{"id":"https://openalex.org/W4391382751","doi":"https://doi.org/10.1109/camsap58249.2023.10403463","title":"Convergence of Nonconvex PNP-ADMM with MMSE Denoisers","display_name":"Convergence of Nonconvex PNP-ADMM with MMSE Denoisers","publication_year":2023,"publication_date":"2023-12-10","ids":{"openalex":"https://openalex.org/W4391382751","doi":"https://doi.org/10.1109/camsap58249.2023.10403463"},"language":"en","primary_location":{"id":"doi:10.1109/camsap58249.2023.10403463","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/camsap58249.2023.10403463","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","raw_type":"proceedings-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/A5113108673","display_name":"Chicago Y. Park","orcid":"https://orcid.org/0000-0002-5868-6557"},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chicago Park","raw_affiliation_strings":["Washington University in St. Louis,Department of Computer Science & Engineering,USA"],"affiliations":[{"raw_affiliation_string":"Washington University in St. Louis,Department of Computer Science & Engineering,USA","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036830065","display_name":"Shirin Shoushtari","orcid":"https://orcid.org/0000-0003-0654-6760"},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shirin Shoushtari","raw_affiliation_strings":["Washington University in St. Louis,Department of Electrical & Systems Engineering,USA"],"affiliations":[{"raw_affiliation_string":"Washington University in St. Louis,Department of Electrical & Systems Engineering,USA","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028095390","display_name":"Weijie Gan","orcid":"https://orcid.org/0000-0003-3604-784X"},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Weijie Gan","raw_affiliation_strings":["Washington University in St. Louis,Department of Computer Science & Engineering,USA"],"affiliations":[{"raw_affiliation_string":"Washington University in St. Louis,Department of Computer Science & Engineering,USA","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024602237","display_name":"Ulugbek S. Kamilov","orcid":"https://orcid.org/0000-0001-6770-3278"},"institutions":[{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ulugbek S. Kamilov","raw_affiliation_strings":["Washington University in St. Louis,Department of Computer Science & Engineering,USA","Department of Electrical & Systems Engineering, Washington University in St. Louis, USA"],"affiliations":[{"raw_affiliation_string":"Washington University in St. Louis,Department of Computer Science & Engineering,USA","institution_ids":["https://openalex.org/I204465549"]},{"raw_affiliation_string":"Department of Electrical & Systems Engineering, Washington University in St. Louis, USA","institution_ids":["https://openalex.org/I204465549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5113108673"],"corresponding_institution_ids":["https://openalex.org/I204465549"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21022464,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":null,"first_page":"511","last_page":"515"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9993000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7326484322547913},{"id":"https://openalex.org/keywords/expansive","display_name":"Expansive","score":0.6404770612716675},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.501737117767334},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49781060218811035},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.49322742223739624},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.49237287044525146},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.48192501068115234},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.46562546491622925},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4363175630569458},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.39771178364753723},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39258673787117004},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3877089023590088},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.27982428669929504},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.09579318761825562},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08385804295539856}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7326484322547913},{"id":"https://openalex.org/C2780502288","wikidata":"https://www.wikidata.org/wiki/Q28838156","display_name":"Expansive","level":3,"score":0.6404770612716675},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.501737117767334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49781060218811035},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.49322742223739624},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.49237287044525146},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.48192501068115234},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.46562546491622925},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4363175630569458},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.39771178364753723},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39258673787117004},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3877089023590088},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27982428669929504},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.09579318761825562},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08385804295539856},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C30407753","wikidata":"https://www.wikidata.org/wiki/Q186191","display_name":"Compressive strength","level":2,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/camsap58249.2023.10403463","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/camsap58249.2023.10403463","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.47999998927116394,"display_name":"Climate action","id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W2087416986","https://openalex.org/W2100556411","https://openalex.org/W2100705753","https://openalex.org/W2110505738","https://openalex.org/W2121927366","https://openalex.org/W2138204001","https://openalex.org/W2141006018","https://openalex.org/W2296055064","https://openalex.org/W2516602727","https://openalex.org/W2613155248","https://openalex.org/W2787172500","https://openalex.org/W2805167149","https://openalex.org/W2963178962","https://openalex.org/W2963814976","https://openalex.org/W2964271484","https://openalex.org/W2999778662","https://openalex.org/W3024822880","https://openalex.org/W3101311698","https://openalex.org/W3105425607","https://openalex.org/W3167568784","https://openalex.org/W3180330028","https://openalex.org/W3196456922","https://openalex.org/W4292363360","https://openalex.org/W4313526215","https://openalex.org/W6748386961","https://openalex.org/W6762438721","https://openalex.org/W6810850610"],"related_works":["https://openalex.org/W3207631643","https://openalex.org/W4300921257","https://openalex.org/W4298284054","https://openalex.org/W2271765275","https://openalex.org/W2964116984","https://openalex.org/W2910590812","https://openalex.org/W1571623370","https://openalex.org/W4302368440","https://openalex.org/W2331917905","https://openalex.org/W3155039083"],"abstract_inverted_index":{"Plug-and-Play":[0],"Alternating":[1],"Direction":[2],"Method":[3],"of":[4,64,70,95,131],"Multipliers":[5],"(PnP-ADMM)":[6],"is":[7],"a":[8,57,75,84,119],"widely-used":[9],"algorithm":[10,93],"for":[11,33,51,60,89],"solving":[12],"inverse":[13],"problems":[14],"by":[15],"integrating":[16],"physical":[17],"measurement":[18],"models":[19],"and":[20,37,98,106,123],"convolutional":[21],"neural":[22],"network":[23],"(CNN)":[24],"priors.":[25],"PnP-ADMM":[26,46,65,117],"has":[27,41],"been":[28,43],"theoretically":[29],"proven":[30],"to":[31],"converge":[32],"convex":[34],"data-fidelity":[35],"terms":[36],"nonexpansive":[38],"CNNs.":[39,53,133],"It":[40],"however":[42],"observed":[44,62],"that":[45],"often":[47],"empirically":[48],"converges":[49],"even":[50],"expansive":[52,124,132],"This":[54],"paper":[55],"presents":[56],"theoretical":[58],"explanation":[59,82],"the":[61,68,71,90,101,113,129],"stability":[63],"based":[66],"on":[67,100],"interpretation":[69],"CNN":[72],"prior":[73],"as":[74],"minimum":[76],"mean-squared":[77],"error":[78],"(MMSE)":[79],"denoiser.":[80],"Our":[81],"parallels":[83],"similar":[85],"argument":[86],"recently":[87],"made":[88],"iterative":[91],"shrinkage/thresholding":[92],"variant":[94],"PnP":[96],"(PnP-ISTA)":[97],"relies":[99],"connection":[102],"between":[103,116],"MMSE":[104],"denoisers":[105],"proximal":[107],"operators.":[108],"We":[109],"also":[110],"numerically":[111],"evaluate":[112],"performance":[114],"gap":[115],"using":[118],"nonexpan-sive":[120],"DnCNN":[121],"denoiser":[122],"DRUNet":[125],"denoiser,":[126],"thus":[127],"motivating":[128],"use":[130]},"counts_by_year":[],"updated_date":"2025-12-21T01:58:51.020947","created_date":"2025-10-10T00:00:00"}