{"id":"https://openalex.org/W4396243049","doi":"https://doi.org/10.1109/tci.2024.3393742","title":"Local Monotone Operator Learning Using Non-Monotone Operators: MnM-MOL","display_name":"Local Monotone Operator Learning Using Non-Monotone Operators: MnM-MOL","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4396243049","doi":"https://doi.org/10.1109/tci.2024.3393742"},"language":"en","primary_location":{"id":"doi:10.1109/tci.2024.3393742","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tci.2024.3393742","pdf_url":null,"source":{"id":"https://openalex.org/S4210233665","display_name":"IEEE Transactions on Computational Imaging","issn_l":"2333-9403","issn":["2333-9403","2334-0118","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/A5078856547","display_name":"Maneesh John","orcid":"https://orcid.org/0000-0002-1528-7759"},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maneesh John","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1528-7759","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA","institution_ids":["https://openalex.org/I126307644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072491757","display_name":"Jyothi Rikhab Chand","orcid":"https://orcid.org/0000-0002-8335-6103"},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jyothi Rikhab Chand","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA"],"raw_orcid":"https://orcid.org/0000-0002-8335-6103","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA","institution_ids":["https://openalex.org/I126307644"]}]},{"author_position":"last","author":{"id":null,"display_name":"Mathews Jacob","orcid":"https://orcid.org/0000-0002-0657-6479"},"institutions":[{"id":"https://openalex.org/I126307644","display_name":"University of Iowa","ror":"https://ror.org/036jqmy94","country_code":"US","type":"education","lineage":["https://openalex.org/I126307644"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mathews Jacob","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA"],"raw_orcid":"https://orcid.org/0000-0002-0657-6479","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA","institution_ids":["https://openalex.org/I126307644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I126307644"],"apc_list":null,"apc_paid":null,"fwci":0.8335,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.75799007,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"10","issue":null,"first_page":"742","last_page":"751"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.9987999796867371,"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/T12676","display_name":"Machine Learning and ELM","score":0.9987999796867371,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9983000159263611,"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":0.9941999912261963,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7387502193450928},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5878885984420776},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4966292977333069},{"id":"https://openalex.org/keywords/pseudo-monotone-operator","display_name":"Pseudo-monotone operator","score":0.45308247208595276},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39766472578048706},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.27501922845840454},{"id":"https://openalex.org/keywords/finite-rank-operator","display_name":"Finite-rank operator","score":0.2105637788772583},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08121922612190247}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7387502193450928},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5878885984420776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4966292977333069},{"id":"https://openalex.org/C201040074","wikidata":"https://www.wikidata.org/wiki/Q7254436","display_name":"Pseudo-monotone operator","level":5,"score":0.45308247208595276},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39766472578048706},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27501922845840454},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.2105637788772583},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08121922612190247},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"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/C176691602","wikidata":"https://www.wikidata.org/wiki/Q7097841","display_name":"Operator space","level":4,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tci.2024.3393742","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tci.2024.3393742","pdf_url":null,"source":{"id":"https://openalex.org/S4210233665","display_name":"IEEE Transactions on Computational