{"id":"https://openalex.org/W3134651463","doi":"https://doi.org/10.1109/tip.2021.3061908","title":"Logarithmic Norm Regularized Low-Rank Factorization for Matrix and Tensor Completion","display_name":"Logarithmic Norm Regularized Low-Rank Factorization for Matrix and Tensor Completion","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3134651463","doi":"https://doi.org/10.1109/tip.2021.3061908","mag":"3134651463","pmid":"https://pubmed.ncbi.nlm.nih.gov/33651693"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2021.3061908","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2021.3061908","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","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/A5100746862","display_name":"Lin Chen","orcid":"https://orcid.org/0000-0001-5144-7855"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin Chen","raw_affiliation_strings":["School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0001-5144-7855","affiliations":[{"raw_affiliation_string":"School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074129836","display_name":"Xue Jiang","orcid":"https://orcid.org/0000-0001-7099-6817"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xue Jiang","raw_affiliation_strings":["School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0001-7099-6817","affiliations":[{"raw_affiliation_string":"School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061319150","display_name":"Xingzhao Liu","orcid":"https://orcid.org/0000-0002-4533-3904"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xingzhao Liu","raw_affiliation_strings":["School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-4533-3904","affiliations":[{"raw_affiliation_string":"School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101854736","display_name":"Zhixin Zhou","orcid":"https://orcid.org/0000-0003-3737-9248"},"institutions":[{"id":"https://openalex.org/I4210148107","display_name":"Space Engineering University","ror":"https://ror.org/04rj1td02","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210148107"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhixin Zhou","raw_affiliation_strings":["Space Engineering University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Space Engineering University, Beijing, China","institution_ids":["https://openalex.org/I4210148107"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.4215,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.9865525,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"30","issue":null,"first_page":"3434","last_page":"3449"},"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/T12303","display_name":"Tensor decomposition and applications","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9843999743461609,"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/mathematics","display_name":"Mathematics","score":0.6686694025993347},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.624068021774292},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5771781802177429},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.5471653938293457},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.489698201417923},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4569339156150818},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.45085209608078003},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4412789046764374},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4383573532104492},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3953874409198761},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39170587062835693},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3219967484474182},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2235061526298523},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.18768516182899475},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15733182430267334},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14755144715309143}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6686694025993347},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.624068021774292},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5771781802177429},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.5471653938293457},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.489698201417923},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4569339156150818},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.45085209608078003},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4412789046764374},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4383573532104492},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3953874409198761},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39170587062835693},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3219967484474182},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2235061526298523},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.18768516182899475},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15733182430267334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14755144715309143},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tip.2021.3061908","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2021.3061908","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},{"id":"pmid:33651693","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33651693","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 