{"id":"https://openalex.org/W4394577179","doi":"https://doi.org/10.1137/23m1581807","title":"NF-ULA: Normalizing Flow-Based Unadjusted Langevin Algorithm for Imaging Inverse Problems","display_name":"NF-ULA: Normalizing Flow-Based Unadjusted Langevin Algorithm for Imaging Inverse Problems","publication_year":2024,"publication_date":"2024-04-08","ids":{"openalex":"https://openalex.org/W4394577179","doi":"https://doi.org/10.1137/23m1581807"},"language":"en","primary_location":{"id":"doi:10.1137/23m1581807","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1581807","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://pure-oai.bham.ac.uk/ws/files/217860394/NF_ULA_accepted_version.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079783943","display_name":"Ziruo Cai","orcid":null},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziruo Cai","raw_affiliation_strings":["School of Mathematical Sciences, Shanghai Jiao Tong University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Shanghai Jiao Tong University, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054394663","display_name":"Junqi Tang","orcid":"https://orcid.org/0000-0003-4996-6079"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Junqi Tang","raw_affiliation_strings":["School of Mathematics, University of Birmingham, Birmingham, UK"],"raw_orcid":"https://orcid.org/0000-0003-4996-6079","affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Birmingham, Birmingham, UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102928532","display_name":"Subhadip Mukherjee","orcid":"https://orcid.org/0000-0002-7957-8758"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Subhadip Mukherjee","raw_affiliation_strings":["Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology (IIT) Kharagpur, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology (IIT) Kharagpur, India","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026669579","display_name":"Jinglai Li","orcid":"https://orcid.org/0000-0001-7980-6901"},"institutions":[{"id":"https://openalex.org/I79619799","display_name":"University of Birmingham","ror":"https://ror.org/03angcq70","country_code":"GB","type":"education","lineage":["https://openalex.org/I79619799"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jinglai Li","raw_affiliation_strings":["School of Mathematics, University of Birmingham, Birmingham, UK"],"raw_orcid":"https://orcid.org/0000-0001-7980-6901","affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Birmingham, Birmingham, UK","institution_ids":["https://openalex.org/I79619799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033880300","display_name":"Carola\u2010Bibiane Sch\u00f6nlieb","orcid":"https://orcid.org/0000-0003-0099-6306"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Carola-Bibiane Sch\u00f6nlieb","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052123856","display_name":"Xiaoqun Zhang","orcid":"https://orcid.org/0000-0002-2723-4451"},"institutions":[{"id":"https://openalex.org/I4210158445","display_name":"Institute of Natural Science","ror":"https://ror.org/004tze884","country_code":"KP","type":"education","lineage":["https://openalex.org/I4210158445"]}],"countries":["KP"],"is_corresponding":false,"raw_author_name":"Xiaoqun Zhang","raw_affiliation_strings":["School of Mathematical Sciences, MOELSC and Institute of Natural Sciences, Shanghai Jiao Tong University, China"],"raw_orcid":"https://orcid.org/0000-0002-2723-4451","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, MOELSC and Institute of Natural Sciences, Shanghai Jiao Tong University, China","institution_ids":["https://openalex.org/I4210158445"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0291,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.86159111,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"17","issue":"2","first_page":"820","last_page":"860"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9976999759674072,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.571173369884491},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.562279999256134},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5336462259292603},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5294746160507202},{"id":"https://openalex.org/keywords/langevin-dynamics","display_name":"Langevin dynamics","score":0.4557307958602905},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4177696704864502},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3738287091255188},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3492136597633362},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.2977849543094635},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25418001413345337},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20191848278045654},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14431136846542358}],"concepts":[{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.571173369884491},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.562279999256134},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5336462259292603},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5294746160507202},{"id":"https://openalex.org/C2780004032","wikidata":"https://www.wikidata.org/wiki/Q6485978","display_name":"Langevin