://openalex.org/W2134332047","https://openalex.org/W2145831204","https://openalex.org/W2155628440","https://openalex.org/W2164278908","https://openalex.org/W2165395308","https://openalex.org/W2187214659","https://openalex.org/W2214177029","https://openalex.org/W2339666411","https://openalex.org/W2471758726","https://openalex.org/W2505029951","https://openalex.org/W2563833337","https://openalex.org/W2587855401","https://openalex.org/W2588939073","https://openalex.org/W2611328865","https://openalex.org/W2752077201","https://openalex.org/W2768166594","https://openalex.org/W2789137832","https://openalex.org/W2791026767","https://openalex.org/W2800791174","https://openalex.org/W2910761930","https://openalex.org/W2949419207","https://openalex.org/W2963218026","https://openalex.org/W2963598490","https://openalex.org/W2963714933","https://openalex.org/W2963965423","https://openalex.org/W3098306969","https://openalex.org/W3100203369","https://openalex.org/W3101767848","https://openalex.org/W4292363360","https://openalex.org/W6607912541","https://openalex.org/W6628883312","https://openalex.org/W6641162989","https://openalex.org/W6681332534","https://openalex.org/W6684295950","https://openalex.org/W6688334558","https://openalex.org/W6749097396"],"related_works":["https://openalex.org/W2952489973","https://openalex.org/W4300776969","https://openalex.org/W2184500224","https://openalex.org/W2963965423","https://openalex.org/W2952857461","https://openalex.org/W2125655865","https://openalex.org/W4300849244","https://openalex.org/W2950824353","https://openalex.org/W4384341135","https://openalex.org/W2921396149"],"abstract_inverted_index":{"Recently,":[0],"there":[1],"is":[2,27,92,133,189],"a":[3,36,79,153,190],"rapidly":[4],"increasing":[5],"attraction":[6],"for":[7],"the":[8,44,96,108,125,130,137,142,146,162,168,175,186,194,212],"efficient":[9],"recovery":[10],"of":[11,24,145,161,185],"low-rank":[12],"matrix":[13,213,238],"in":[14,157,211],"computer":[15],"vision":[16],"and":[17,47,71,81,141,181,222,236],"machine":[18],"learning.":[19],"The":[20],"popular":[21],"convex":[22,70,235],"solution":[23,38,144],"rank":[25,45,50,60,73,83],"minimization":[26,30,139],"nuclear":[28],"norm-based":[29],"(NNM),":[31],"which":[32,91,158],"usually":[33,166],"leads":[34],"to":[35,42,128,135],"biased":[37],"since":[39],"NNM":[40],"tends":[41],"overshrink":[43],"components":[46],"treats":[48],"each":[49,159],"component":[51],"equally.":[52],"To":[53],"address":[54],"this":[55,75],"issue,":[56],"some":[57,198],"nonconvex":[58,72,109,237],"nonsmooth":[59],"(NNR)":[61],"relaxations":[62],"have":[63],"been":[64],"exploited":[65],"widely.":[66],"Different":[67],"from":[68,95],"these":[69],"substitutes,":[74],"paper":[76],"first":[77],"introduces":[78],"general":[80,154],"flexible":[82],"relaxation":[84,89,104],"function":[85,105,112,177],"named":[86],"weighted":[87],"NNR":[88,99],"function,":[90],"actually":[93],"derived":[94],"initial":[97],"double":[98],"(DNNR)":[100],"relaxations,":[101],"i.e.,":[102],"DNNR":[103,138],"acts":[106],"on":[107,218],"singular":[110],"values":[111,127,178],"(SVF).":[113],"An":[114],"iteratively":[115],"reweighted":[116],"SVF":[117],"optimization":[118],"algorithm":[119],"with":[120,197,232],"continuation":[121],"technology":[122],"through":[123],"computing":[124],"supergradient":[126],"define":[129],"weighting":[131,164],"vector":[132,165],"devised":[134],"solve":[136],"problem,":[140,215],"closed-form":[143],"subproblem":[147],"can":[148,225],"be":[149],"efficiently":[150],"obtained":[151],"by":[152],"proximal":[155],"operator,":[156],"element":[160],"desired":[163],"satisfies":[167],"nondecreasing":[169],"order.":[170],"We":[171],"next":[172],"prove":[173],"that":[174,227],"objective":[176],"decrease":[179],"monotonically,":[180],"any":[182],"limit":[183],"point":[184],"generated":[187],"subsequence":[188],"critical":[191],"point.":[192],"Combining":[193],"Kurdyka-\u0141ojasiewicz":[195],"property":[196],"milder":[199],"assumptions,":[200],"we":[201],"further":[202],"give":[203],"its":[204],"global":[205],"convergence":[206],"guarantee.":[207],"As":[208],"an":[209],"application":[210],"completion":[214,239],"experimental":[216],"results":[217],"both":[219],"synthetic":[220],"data":[221,224],"real-world":[223],"show":[226],"our":[228],"methods":[229],"are":[230],"competitive":[231],"several":[233],"state-of-the-art":[234],"methods.":[240]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":17},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}