{"id":"https://openalex.org/W3204636424","doi":"https://doi.org/10.1155/2021/3047712","title":"New Robust PCA for Outliers and Heavy Sparse Noises\u2019 Detection via Affine Transformation, the <i>L</i><sub>\u2217,<i>w</i></sub> and <i>L</i><sub>2,1</sub> Norms, and Spatial Weight Matrix in High\u2010Dimensional Images: From the Perspective of Signal Processing","display_name":"New Robust PCA for Outliers and Heavy Sparse Noises\u2019 Detection via Affine Transformation, the <i>L</i><sub>\u2217,<i>w</i></sub> and <i>L</i><sub>2,1</sub> Norms, and Spatial Weight Matrix in High\u2010Dimensional Images: From the Perspective of Signal Processing","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3204636424","doi":"https://doi.org/10.1155/2021/3047712","mag":"3204636424"},"language":"en","primary_location":{"id":"doi:10.1155/2021/3047712","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/3047712","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2021/3047712.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2021/3047712.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109423323","display_name":"Peidong Liang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peidong Liang","raw_affiliation_strings":["Fujian (Quanzhou)-HIT Research Institute of Engineering and Technology, Quanzhou 362000, China"],"affiliations":[{"raw_affiliation_string":"Fujian (Quanzhou)-HIT Research Institute of Engineering and Technology, Quanzhou 362000, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027563113","display_name":"Habte Tadesse Likassa","orcid":"https://orcid.org/0000-0002-2149-0956"},"institutions":[{"id":"https://openalex.org/I4537092","display_name":"Addis Ababa University","ror":"https://ror.org/038b8e254","country_code":"ET","type":"education","lineage":["https://openalex.org/I4537092"]}],"countries":["ET"],"is_corresponding":false,"raw_author_name":"Habte Tadesse Likassa","raw_affiliation_strings":["Department of Statistics, College of Natural and Computational Sciences, Addis Ababa University, Addis Ababa, Ethiopia"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, College of Natural and Computational Sciences, Addis Ababa University, Addis Ababa, Ethiopia","institution_ids":["https://openalex.org/I4537092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014692545","display_name":"Chentao Zhang","orcid":"https://orcid.org/0000-0002-3272-3735"},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chentao Zhang","raw_affiliation_strings":["Department of Instrumental and Electrical Engineering, Xiamen University, Xiamen, China","Fujian (Quanzhou)-HIT Research Institute of Engineering and Technology, Quanzhou 362000, China"],"affiliations":[{"raw_affiliation_string":"Department of Instrumental and Electrical Engineering, Xiamen University, Xiamen, China","institution_ids":["https://openalex.org/I191208505"]},{"raw_affiliation_string":"Fujian (Quanzhou)-HIT Research Institute of Engineering and Technology, Quanzhou 362000, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023434920","display_name":"Jielong Guo","orcid":null},"institutions":[{"id":"https://openalex.org/I4210119098","display_name":"Fujian Institute of Research on the Structure of Matter","ror":"https://ror.org/02j89k719","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210119098"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jielong Guo","raw_affiliation_strings":["Fujian Institute of Research on the Structure of Matter Fuzhou, Chinese Academy of Sciences, Fuzhou, China"],"affiliations":[{"raw_affiliation_string":"Fujian Institute of Research on the Structure of Matter Fuzhou, Chinese Academy of Sciences, Fuzhou, China","institution_ids":["https://openalex.org/I4210119098","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5014692545"],"corresponding_institution_ids":["https://openalex.org/I191208505"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.0614,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.73748603,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2021","issue":"1","first_page":null,"last_page":null},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9994000196456909,"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":0.9990000128746033,"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/affine-transformation","display_name":"Affine transformation","score":0.7316058874130249},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.6735213994979858},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5861652493476868},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5827488899230957},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5277909636497498},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.525309145450592},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.45509713888168335},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.41414108872413635},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3563280999660492},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1531691551208496},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10016071796417236}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7316058874130249},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.6735213994979858},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5861652493476868},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5827488899230957},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5277909636497498},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.525309145450592},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.45509713888168335},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.41414108872413635},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3563280999660492},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1531691551208496},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10016071796417236},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2021/3047712","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/3047712","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2021/3047712.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:4098645d522c47d08ae9f491bef8bb77","is_oa":true,"landing_page_url":"https://doaj.org/article/4098645d522c47d08ae9f491bef8bb77","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2021 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2021/3047712","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/3047712","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2021/3047712.