Imaging","issn_l":"2333-9403","issn":["2333-9403","2334-0118","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1686180572","https://openalex.org/W2087332491","https://openalex.org/W2087416986","https://openalex.org/W2101675075","https://openalex.org/W2573726823","https://openalex.org/W2604388535","https://openalex.org/W2742774307","https://openalex.org/W2773850766","https://openalex.org/W2785678896","https://openalex.org/W2889700716","https://openalex.org/W2900756484","https://openalex.org/W2911290743","https://openalex.org/W2962840844","https://openalex.org/W2964215687","https://openalex.org/W3047238636","https://openalex.org/W3098020164","https://openalex.org/W3099748020","https://openalex.org/W3100730608","https://openalex.org/W3118064383","https://openalex.org/W3124596402","https://openalex.org/W3165333460","https://openalex.org/W3180330028","https://openalex.org/W3206211787","https://openalex.org/W4225513576","https://openalex.org/W4249760698","https://openalex.org/W4308758965","https://openalex.org/W4321782575","https://openalex.org/W4323338375","https://openalex.org/W4385938192","https://openalex.org/W6727685206","https://openalex.org/W6748582592","https://openalex.org/W6755625687","https://openalex.org/W6762438721","https://openalex.org/W6767563556","https://openalex.org/W6790560385","https://openalex.org/W6810920627","https://openalex.org/W6847408952"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2011614914","https://openalex.org/W1561249172","https://openalex.org/W1816587483","https://openalex.org/W2078458933","https://openalex.org/W3101041205","https://openalex.org/W2951312832","https://openalex.org/W4300843901","https://openalex.org/W4299588902","https://openalex.org/W2953039038"],"abstract_inverted_index":{"The":[0,121],"recovery":[1],"of":[2,19,32,51,124,154,157],"magnetic":[3],"resonance":[4],"(MR)":[5],"images":[6],"from":[7],"undersampled":[8],"measurements":[9],"is":[10,127,219,231,239],"a":[11,48,93,173,204],"key":[12],"problem":[13],"that":[14,101,215,228,237,250,259],"has":[15],"been":[16],"the":[17,68,79,85,97,102,109,118,130,133,148,152,155,158,162,168,179,198,208,216,224,229,243,251,260],"subject":[18],"extensive":[20],"research":[21],"in":[22,60,113,136,203],"recent":[23,69],"years.":[24],"Unrolled":[25],"approaches,":[26],"which":[27,187],"rely":[28],"on":[29,96,132,151],"end-to-end":[30],"training":[31],"convolutional":[33],"neural":[34],"network":[35,98],"(CNN)":[36],"blocks":[37],"within":[38],"iterative":[39],"reconstruction":[40],"algorithms,":[41],"offer":[42],"state-of-the-art":[43],"performance.":[44,192],"These":[45],"algorithms":[46],"require":[47,92],"large":[49],"amount":[50],"memory":[52,86],"during":[53,88],"training,":[54],"making":[55],"them":[56],"difficult":[57],"to":[58,77,99,117,128,171,181,190,200,221,223,233,242,255,264,268],"employ":[59],"high-dimensional":[61],"applications.":[62],"Deep":[63],"equilibrium":[64],"(DEQ)":[65],"models":[66],"and":[67,104,161,227,258],"monotone":[70,149,174,202],"operator":[71,199],"learning":[72],"(MOL)":[73],"approach":[74,177,261],"were":[75],"introduced":[76],"eliminate":[78],"need":[80],"for":[81],"unrolling,":[82],"thus":[83],"reducing":[84],"demand":[87],"training.":[89],"Both":[90],"approaches":[91],"Lipschitz":[94],"constraint":[95,110,131,150],"ensure":[100],"forward":[103],"backpropagation":[105],"iterations":[106],"converge.":[107],"Unfortunately,":[108],"often":[111],"results":[112,213,248],"reduced":[114],"performance":[115,257],"compared":[116],"unrolled":[119],"methods.":[120],"main":[122],"focus":[123],"this":[125],"work":[126],"relax":[129],"CNN":[134,163,169,180],"block":[135],"two":[137],"different":[138],"ways.":[139],"Inspired":[140],"by":[141],"convex-non-convex":[142],"regularization":[143],"strategies,":[144],"we":[145,195],"now":[146],"impose":[147],"sum":[153],"gradient":[156],"data":[159],"term":[160],"block,":[164],"rather":[165],"than":[166],"constrain":[167],"itself":[170],"be":[172,201],"operator.":[175],"This":[176],"enables":[178],"learn":[182],"possibly":[183],"non-monotone":[184],"score":[185],"functions,":[186],"can":[188],"translate":[189,254],"improved":[191,256],"In":[193],"addition,":[194],"only":[196],"restrict":[197],"local":[205],"neighborhood":[206],"around":[207],"image":[209],"manifold.":[210],"Our":[211,246],"theoretical":[212],"show":[214,249],"proposed":[217],"algorithm":[218],"guaranteed":[220],"converge":[222],"fixed":[225],"point":[226],"solution":[230],"robust":[232],"input":[234,265],"perturbations,":[235],"provided":[236],"it":[238],"initialized":[240],"close":[241],"true":[244],"solution.":[245],"empirical":[247],"relaxed":[252],"constraints":[253],"enjoys":[262],"robustness":[263],"perturbations":[266],"similar":[267],"MOL.":[269]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-12-26T23:08:49.675405","created_date":"2025-10-10T00:00:00"}
