{"id":"https://openalex.org/W4387447990","doi":"https://doi.org/10.1109/lsp.2023.3323248","title":"On the Contractivity of Plug-and-Play Operators","display_name":"On the Contractivity of Plug-and-Play Operators","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4387447990","doi":"https://doi.org/10.1109/lsp.2023.3323248"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2023.3323248","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2023.3323248","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","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/A5010998900","display_name":"Chirayu D. Athalye","orcid":"https://orcid.org/0000-0002-1147-2586"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Chirayu D. Athalye","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Science, Bengaluru, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Science, Bengaluru, India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045035201","display_name":"Kunal N. Chaudhury","orcid":"https://orcid.org/0000-0002-8136-605X"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kunal N. Chaudhury","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Science, Bengaluru, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Science, Bengaluru, India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020326036","display_name":"Bhartendu Kumar","orcid":"https://orcid.org/0009-0003-4456-0165"},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Bhartendu Kumar","raw_affiliation_strings":["Department of Electrical Engineering, Indian Institute of Science, Bengaluru, India"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Indian Institute of Science, Bengaluru, India","institution_ids":["https://openalex.org/I59270414"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010998900"],"corresponding_institution_ids":["https://openalex.org/I59270414"],"apc_list":null,"apc_paid":null,"fwci":1.6973,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82006437,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"30","issue":null,"first_page":"1447","last_page":"1451"},"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":0.9993000030517578,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6516157984733582},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6431878805160522},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.574953019618988},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5029963850975037},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.46621236205101013},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4443340003490448},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43310999870300293},{"id":"https://openalex.org/keywords/inpainting","display_name":"Inpainting","score":0.4264912009239197},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4235432744026184},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38208919763565063},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34698933362960815},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34143301844596863},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2397783100605011},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.1794179081916809},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.17926955223083496},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.09040239453315735}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6516157984733582},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6431878805160522},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.574953019618988},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5029963850975037},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46621236205101013},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4443340003490448},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43310999870300293},{"id":"https://openalex.org/C11727466","wikidata":"https://www.wikidata.org/wiki/Q1628157","display_name":"Inpainting","level":3,"score":0.4264912009239197},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4235432744026184},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38208919763565063},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34698933362960815},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34143301844596863},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2397783100605011},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.1794179081916809},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.17926955223083496},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.09040239453315735},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2023.3323248","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2023.3323248","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai::84403","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401429","display_name":"ePrints@IISc (Indian Institute of Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I59270414","host_organization_name":"Indian Institute of Science Bangalore","host_organization_lineage":["https://openalex.org/I59270414"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3834246363","display_name":null,"funder_award_id":"IFA17-ENG227","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"}],"funders":[{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W1494195692","https://openalex.org/W1579559187","https://openalex.org/W1963816084","https://openalex.org/W1964394948","https://openalex.org/W1998419211","https://openalex.org/W2006262236","https://openalex.org/W2026849320","https://openalex.org/W2097073572","https://openalex.org/W2099244020","https://openalex.org/W2100522270","https://openalex.org/W2100556411","https://openalex.org/W2103559027","https://openalex.org/W2172275395","https://openalex.org/W2296055064","https://openalex.org/W2508457857","https://openalex.org/W2573726823","https://openalex.org/W2574952845","https://openalex.org/W2595897327","https://openalex.org/W2613155248","https://openalex.org/W2784344583","https://openalex.org/W2889923760","https://openalex.org/W2937841231","https://openalex.org/W2943669936","https://openalex.org/W2949440985","https://openalex.org/W2963299521","https://openalex.org/W2963814976","https://openalex.org/W2999778662","https://openalex.org/W3016440669","https://openalex.org/W3024822880","https://openalex.org/W3101311698","https://openalex.org/W3105425607","https://openalex.org/W3105776658","https://openalex.org/W3138006921","https://openalex.org/W3159379662","https://openalex.org/W3161177714","https://openalex.org/W3200625292","https://openalex.org/W4250589301","https://openalex.org/W4299356270","https://openalex.org/W4301621763","https://openalex.org/W4304480823","https://openalex.org/W4312788179","https://openalex.org/W4313526215","https://openalex.org/W4375948029","https://openalex.org/W6762438721"],"related_works":["https://openalex.org/W2380775572","https://openalex.org/W2213520135","https://openalex.org/W4242046654","https://openalex.org/W1504109132","https://openalex.org/W3134074939","https://openalex.org/W2117562399","https://openalex.org/W3174923100","https://openalex.org/W2244018504","https://openalex.org/W4298074124","https://openalex.org/W3172664294"],"abstract_inverted_index":{"In":[0,28,118],"plug-and-play":[1],"(PnP)":[2],"regularization,":[3],"the":[4,72,83,92,98,101,105,115,126],"proximal":[5],"operator":[6],"in":[7,26,56,63],"algorithms":[8],"such":[9,70],"as":[10,71],"ISTA":[11],"and":[12,141,146,155],"ADMM":[13],"is":[14,89],"replaced":[15],"by":[16,91],"a":[17],"powerful":[18],"denoiser.":[19],"This":[20],"formal":[21],"substitution":[22],"works":[23],"surprisingly":[24],"well":[25],"practice.":[27],"fact,":[29],"PnP":[30,46],"has":[31,47],"been":[32],"shown":[33,62],"to":[34,50,110],"give":[35],"state-of-the-art":[36],"results":[37],"for":[38,67,131,148,159],"various":[39],"imaging":[40],"applications.":[41],"The":[42,86],"empirical":[43],"success":[44],"of":[45],"motivated":[48,90],"researchers":[49],"understand":[51],"its":[52,58],"theoretical":[53,165],"underpinnings":[54],"and,":[55],"particular,":[57],"convergence.":[59],"It":[60],"was":[61],"prior":[64],"work":[65,88],"that":[66,136,153],"kernel":[68,149],"denoisers":[69],"nonlocal":[73],"means,":[74],"PnP-ISTA":[75,140,154],"provably":[76],"converges":[77],"under":[78],"some":[79],"strong":[80],"assumptions":[81,99],"on":[82,100],"forward":[84,102],"model.":[85],"present":[87],"following":[93],"questions:":[94],"Can":[95,104,112],"we":[96,113,121,134,151],"relax":[97],"model?":[103],"convergence":[106,116],"analysis":[107],"be":[108],"extended":[109],"PnP-ADMM?":[111],"estimate":[114],"rate?":[117],"this":[119],"letter,":[120],"resolve":[122],"these":[123],"questions":[124],"using":[125,167],"contraction":[127],"mapping":[128],"theorem:":[129],"(i)":[130],"symmetric":[132],"denoisers,":[133,150],"show":[135,152],"(under":[137],"mild":[138],"conditions)":[139],"PnP-ADMM":[142,156],"exhibit":[143],"linear":[144],"convergence;":[145],"(ii)":[147],"converge":[157],"linearly":[158],"image":[160],"inpainting.":[161],"We":[162],"validate":[163],"our":[164],"findings":[166],"reconstruction":[168],"experiments.":[169]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}