dynamics","level":2,"score":0.4557307958602905},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4177696704864502},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3738287091255188},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3492136597633362},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2977849543094635},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25418001413345337},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20191848278045654},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14431136846542358}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/23m1581807","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1581807","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/6bcaa99e-b1f6-4ebf-8123-20aae02e15ce","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/6bcaa99e-b1f6-4ebf-8123-20aae02e15ce","pdf_url":"https://pure-oai.bham.ac.uk/ws/files/217860394/NF_ULA_accepted_version.pdf","source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cai , Z , Tang , J , Mukherjee , S , Li , J , Scho\u0308nlieb , C-B & Zhang , X 2024 , ' NF-ULA : Normalizing Flow-Based Unadjusted Langevin Algorithm for Imaging Inverse Problems ' , SIAM Journal on Imaging Sciences , vol. 17 , no. 2 , pp. 820-860 . https://doi.org/10.1137/23M1581807","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/6bcaa99e-b1f6-4ebf-8123-20aae02e15ce","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/6bcaa99e-b1f6-4ebf-8123-20aae02e15ce","pdf_url":"https://pure-oai.bham.ac.uk/ws/files/217860394/NF_ULA_accepted_version.pdf","source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cai , Z , Tang , J , Mukherjee , S , Li , J , Scho\u0308nlieb , C-B & Zhang , X 2024 , ' NF-ULA : Normalizing Flow-Based Unadjusted Langevin Algorithm for Imaging Inverse Problems ' , SIAM Journal on Imaging Sciences , vol. 17 , no. 2 , pp. 820-860 . https://doi.org/10.1137/23M1581807","raw_type":"article"},"sustainable_development_goals":[{"score":0.4399999976158142,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[{"id":"https://openalex.org/G1424764954","display_name":null,"funder_award_id":"EP/T017961/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1755984640","display_name":null,"funder_award_id":"EP/N014588/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2763947431","display_name":"Nonlocal Methods for Arbitrary Data Sources","funder_award_id":"777826","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2861870519","display_name":"Robust and Efficient Analysis Approaches of Remote Imagery for Assessing Population and Forest Health in India","funder_award_id":"EP/T003553/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2978676218","display_name":null,"funder_award_id":"EP/S026045/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3055915260","display_name":null,"funder_award_id":"215733/Z/19/Z","funder_id":"https://openalex.org/F4320307874","funder_display_name":"Wellcome"},{"id":"https://openalex.org/G606079916","display_name":null,"funder_award_id":"12090024","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6096796963","display_name":"Cambridge Mathematics of Information in Healthcare (CMIH)","funder_award_id":"EP/T017961/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6438779272","display_name":null,"funder_award_id":"M-0187","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6579398875","display_name":"EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging","funder_award_id":"EP/N014588/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7243674615","display_name":null,"funder_award_id":"EP/V029428/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7534764778","display_name":"Combining Knowledge And Data Driven Approaches to Inverse Imaging Problems","funder_award_id":"EP/V029428/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G763414266","display_name":"PET++: Improving Localisation, Diagnosis and Quantification in Clinical and Medical PET Imaging with Randomised Optimisation","funder_award_id":"EP/S026045/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7842005466","display_name":null,"funder_award_id":"Horizon 2020","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8252974818","display_name":null,"funder_award_id":"777826 NoMADS","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"},{"id":"https://openalex.org/G89795682","display_name":null,"funder_award_id":"221633/Z/20/Z","funder_id":"https://openalex.org/F4320307874","funder_display_name":"Wellcome"},{"id":"https://openalex.org/G8996992023","display_name":null,"funder_award_id":"M-0187","funder_id":"https://openalex.org/F4320326177","funder_display_name":"Chinesisch-Deutsche Zentrum f\u00fcr Wissenschaftsf\u00f6rderung"}],"funders":[{"id":"https://openalex.org/F4320307874","display_name":"Wellcome","ror":"https://ror.org/029chgv08"},{"id":"https://openalex.org/F4320313467","display_name":"Alan Turing