image processing : a publication of the IEEE Signal Processing Society","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2463320017","display_name":null,"funder_award_id":"61971279","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6895605005","display_name":null,"funder_award_id":"62022054","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W195665135","https://openalex.org/W1482071412","https://openalex.org/W1488435683","https://openalex.org/W1557899381","https://openalex.org/W1736339626","https://openalex.org/W1860736741","https://openalex.org/W1959158481","https://openalex.org/W1963826206","https://openalex.org/W1969698720","https://openalex.org/W1985124715","https://openalex.org/W1985629697","https://openalex.org/W1992426838","https://openalex.org/W2021361347","https://openalex.org/W2038891887","https://openalex.org/W2043571470","https://openalex.org/W2056532343","https://openalex.org/W2073382079","https://openalex.org/W2074577749","https://openalex.org/W2074682976","https://openalex.org/W2076430826","https://openalex.org/W2091449379","https://openalex.org/W2103972604","https://openalex.org/W2107861471","https://openalex.org/W2110531331","https://openalex.org/W2116413942","https://openalex.org/W2129732816","https://openalex.org/W2134332047","https://openalex.org/W2294540049","https://openalex.org/W2339666411","https://openalex.org/W2414540177","https://openalex.org/W2463532177","https://openalex.org/W2505029951","https://openalex.org/W2598601363","https://openalex.org/W2752077201","https://openalex.org/W2762772695","https://openalex.org/W2778192313","https://openalex.org/W2789612570","https://openalex.org/W2913535645","https://openalex.org/W2949419207","https://openalex.org/W2962791795","https://openalex.org/W2963648037","https://openalex.org/W2963703858","https://openalex.org/W2963885538","https://openalex.org/W2964024693","https://openalex.org/W2964135750","https://openalex.org/W2964214749","https://openalex.org/W2969770677","https://openalex.org/W2970259623","https://openalex.org/W3010488673","https://openalex.org/W3088225538","https://openalex.org/W3098683815","https://openalex.org/W3102415113","https://openalex.org/W3105952791","https://openalex.org/W4213272153","https://openalex.org/W4288345424","https://openalex.org/W6607912541","https://openalex.org/W6640851963","https://openalex.org/W6641162989","https://openalex.org/W6677204830","https://openalex.org/W6697296471","https://openalex.org/W6714532095","https://openalex.org/W6715531958","https://openalex.org/W6758920291","https://openalex.org/W6763624801","https://openalex.org/W6929385289"],"related_works":["https://openalex.org/W2964006653","https://openalex.org/W2788826952","https://openalex.org/W2084983808","https://openalex.org/W4318564253","https://openalex.org/W4302315572","https://openalex.org/W1969698720","https://openalex.org/W1991825408","https://openalex.org/W1507830821","https://openalex.org/W2963965423","https://openalex.org/W195665135"],"abstract_inverted_index":{"Matrix":[0,100],"and":[1,10,103,122,129,155,166,177],"tensor":[2],"completion":[3],"aim":[4],"to":[5,34,54],"recover":[6],"the":[7,14,21,28,35,39,63,76,114,119,140,146,159,163,170],"incomplete":[8],"two-":[9],"higher-dimensional":[11],"observations":[12],"using":[13,139],"low-rank":[15,40,127],"property.":[16],"Conventional":[17],"techniques":[18],"usually":[19],"minimize":[20],"convex":[22],"surrogate":[23,58,67,89],"of":[24,50,74,78,83,142,148,162,175],"rank":[25],"(such":[26],"as":[27],"nuclear":[29],"norm),":[30],"which,":[31],"however,":[32],"leads":[33],"suboptimal":[36],"solution":[37],"for":[38,59],"recovery.":[41],"In":[42],"this":[43],"paper,":[44],"we":[45,91],"propose":[46,92],"a":[47,56],"new":[48,94],"definition":[49],"matrix/tensor":[51,65,80,120],"logarithmic":[52,115],"norm":[53,66,77,98,105,116],"induce":[55],"sparsity-driven":[57],"rank.":[60],"More":[61],"importantly,":[62],"factor":[64],"theorems":[68],"are":[69,72,137],"derived,":[70],"which":[71],"capable":[73],"factoring":[75],"large-scale":[79],"into":[81],"those":[82],"small-scale":[84],"matrices/tensors":[85],"equivalently.":[86],"Based":[87],"upon":[88],"theorems,":[90],"two":[93,111],"algorithms":[95,112,168,172],"called":[96],"Logarithmic":[97,104],"Regularized":[99,106],"Factorization":[101,108],"(LRMF)":[102],"Tensor":[107],"(LRTF).":[109],"These":[110],"incorporate":[113],"regularization":[117],"with":[118,145],"factorization":[121],"hence":[123],"achieve":[124],"more":[125],"accurate":[126],"approximation":[128],"high":[130],"computational":[131],"efficiency.":[132,178],"The":[133],"resulting":[134],"optimization":[135],"problems":[136],"solved":[138],"framework":[141],"alternating":[143],"minimization":[144],"proof":[147],"convergence.":[149],"Simulation":[150],"results":[151],"on":[152],"both":[153],"synthetic":[154],"real-world":[156],"data":[157],"demonstrate":[158],"superior":[160],"performance":[161],"proposed":[164],"LRMF":[165],"LRTF":[167],"over":[169],"state-of-the-art":[171],"in":[173],"terms":[174],"accuracy":[176]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":18},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}