{"id":"https://openalex.org/W2982258910","doi":"https://doi.org/10.1109/icassp40776.2020.9054731","title":"Building Firmly Nonexpansive Convolutional Neural Networks","display_name":"Building Firmly Nonexpansive Convolutional Neural Networks","publication_year":2020,"publication_date":"2020-04-09","ids":{"openalex":"https://openalex.org/W2982258910","doi":"https://doi.org/10.1109/icassp40776.2020.9054731","mag":"2982258910"},"language":"en","primary_location":{"id":"doi:10.1109/icassp40776.2020.9054731","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp40776.2020.9054731","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","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/A5045608650","display_name":"Matthieu Terris","orcid":null},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Matthieu Terris","raw_affiliation_strings":["Heriot-Watt University,Institute of Sensors, Signals and Systems,Edinburgh,United Kingdom,EH14 4AS"],"affiliations":[{"raw_affiliation_string":"Heriot-Watt University,Institute of Sensors, Signals and Systems,Edinburgh,United Kingdom,EH14 4AS","institution_ids":["https://openalex.org/I32062511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083254809","display_name":"Audrey Repetti","orcid":"https://orcid.org/0000-0002-6296-6957"},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Audrey Repetti","raw_affiliation_strings":["Heriot-Watt University,Institute of Sensors, Signals and Systems,Edinburgh,United Kingdom,EH14 4AS"],"affiliations":[{"raw_affiliation_string":"Heriot-Watt University,Institute of Sensors, Signals and Systems,Edinburgh,United Kingdom,EH14 4AS","institution_ids":["https://openalex.org/I32062511"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062845079","display_name":"Jean\u2010Christophe Pesquet","orcid":"https://orcid.org/0000-0002-5943-8061"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jean-Christophe Pesquet","raw_affiliation_strings":["Université Paris-Saclay,CentraleSupélec, Inria, Center for Visual Computing,Gif sur Yvette,France,91190"],"affiliations":[{"raw_affiliation_string":"Université Paris-Saclay,CentraleSupélec, Inria, Center for Visual Computing,Gif sur Yvette,France,91190","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041620227","display_name":"Yves Wiaux","orcid":"https://orcid.org/0000-0002-1658-0121"},"institutions":[{"id":"https://openalex.org/I32062511","display_name":"Heriot-Watt University","ror":"https://ror.org/04mghma93","country_code":"GB","type":"education","lineage":["https://openalex.org/I32062511"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Yves Wiaux","raw_affiliation_strings":["Heriot-Watt University,Institute of Sensors, Signals and Systems,Edinburgh,United Kingdom,EH14 4AS"],"affiliations":[{"raw_affiliation_string":"Heriot-Watt University,Institute of Sensors, Signals and Systems,Edinburgh,United Kingdom,EH14 4AS","institution_ids":["https://openalex.org/I32062511"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5045608650"],"corresponding_institution_ids":["https://openalex.org/I32062511"],"apc_list":null,"apc_paid":null,"fwci":2.7837,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.92042874,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"8658","last_page":"8662"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11105","display_name":"Advanced Image Processing Techniques","score":0.9944999814033508,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.8443933725357056},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.76478111743927},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.7199333310127258},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5702824592590332},{"id":"https://openalex.org/keywords/image-denoising","display_name":"Image denoising","score":0.5230528116226196},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5133696794509888},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.45327815413475037},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33290570974349976},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.2721734046936035},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.138988196849823}],"concepts":[{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.8443933725357056},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.76478111743927},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7199333310127258},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5702824592590332},{"id":"https://openalex.org/C2983327147","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Image denoising","level":3,"score":0.5230528116226196},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5133696794509888},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.45327815413475037},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33290570974349976},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.2721734046936035},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.138988196849823},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"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":1,"locations":[{"id":"doi:10.1109/icassp40776.2020.9054731","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp40776.2020.9054731","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1205052666","display_name":null,"funder_award_id":"EP/M019306/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4145709284","display_name":null,"funder_award_id":"EP/P020267/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G802533138","display_name":null,"funder_award_id":"EP/M008843/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W1572063013","https://openalex.org/W1946620893","https://openalex.org/W1972440447","https://openalex.org/W2056370875","https://openalex.org/W2117539524","https://openalex.org/W2121927366","https://openalex.org/W2142280715","https://openalex.org/W2254152852","https://openalex.org/W2604885021","https://openalex.org/W2613155248","https://openalex.org/W2618017917","https://openalex.org/W2785678896","https://openalex.org/W2803968356","https://openalex.org/W2905472194","https://openalex.org/W2907210743","https://openalex.org/W2945291039","https://openalex.org/W2949128855","https://openalex.org/W2949440985","https://openalex.org/W2962851953","https://openalex.org/W2963247530","https://openalex.org/W2963424732","https://openalex.org/W2963836885","https://openalex.org/W2964294232","https://openalex.org/W3006592723","https://openalex.org/W3102025760","https://openalex.org/W4289293305","https://openalex.org/W4300167250","https://openalex.org/W6736987314","https://openalex.org/W6738248287","https://openalex.org/W6748582592","https://openalex.org/W6751707404","https://openalex.org/W6756052093","https://openalex.org/W6756840390","https://openalex.org/W6757465018","https://openalex.org/W6762438721"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2911623553","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2318923278","https://openalex.org/W2417585376","https://openalex.org/W1994157709","https://openalex.org/W3185441898"],"abstract_inverted_index":{"Building":[0],"nonexpansive":[1,83,120],"Convolutional":[2],"Neural":[3],"Networks":[4,60],"(CNNs)":[5],"is":[6,112],"a":[7,14,101,129],"challenging":[8],"problem":[9],"that":[10,93],"has":[11,53,77],"recently":[12],"gained":[13],"lot":[15],"of":[16,44,49,71,100,107],"attention":[17],"from":[18],"the":[19,29,45,46,50,69,98,105,124],"image":[20,133],"processing":[21],"community.":[22],"In":[23,85],"particular,":[24],"it":[25],"appears":[26],"to":[27,31,61,64,68,81,103,114,117,127],"be":[28,95],"key":[30],"obtain":[32],"convergent":[33],"Plugand-Play":[34],"algorithms.":[35],"This":[36,111],"problem,":[37],"which":[38],"relies":[39],"on":[40],"an":[41,90,132],"accurate":[42],"control":[43],"Lipschitz":[47],"constant":[48],"convolutional":[51,109],"layers,":[52],"also":[54],"been":[55,78],"investigated":[56],"for":[57,131],"Generative":[58],"Adversarial":[59],"improve":[62],"robustness":[63],"adversarial":[65],"perturbations.":[66],"However,":[67],"best":[70],"our":[72],"knowledge,":[73],"no":[74],"efficient":[75],"method":[76],"developed":[79],"yet":[80],"build":[82,118],"CNNs.":[84,121],"this":[86],"paper,":[87],"we":[88],"develop":[89],"optimization":[91],"algorithm":[92],"can":[94],"incorporated":[96],"in":[97],"training":[99],"network":[102],"ensure":[104],"nonexpansiveness":[106],"its":[108,138],"layers.":[110],"shown":[113],"allow":[115],"us":[116],"firmly":[119],"We":[122],"apply":[123],"proposed":[125],"approach":[126],"train":[128],"CNN":[130],"denoising":[134],"task":[135],"and":[136],"show":[137],"effectiveness":[139],"through":[140],"simulations.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}