{"id":"https://openalex.org/W4413786048","doi":"https://doi.org/10.1109/tci.2025.3603689","title":"Closed-Form Approximation of the Total Variation Proximal Operator","display_name":"Closed-Form Approximation of the Total Variation Proximal Operator","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4413786048","doi":"https://doi.org/10.1109/tci.2025.3603689"},"language":"en","primary_location":{"id":"doi:10.1109/tci.2025.3603689","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tci.2025.3603689","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/A5038419043","display_name":"E. A. Chandler","orcid":"https://orcid.org/0009-0006-2650-1083"},"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":"Edward P. Chandler","raw_affiliation_strings":["Washington University in St. Louis, Saint Louis, MO, USA"],"raw_orcid":"https://orcid.org/0009-0006-2650-1083","affiliations":[{"raw_affiliation_string":"Washington University in St. Louis, Saint Louis, MO, 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, Saint Louis, MO, USA"],"raw_orcid":"https://orcid.org/0000-0003-0654-6760","affiliations":[{"raw_affiliation_string":"Washington University in St. Louis, Saint Louis, MO, USA","institution_ids":["https://openalex.org/I204465549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015244709","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":["Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, USA"],"raw_orcid":"https://orcid.org/0000-0002-4767-1843","affiliations":[{"raw_affiliation_string":"Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, USA","institution_ids":["https://openalex.org/I1343871089"]}]},{"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, Saint Louis, MO, USA"],"raw_orcid":"https://orcid.org/0000-0001-6770-3278","affiliations":[{"raw_affiliation_string":"Washington University in St. Louis, Saint Louis, MO, USA","institution_ids":["https://openalex.org/I204465549"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1146,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.92496571,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"11","issue":null,"first_page":"1217","last_page":"1228"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9904999732971191,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9854999780654907,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/operator","display_name":"Operator (biology)","score":0.46939200162887573},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46320924162864685},{"id":"https://openalex.org/keywords/variation","display_name":"Variation (astronomy)","score":0.45340484380722046},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37599819898605347},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3551899790763855},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34518784284591675},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2122529149055481}],"concepts":[{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46939200162887573},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46320924162864685},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.45340484380722046},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37599819898605347},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3551899790763855},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34518784284591675},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2122529149055481},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"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/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/tci.2025.3603689","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tci.2025.3603689","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":[{"id":"https://metadata.un.org/sdg/10","score":0.47999998927116394,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W1953936588","https://openalex.org/W2019786292","https://openalex.org/W2037679050","https://openalex.org/W2038497950","https://openalex.org/W2046033161","https://openalex.org/W2050023599","https://openalex.org/W2054656164","https://openalex.org/W2067243588","https://openalex.org/W2073750241","https://openalex.org/W2092663520","https://openalex.org/W2094757833","https://openalex.org/W2095106682","https://openalex.org/W2096548851","https://openalex.org/W2097463283","https://openalex.org/W2100556411","https://openalex.org/W2100705753","https://openalex.org/W2101675075","https://openalex.org/W2103559027","https://openalex.org/W2107844156","https://openalex.org/W2107882641","https://openalex.org/W2110505738","https://openalex.org/W2121210949","https://openalex.org/W2122768752","https://openalex.org/W2124768887","https://openalex.org/W2138144773","https://openalex.org/W2142058898","https://openalex.org/W2142224912","https://openalex.org/W2145096794","https://openalex.org/W2152537098","https://openalex.org/W2157827154","https://openalex.org/W2176777789","https://openalex.org/W2405803404","https://openalex.org/W2554591675","https://openalex.org/W2570790349","https://openalex.org/W2590642430","https://openalex.org/W2628535015","https://openalex.org/W2761037628","https://openalex.org/W2775062332","https://openalex.org/W2962912897","https://openalex.org/W2963426457","https://openalex.org/W2963910090","https://openalex.org/W2972301798","https://openalex.org/W2998382672","https://openalex.org/W3012206945","https://openalex.org/W3092479710","https://openalex.org/W3101674152","https://openalex.org/W3155734608","https://openalex.org/W4205830743","https://openalex.org/W4207006019","https://openalex.org/W4210254983","https://openalex.org/W4244393449","https://openalex.org/W4249667877","https://openalex.org/W4250589301","https://openalex.org/W4292363360","https://openalex.org/W4295250184","https://openalex.org/W4304014575","https://openalex.org/W4307468099","https://openalex.org/W4308361231","https://openalex.org/W4391875600"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2386430105","https://openalex.org/W2356521405","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2038534795","https://openalex.org/W2384358604","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819"],"abstract_inverted_index":{"Total":[0],"variation":[1],"(TV)":[2],"is":[3,14,22,43,105],"a":[4,49,97,108,113],"widely":[5],"used":[6],"function":[7],"for":[8,17,52],"regularizing":[9],"imaging":[10],"inverse":[11],"problems":[12,28],"that":[13,92,119],"particularly":[15],"appropriate":[16],"images":[18],"whose":[19],"underlying":[20],"structure":[21],"piecewise":[23],"constant.":[24],"TV":[25,58,65],"regularized":[26],"optimization":[27],"are":[29,41],"typically":[30],"solved":[31],"using":[32],"proximal":[33,54,66,98],"methods,":[34],"but":[35,72],"the":[36,46,53,57,64,93],"way":[37],"in":[38,79],"which":[39],"they":[40],"applied":[42],"constrained":[44],"by":[45,85],"absence":[47],"of":[48,56,63,100,116],"closed-form":[50,61],"expression":[51],"operator":[55,67,99],"function.":[59],"A":[60],"approximation":[62,94],"has":[68],"previously":[69],"been":[70],"proposed,":[71],"its":[73,120,129],"accuracy":[74],"was":[75],"not":[76],"theoretically":[77],"explored":[78],"detail.":[80],"We":[81,132],"address":[82],"this":[83],"gap":[84],"making":[86],"several":[87],"new":[88],"theoretical":[89,136],"contributions,":[90],"proving":[91],"leads":[95],"to":[96,107],"some":[101],"convex":[102],"function,":[103],"it":[104],"equivalent":[106],"gradient":[109],"descent":[110],"step":[111],"on":[112,138],"smoothed":[114],"version":[115],"TV,":[117],"and":[118,126,141],"error":[121],"can":[122],"be":[123],"fully":[124],"characterized":[125],"controlled":[127],"with":[128],"scaling":[130],"parameter.":[131],"experimentally":[133],"validate":[134],"our":[135],"results":[137],"image":[139,146],"denoising":[140],"sparse-view":[142],"computed":[143],"tomography":[144],"(CT)":[145],"reconstruction.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