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1137917739","display_name":null,"funder_award_id":"61806186","funder_id":"https://openalex.org/F4320324791","funder_display_name":"Addis Ababa University"},{"id":"https://openalex.org/G1673456586","display_name":null,"funder_award_id":"2019CT009","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G2309189552","display_name":null,"funder_award_id":"2018YFB1305700","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G2484032625","display_name":null,"funder_award_id":"2018YFB1305700","funder_id":"https://openalex.org/F4320324791","funder_display_name":"Addis Ababa University"},{"id":"https://openalex.org/G5211690661","display_name":null,"funder_award_id":"2018H2001","funder_id":"https://openalex.org/F4320324791","funder_display_name":"Addis Ababa University"},{"id":"https://openalex.org/G5919615586","display_name":null,"funder_award_id":"SKLRS-2019-KF-15","funder_id":"https://openalex.org/F4320324791","funder_display_name":"Addis Ababa University"},{"id":"https://openalex.org/G647575960","display_name":null,"funder_award_id":"2018H2001","funder_id":"https://openalex.org/F4320327001","funder_display_name":"State Key Laboratory of Robotics and System"},{"id":"https://openalex.org/G8568696245","display_name":null,"funder_award_id":"2019CT009","funder_id":"https://openalex.org/F4320324791","funder_display_name":"Addis Ababa University"}],"funders":[{"id":"https://openalex.org/F4320324791","display_name":"Addis Ababa University","ror":"https://ror.org/038b8e254"},{"id":"https://openalex.org/F4320326907","display_name":"State Key Laboratory of Robotics","ror":null},{"id":"https://openalex.org/F4320327001","display_name":"State Key Laboratory of Robotics and System","ror":null},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3204636424.pdf","grobid_xml":"https://content.openalex.org/works/W3204636424.grobid-xml"},"referenced_works_count":60,"referenced_works":["https://openalex.org/W56210758","https://openalex.org/W79405465","https://openalex.org/W1151238758","https://openalex.org/W1482071412","https://openalex.org/W1565566802","https://openalex.org/W1942100749","https://openalex.org/W1974042113","https://openalex.org/W1997201895","https://openalex.org/W2047291883","https://openalex.org/W2048695508","https://openalex.org/W2064076387","https://openalex.org/W2083138589","https://openalex.org/W2093922090","https://openalex.org/W2097018403","https://openalex.org/W2111861511","https://openalex.org/W2112796928","https://openalex.org/W2117121484","https://openalex.org/W2124463833","https://openalex.org/W2129812935","https://openalex.org/W2131628350","https://openalex.org/W2144582955","https://openalex.org/W2145962650","https://openalex.org/W2158497838","https://openalex.org/W2160225842","https://openalex.org/W2164278908","https://openalex.org/W2291202727","https://openalex.org/W2294181535","https://openalex.org/W2410894298","https://openalex.org/W2499274593","https://openalex.org/W2573153056","https://openalex.org/W2583591231","https://openalex.org/W2604338506","https://openalex.org/W2605217922","https://openalex.org/W2778795933","https://openalex.org/W2790756571","https://openalex.org/W2803590177","https://openalex.org/W2810585144","https://openalex.org/W2920817064","https://openalex.org/W2930181195","https://openalex.org/W2946008617","https://openalex.org/W2952393781","https://openalex.org/W2963295147","https://openalex.org/W2963885538","https://openalex.org/W2964691533","https://openalex.org/W2965256058","https://openalex.org/W3015585990","https://openalex.org/W3023553797","https://openalex.org/W3096193736","https://openalex.org/W3099326817","https://openalex.org/W3106018697","https://openalex.org/W3111652977","https://openalex.org/W3118450185","https://openalex.org/W3120295820","https://openalex.org/W3160041341","https://openalex.org/W3198134824","https://openalex.org/W3205245241","https://openalex.org/W4250630666","https://openalex.org/W4256139400","https://openalex.org/W4292363360","https://openalex.org/W6696701828"],"related_works":["https://openalex.org/W2018239771","https://openalex.org/W2092550984","https://openalex.org/W2736885024","https://openalex.org/W3135078450","https://openalex.org/W2311542041","https://openalex.org/W2732461152","https://openalex.org/W2026469060","https://openalex.org/W4221157057","https://openalex.org/W2890338455","https://openalex.org/W3204636424"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"a":[5,111,133,150],"novel":[6],"robust":[7],"algorithm":[8,155],"for":[9],"image":[10],"recovery":[11],"via":[12],"affine":[13,106,146],"transformations,":[14],"the":[15,23,31,37,41,43,49,55,59,68,78,91,100,105,117,141,145,159],"weighted":[16],"nuclear,":[17],"L":[18,24,44,60],"\u2217,":[19,61],"w":[20,62],",":[21],"and":[22,58,73,87,104,144],"2,1":[25,45],"norms.":[26],"The":[27,97,153],"new":[28,79,134,154],"method":[29,124,128],"considers":[30],"spatial":[32],"weight":[33],"matrix":[34],"to":[35,47,66,81,85,131,139,158],"account":[36],"correlated":[38],"samples":[39],"in":[40,54,90,94,149,162],"data,":[42],"norm":[46,63],"tackle":[48],"dilemma":[50],"of":[51,71,99,125,136,164],"extreme":[52],"values":[53],"high\u2010dimensional":[56,92],"images,":[57],"newly":[64],"added":[65],"alleviate":[67],"potential":[69],"effects":[70],"outliers":[72,86],"heavy":[74],"sparse":[75],"noises,":[76],"enabling":[77],"approach":[80],"be":[82],"more":[83],"resilient":[84],"large":[88],"variations":[89],"images":[93],"signal":[95],"processing.":[96],"determination":[98],"parameters":[101],"is":[102,129,156],"involved,":[103],"transformations":[107,147],"are":[108],"cast":[109],"as":[110],"convex":[112],"optimization":[113,142],"problem.":[114],"To":[115],"mitigate":[116],"computational":[118],"complexity,":[119],"alternating":[120],"iteratively":[121,148],"reweighted":[122],"direction":[123],"multipliers":[126],"(ADMM)":[127],"utilized":[130],"derive":[132],"set":[135],"recursive":[137],"equations":[138],"update":[140],"variables":[143],"round\u2010robin":[151],"manner.":[152],"superior":[157],"state\u2010of\u2010the\u2010art":[160],"works":[161],"terms":[163],"accuracy":[165],"on":[166],"various":[167],"public":[168],"databases.":[169]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2021-10-11T00:00:00"}