{"id":"https://openalex.org/W3024822880","doi":"https://doi.org/10.1109/lsp.2020.3006390","title":"Provable Convergence of Plug-and-Play Priors With MMSE Denoisers","display_name":"Provable Convergence of Plug-and-Play Priors With MMSE Denoisers","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3024822880","doi":"https://doi.org/10.1109/lsp.2020.3006390","mag":"3024822880"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2020.3006390","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2020.3006390","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2005.07685","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Xiaojian Xu","orcid":"https://orcid.org/0000-0002-5264-8963"},"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":"Xiaojian Xu","raw_affiliation_strings":["Department of Computer Science and Engineering, Washington University in St. Louis, St. Louis, USA"],"raw_orcid":"https://orcid.org/0000-0002-5264-8963","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Washington University in St. Louis, St. Louis, USA","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yu Sun","orcid":"https://orcid.org/0000-0001-7225-9677"},"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":"Yu Sun","raw_affiliation_strings":["Department of Computer Science and Engineering, Washington University in St. Louis, St. Louis, USA"],"raw_orcid":"https://orcid.org/0000-0001-7225-9677","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Washington University in St. Louis, St. Louis, USA","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Jiaming Liu","orcid":"https://orcid.org/0000-0002-1042-4443"},"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":"Jiaming Liu","raw_affiliation_strings":["Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, USA"],"raw_orcid":"https://orcid.org/0000-0002-1042-4443","affiliations":[{"raw_affiliation_string":"Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, USA","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Brendt Wohlberg","orcid":"https://orcid.org/0000-0002-4767-1843"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brendt Wohlberg","raw_affiliation_strings":["the Theoretical Division, Los Alamos National Laboratory, Los Alamos, USA"],"raw_orcid":"https://orcid.org/0000-0002-4767-1843","affiliations":[{"raw_affiliation_string":"the Theoretical Division, Los Alamos National Laboratory, Los Alamos, USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":null,"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":["Department of Computer Science and Engineering and also with the Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, USA"],"raw_orcid":"https://orcid.org/0000-0001-6770-3278","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering and also with the Department of Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, USA","institution_ids":["https://openalex.org/I204465549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.8425,"has_fulltext":true,"cited_by_count":55,"citation_normalized_percentile":{"value":0.98276461,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"27","issue":null,"first_page":"1280","last_page":"1284"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.8118000030517578,"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":0.8118000030517578,"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":0.07259999960660934,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.03970000147819519,"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/prior-probability","display_name":"Prior probability","score":0.8076000213623047},{"id":"https://openalex.org/keywords/maximum-a-posteriori-estimation","display_name":"Maximum a posteriori estimation","score":0.6707000136375427},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6158999800682068},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.5831999778747559},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.5827000141143799},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5561000108718872},{"id":"https://openalex.org/keywords/minimum-mean-square-error","display_name":"Minimum mean square error","score":0.5446000099182129},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5206000208854675},{"id":"https://openalex.org/keywords/signal-reconstruction","display_name":"Signal reconstruction","score":0.5027999877929688},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.482699990272522}],"concepts":[{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.8076000213623047},{"id":"https://openalex.org/C9810830","wikidata":"https://www.wikidata.org/wiki/Q635384","display_name":"Maximum a posteriori estimation","level":3,"score":0.6707000136375427},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6158999800682068},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.5831999778747559},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.5827000141143799},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5799000263214111},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5561000108718872},{"id":"https://openalex.org/C90652560","wikidata":"https://www.wikidata.org/wiki/Q11091747","display_name":"Minimum mean square error","level":3,"score":0.5446000099182129},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5206000208854675},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.5027999877929688},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.482699990272522},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4672999978065491},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4652000069618225},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43560001254081726},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.4097000062465668},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.4065000116825104},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.3386000096797943},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32919999957084656},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3183000087738037},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C854659","wikidata":"https://www.wikidata.org/wiki/Q1859284","display_name":"Message