Institute","ror":"https://ror.org/035dkdb55"},{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320326177","display_name":"Chinesisch-Deutsche Zentrum f\u00fcr Wissenschaftsf\u00f6rderung","ror":"https://ror.org/03ny8r668"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4394577179.pdf"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W35586085","https://openalex.org/W170092604","https://openalex.org/W1512208174","https://openalex.org/W1558572410","https://openalex.org/W1946620893","https://openalex.org/W1954227087","https://openalex.org/W1983452151","https://openalex.org/W2006262045","https://openalex.org/W2012910518","https://openalex.org/W2015810892","https://openalex.org/W2021290840","https://openalex.org/W2130416410","https://openalex.org/W2149498546","https://openalex.org/W2222154095","https://openalex.org/W2225156818","https://openalex.org/W2296055064","https://openalex.org/W2508457857","https://openalex.org/W2566924527","https://openalex.org/W2573726823","https://openalex.org/W2574952845","https://openalex.org/W2615566168","https://openalex.org/W2615644062","https://openalex.org/W2730550322","https://openalex.org/W2738743584","https://openalex.org/W2765811365","https://openalex.org/W2952020389","https://openalex.org/W2963399478","https://openalex.org/W2963599479","https://openalex.org/W2978079668","https://openalex.org/W2992005611","https://openalex.org/W3001315751","https://openalex.org/W3011587674","https://openalex.org/W3013170474","https://openalex.org/W3021094251","https://openalex.org/W3021350626","https://openalex.org/W3103335497","https://openalex.org/W3103586216","https://openalex.org/W3104702830","https://openalex.org/W3105425607","https://openalex.org/W3118064383","https://openalex.org/W3126106683","https://openalex.org/W3129907242","https://openalex.org/W3133902371","https://openalex.org/W3167568784","https://openalex.org/W3196943155","https://openalex.org/W3199585919","https://openalex.org/W3206211787","https://openalex.org/W3211066356","https://openalex.org/W4205537960","https://openalex.org/W4229650096","https://openalex.org/W4233762729","https://openalex.org/W4281980169","https://openalex.org/W4289253326","https://openalex.org/W4292198165","https://openalex.org/W4313526215","https://openalex.org/W4366446336"],"related_works":["https://openalex.org/W4286224695","https://openalex.org/W3212252908","https://openalex.org/W2144266858","https://openalex.org/W136660877","https://openalex.org/W2039781258","https://openalex.org/W3110011426","https://openalex.org/W3102244421","https://openalex.org/W3168129901","https://openalex.org/W2331917905","https://openalex.org/W3155039083"],"abstract_inverted_index":{"Bayesian":[0,15,62],"methods":[1,12,187],"for":[2,32,61,101,188],"solving":[3,33],"inverse":[4,34,66,130,191],"problems":[5,35,165],"are":[6],"a":[7,55,81,97,117],"powerful":[8],"alternative":[9],"to":[10,20,42,92,182],"classical":[11],"since":[13],"the":[14,18,22,25,86,94,102,106,128,133,142,148,155],"approach":[16],"offers":[17],"ability":[19],"quantify":[21],"uncertainty":[23],"in":[24,64,161],"solution.":[26],"In":[27,47,68],"recent":[28],"years,":[29],"data-driven":[30],"techniques":[31],"have":[36],"also":[37],"been":[38],"remarkably":[39],"successful,":[40],"due":[41],"their":[43],"superior":[44],"representation":[45],"ability.":[46],"this":[48],"work,":[49],"we":[50,70],"incorporate":[51],"data-based":[52],"models":[53],"into":[54],"class":[56],"of":[57,108,127,147,154],"Langevin-based":[58],"sampling":[59],"algorithms":[60],"inference":[63],"imaging":[65],"problems.":[67,192],"particular,":[69],"introduce":[71],"NF-ULA":[72,150,157,179],"(Normalizing":[73],"Flow-based":[74],"Unadjusted":[75],"Langevin":[76],"algorithm),":[77],"which":[78,122],"involves":[79],"learning":[80],"<i>normalizing":[82],"flow</i>":[83],"(NF)":[84],"as":[85,167],"image":[87,163,168,170],"prior.":[88],"We":[89,136],"use":[90],"NF":[91],"learn":[93],"prior":[95,104],"because":[96],"tractable":[98],"closed-form":[99],"expression":[100],"log":[103],"enables":[105],"differentiation":[107],"it":[109],"using":[110],"<i>autograd":[111],"</i>libraries.":[112],"Our":[113],"algorithm":[114,158],"only":[115],"requires":[116],"normalizing":[118],"flow-based":[119],"generative":[120],"network,":[121],"can":[123],"be":[124],"pre-trained":[125],"independently":[126],"considered":[129],"problem":[131],"and":[132,144,172],"forward":[134],"operator.":[135],"perform":[137,183],"theoretical":[138],"analysis":[139],"by":[140],"investigating":[141],"well-posedness":[143],"non-asymptotic":[145],"convergence":[146],"resulting":[149],"algorithm.":[151],"The":[152],"efficacy":[153],"proposed":[156],"is":[159,180],"demonstrated":[160],"various":[162],"restoration":[164],"such":[166],"deblurring,":[169],"inpainting,":[171],"limited-angle":[173],"X-ray":[174],"computed":[175],"tomography":[176],"(CT)":[177],"reconstruction.":[178],"found":[181],"better":[184],"than":[185],"competing":[186],"severely":[189],"ill-posed":[190]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3}],"updated_date":"2026-07-14T08:27:34.040176","created_date":"2025-10-10T00:00:00"}