{"id":"https://openalex.org/W4403674677","doi":"https://doi.org/10.1109/tci.2024.3485467","title":"Fixed-Point Convergence of Multi-Block PnP ADMM and Its Application to Hyperspectral Image Restoration","display_name":"Fixed-Point Convergence of Multi-Block PnP ADMM and Its Application to Hyperspectral Image Restoration","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4403674677","doi":"https://doi.org/10.1109/tci.2024.3485467"},"language":"en","primary_location":{"id":"doi:10.1109/tci.2024.3485467","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tci.2024.3485467","pdf_url":null,"source":{"id":"https://openalex.org/S4210233665","display_name":"IEEE Transactions on Computational Imaging","issn_l":"2333-9403","issn":["2333-9403","2573-0436"],"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 Computational Imaging","raw_type":"journal-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/A5077310566","display_name":"Wei-Jie Liang","orcid":"https://orcid.org/0009-0002-4091-7182"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Weijie Liang","raw_affiliation_strings":["Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, China"],"raw_orcid":"https://orcid.org/0009-0002-4091-7182","affiliations":[{"raw_affiliation_string":"Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025149374","display_name":"Zhihui Tu","orcid":"https://orcid.org/0000-0003-0259-0465"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhihui Tu","raw_affiliation_strings":["Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0003-0259-0465","affiliations":[{"raw_affiliation_string":"Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066196985","display_name":"Jian L\u00fc","orcid":"https://orcid.org/0000-0003-4599-7281"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Lu","raw_affiliation_strings":["Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0003-4599-7281","affiliations":[{"raw_affiliation_string":"Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000747447","display_name":"Kai Tu","orcid":"https://orcid.org/0000-0002-0557-6792"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Tu","raw_affiliation_strings":["Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0002-0557-6792","affiliations":[{"raw_affiliation_string":"Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010561682","display_name":"Michael K. Ng","orcid":"https://orcid.org/0000-0001-6833-5227"},"institutions":[{"id":"https://openalex.org/I889458895","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86","country_code":"HK","type":"education","lineage":["https://openalex.org/I889458895"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Michael K. Ng","raw_affiliation_strings":["Department of Mathematics, The University of Hong Kong, Hong Kong"],"raw_orcid":"https://orcid.org/0000-0001-6833-5227","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I889458895"]}]},{"author_position":"last","author":{"id":null,"display_name":"Chen Xu","orcid":"https://orcid.org/0000-0002-1271-0734"},"institutions":[{"id":"https://openalex.org/I180726961","display_name":"Shenzhen University","ror":"https://ror.org/01vy4gh70","country_code":"CN","type":"education","lineage":["https://openalex.org/I180726961"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen Xu","raw_affiliation_strings":["Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, China"],"raw_orcid":"https://orcid.org/0000-0002-1271-0734","affiliations":[{"raw_affiliation_string":"Shenzhen Key Laboratory of Advanced Machine Learning and Applications, School of Mathematical Sciences, Shenzhen University, Shenzhen, China","institution_ids":["https://openalex.org/I180726961"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5077310566"],"corresponding_institution_ids":["https://openalex.org/I180726961"],"apc_list":null,"apc_paid":null,"fwci":0.9469,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75668231,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"10","issue":null,"first_page":"1571","last_page":"1587"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14158","display_name":"Optical Systems and Laser Technology","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T14158","display_name":"Optical Systems and Laser Technology","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T12050","display_name":"Optical Polarization and Ellipsometry","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/T12389","display_name":"Infrared Target Detection Methodologies","score":0.986299991607666,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/hyperspectral-imaging","display_name":"Hyperspectral imaging","score":0.8571075201034546},{"id":"https://openalex.org/keywords/image-restoration","display_name":"Image restoration","score":0.6550464630126953},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6041790843009949},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5394433736801147},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49957799911499023},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.4837798774242401},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.47286558151245117},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.4599423110485077},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4303247928619385},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4180278778076172},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.4177374243736267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3932451009750366},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38908830285072327}],"concepts":[{"id":"https://openalex.org/C159078339","wikidata":"https://www.wikidata.org/wiki/Q959005","display_name":"Hyperspectral imaging","level":2,"score":0.8571075201034546},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.6550464630126953},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6041790843009949},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5394433736801147},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49957799911499023},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.4837798774242401},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.47286558151245117},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4599423110485077},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4303247928619385},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4180278778076172},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.4177374243736267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3932451009750366},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38908830285072327},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tci.2024.3485467","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tci.2024.3485467","pdf_url":null,"source":{"id":"https://openalex.org/S4210233665","display_name":"IEEE