passing","level":2,"score":0.28200000524520874},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.2815999984741211},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27900001406669617},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.2712000012397766},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.2524999976158142},{"id":"https://openalex.org/C2989281035","wikidata":"https://www.wikidata.org/wiki/Q120811","display_name":"Signal recovery","level":3,"score":0.2524999976158142},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/lsp.2020.3006390","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2020.3006390","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:arXiv.org:2005.07685","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.07685","pdf_url":"https://arxiv.org/pdf/2005.07685","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:osti.gov:1726206","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1726206","pdf_url":"https://www.osti.gov/servlets/purl/1726206","source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2005.07685","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.07685","pdf_url":"https://arxiv.org/pdf/2005.07685","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6995210142","display_name":null,"funder_award_id":"89233218CNA000001","funder_id":"https://openalex.org/F4320332369","funder_display_name":"National Nuclear Security Administration"},{"id":"https://openalex.org/G7500863821","display_name":null,"funder_award_id":"89233218CNA000001","funder_id":"https://openalex.org/F4320338304","funder_display_name":"Los Alamos National Laboratory"},{"id":"https://openalex.org/G8659807574","display_name":null,"funder_award_id":"89233218CNA000001","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332369","display_name":"National Nuclear Security Administration","ror":"https://ror.org/03sk1we31"},{"id":"https://openalex.org/F4320338304","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1491719355","https://openalex.org/W1967020502","https://openalex.org/W2018322127","https://openalex.org/W2039284087","https://openalex.org/W2049633694","https://openalex.org/W2063650998","https://openalex.org/W2082029531","https://openalex.org/W2083609718","https://openalex.org/W2087416986","https://openalex.org/W2110505738","https://openalex.org/W2115706991","https://openalex.org/W2120717492","https://openalex.org/W2124541940","https://openalex.org/W2135046866","https://openalex.org/W2141006018","https://openalex.org/W2142224912","https://openalex.org/W2145096794","https://openalex.org/W2166670884","https://openalex.org/W2271221198","https://openalex.org/W2296055064","https://openalex.org/W2508457857","https://openalex.org/W2613155248","https://openalex.org/W2620976957","https://openalex.org/W2765431787","https://openalex.org/W2784344583","https://openalex.org/W2888957705","https://openalex.org/W2889700716","https://openalex.org/W2889923760","https://openalex.org/W2890592331","https://openalex.org/W2898685680","https://openalex.org/W2949128855","https://openalex.org/W2963814976","https://openalex.org/W2963840043","https://openalex.org/W2964215687","https://openalex.org/W3007179209","https://openalex.org/W3016440669","https://openalex.org/W3166469601","https://openalex.org/W4241652050","https://openalex.org/W4250955649","https://openalex.org/W6635437809","https://openalex.org/W6662481968","https://openalex.org/W6762438721"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2921424886","https://openalex.org/W2071782175","https://openalex.org/W1987033902","https://openalex.org/W2079475979","https://openalex.org/W2298446516","https://openalex.org/W2056388771","https://openalex.org/W2064786892","https://openalex.org/W2371447506","https://openalex.org/W2386767533"],"abstract_inverted_index":{"Plug-and-play":[0],"priors":[1],"(PnP)":[2],"is":[3],"a":[4,28,84,122],"methodology":[5],"for":[6,24,38,58,67],"regularized":[7],"image":[8,16],"reconstruction":[9],"that":[10,72],"specifies":[11],"the":[12,39,53,59,73,110,115],"prior":[13],"through":[14],"an":[15,79],"denoiser.":[17],"While":[18],"PnP":[19,66],"algorithms":[20],"are":[21],"well":[22],"understood":[23],"denoisers":[25],"performing":[26],"maximum":[27],"posteriori":[29],"probability":[30],"(MAP)":[31],"estimation,":[32],"they":[33],"have":[34],"not":[35],"been":[36],"analyzed":[37],"minimum":[40],"mean":[41],"squared":[42],"error":[43],"(MMSE)":[44],"denoisers.":[45,69],"This":[46],"letter":[47],"addresses":[48],"this":[49],"gap":[50],"by":[51,76,103,120],"establishing":[52],"first":[54],"theoretical":[55],"convergence":[56],"result":[57],"iterative":[60],"shrinkage/thresholding":[61],"algorithm":[62],"(ISTA)":[63],"variant":[64],"of":[65,87,107],"MMSE":[68,80,112,117],"We":[70,92],"show":[71],"iterates":[74],"produced":[75],"PnP-ISTA":[77],"with":[78],"denoiser":[81,113,118],"converge":[82],"to":[83],"stationary":[85],"point":[86],"some":[88],"global":[89],"cost":[90],"function.":[91],"validate":[93],"our":[94],"analysis":[95],"on":[96],"sparse":[97],"signal":[98],"recovery":[99],"in":[100],"compressive":[101],"sensing":[102],"comparing":[104],"two":[105],"types":[106],"denoisers,":[108],"namely":[109],"exact":[111],"and":[114],"approximate":[116],"obtained":[119],"training":[121],"deep":[123],"neural":[124],"net.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":17},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2020-05-21T00:00:00"}