Transactions on Computational Imaging","issn_l":"2333-9403","issn":["2333-9403","2573-0436"],"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 Computational Imaging","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6600000262260437,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1795570172","display_name":null,"funder_award_id":"2020B1515310008","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G2174765794","display_name":null,"funder_award_id":"12101436","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2722939784","display_name":null,"funder_award_id":"2023A1515011691","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G2866563306","display_name":null,"funder_award_id":"2024A1515011913","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G3014979221","display_name":null,"funder_award_id":"6237230","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3105280189","display_name":null,"funder_award_id":"U21A20455","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6262497296","display_name":null,"funder_award_id":"12326619","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7972534515","display_name":null,"funder_award_id":"62372302","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8017764705","display_name":null,"funder_award_id":"61972265","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"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":64,"referenced_works":["https://openalex.org/W1925324463","https://openalex.org/W1944540851","https://openalex.org/W1974438823","https://openalex.org/W1992426838","https://openalex.org/W1992841740","https://openalex.org/W1993482030","https://openalex.org/W2024165284","https://openalex.org/W2056370875","https://openalex.org/W2079075663","https://openalex.org/W2082590963","https://openalex.org/W2087416986","https://openalex.org/W2095906131","https://openalex.org/W2117852776","https://openalex.org/W2123031198","https://openalex.org/W2296055064","https://openalex.org/W2336406062","https://openalex.org/W2628535015","https://openalex.org/W2764207251","https://openalex.org/W2765431787","https://openalex.org/W2766545274","https://openalex.org/W2889700716","https://openalex.org/W2909669418","https://openalex.org/W2949128855","https://openalex.org/W2962708900","https://openalex.org/W2963814976","https://openalex.org/W2963840043","https://openalex.org/W2964179170","https://openalex.org/W2964215687","https://openalex.org/W2972301798","https://openalex.org/W2972939024","https://openalex.org/W2979001238","https://openalex.org/W2991209609","https://openalex.org/W3017506038","https://openalex.org/W3075397214","https://openalex.org/W3090929676","https://openalex.org/W3102186658","https://openalex.org/W3120342934","https://openalex.org/W3125860323","https://openalex.org/W3128465615","https://openalex.org/W3167568784","https://openalex.org/W3173891418","https://openalex.org/W3180330028","https://openalex.org/W3200625292","https://openalex.org/W3201868929","https://openalex.org/W3203729400","https://openalex.org/W3209789097","https://openalex.org/W4206151466","https://openalex.org/W4206319168","https://openalex.org/W4285203066","https://openalex.org/W4292363360","https://openalex.org/W4310177400","https://openalex.org/W4311378005","https://openalex.org/W4313526215","https://openalex.org/W4323644179","https://openalex.org/W4361294183","https://openalex.org/W4382457956","https://openalex.org/W4388017392","https://openalex.org/W4393252942","https://openalex.org/W4393906060","https://openalex.org/W6762438721","https://openalex.org/W6767563556","https://openalex.org/W6779806301","https://openalex.org/W6852540608","https://openalex.org/W6869337796"],"related_works":["https://openalex.org/W2072166414","https://openalex.org/W3209970181","https://openalex.org/W2060875994","https://openalex.org/W3034375524","https://openalex.org/W4230131218","https://openalex.org/W2070598848","https://openalex.org/W2404757046","https://openalex.org/W2044184146","https://openalex.org/W4313014865","https://openalex.org/W2019190440"],"abstract_inverted_index":{"Coupling":[0],"methods":[1,38],"of":[2,36,47,68,82,103,106,128],"integrating":[3],"multiple":[4,73],"priors":[5],"have":[6],"emerged":[7],"as":[8,54],"a":[9,29,112,135,150],"pivotal":[10],"research":[11],"focus":[12],"in":[13],"hyperspectral":[14],"image":[15],"(HSI)":[16],"restoration.":[17,121],"Among":[18],"these":[19],"methods,":[20],"the":[21,43,48,66,79,94,99,107,124,129,141,176],"Plug-and-Play":[22],"(PnP)":[23],"framework":[24,50,96,118],"stands":[25],"out":[26],"and":[27,97,148,170,179],"pioneers":[28],"novel":[30],"coupling":[31,69],"approach,":[32],"enabling":[33],"flexible":[34],"integration":[35],"diverse":[37],"into":[39],"model-based":[40],"approaches.":[41],"However,":[42],"current":[44],"convergence":[45,80,126,138],"analyses":[46],"PnP":[49,95,115,131,143],"are":[51,56],"highly":[52],"unexplored,":[53],"they":[55],"limited":[57],"to":[58,64],"2-block":[59,130],"composite":[60,87],"optimization":[61,88],"problems,":[62],"failing":[63],"meet":[65],"need":[67],"modeling":[70],"for":[71,85,119,140],"incorporating":[72,167],"priors.":[74,172],"This":[75],"paper":[76],"focuses":[77],"on":[78,156],"analysis":[81],"PnP-based":[83],"algorithms":[84],"multi-block":[86,114,142],"problems.":[89],"In":[90],"this":[91,157],"work,":[92],"under":[93],"utilizing":[98],"alternating":[100],"direction":[101],"method":[102],"multipliers":[104],"(ADMM)":[105],"continuation":[108],"scheme,":[109],"we":[110,133,159],"propose":[111],"unified":[113],"ADMM":[116,144],"algorithm":[117,166],"HSI":[120],"Inspired":[122],"by":[123],"fixed-point":[125,137],"theory":[127],"ADMM,":[132],"establish":[134],"similar":[136],"guarantee":[139],"with":[145],"extended":[146],"condition":[147],"provide":[149],"feasible":[151],"parameter":[152],"tuning":[153],"methodology.":[154],"Based":[155],"framework,":[158],"design":[160],"an":[161],"effective":[162],"mixed":[163],"noise":[164],"removal":[165],"global,":[168],"nonlocal":[169],"deep":[171],"Extensive":[173],"experiments":[174],"validate":[175],"algorithm's":[177],"superiority":[178],"competitiveness.":[180]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3}],"updated_date":"2026-05-29T09:21:14.243279","created_date":"2025-10-10T00:00:00"}