{"id":"https://openalex.org/W2755366633","doi":"https://doi.org/10.1137/15m1049051","title":"A Study on Regularization for Discrete Inverse Problems with Model-Dependent Noise","display_name":"A Study on Regularization for Discrete Inverse Problems with Model-Dependent Noise","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2755366633","doi":"https://doi.org/10.1137/15m1049051","mag":"2755366633"},"language":"en","primary_location":{"id":"doi:10.1137/15m1049051","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1049051","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5019072618","display_name":"Federico Benvenuto","orcid":"https://orcid.org/0000-0002-4776-0256"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Federico Benvenuto","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019072618"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2083,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.58470472,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"55","issue":"5","first_page":"2187","last_page":"2203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9994000196456909,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9994000196456909,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9993000030517578,"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/T12386","display_name":"Advanced X-ray and CT Imaging","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.7704595327377319},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7398822903633118},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6960553526878357},{"id":"https://openalex.org/keywords/regularization-perspectives-on-support-vector-machines","display_name":"Regularization perspectives on support vector machines","score":0.6056461930274963},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5844059586524963},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5752650499343872},{"id":"https://openalex.org/keywords/deconvolution","display_name":"Deconvolution","score":0.538786768913269},{"id":"https://openalex.org/keywords/backus\u2013gilbert-method","display_name":"Backus\u2013Gilbert method","score":0.5290704369544983},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4588618278503418},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.4539785087108612},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4439641237258911},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.41885823011398315},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.4166812300682068},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38442230224609375},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.26766830682754517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17666566371917725},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12775936722755432},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07719758152961731}],"concepts":[{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.7704595327377319},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7398822903633118},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6960553526878357},{"id":"https://openalex.org/C141718189","wikidata":"https://www.wikidata.org/wiki/Q7309628","display_name":"Regularization perspectives on support vector machines","level":4,"score":0.6056461930274963},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5844059586524963},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5752650499343872},{"id":"https://openalex.org/C174576160","wikidata":"https://www.wikidata.org/wiki/Q1183700","display_name":"Deconvolution","level":2,"score":0.538786768913269},{"id":"https://openalex.org/C27872270","wikidata":"https://www.wikidata.org/wiki/Q4839810","display_name":"Backus\u2013Gilbert method","level":5,"score":0.5290704369544983},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4588618278503418},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4539785087108612},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4439641237258911},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.41885823011398315},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.4166812300682068},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38442230224609375},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26766830682754517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17666566371917725},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12775936722755432},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07719758152961731},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/15m1049051","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1049051","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:iris.unige.it:11567/883210","is_oa":false,"landing_page_url":"http://hdl.handle.net/11567/883210","pdf_url":null,"source":{"id":"https://openalex.org/S4377196291","display_name":"CINECA IRIS Institutial Research Information System (University of Genoa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I83816512","host_organization_name":"University of Genoa","host_organization_lineage":["https://openalex.org/I83816512"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2393757743","display_name":null,"funder_award_id":"246016","funder_id":"https://openalex.org/F4320333065","funder_display_name":"Seventh Framework Programme"}],"funders":[{"id":"https://openalex.org/F4320320885","display_name":"European Research Consortium for Informatics and Mathematics","ror":"https://ror.org/055zrhj18"},{"id":"https://openalex.org/F4320333065","display_name":"Seventh Framework Programme","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1974231626","https://openalex.org/W1985434901","https://openalex.org/W1996589899","https://openalex.org/W1998066475","https://openalex.org/W2005836623","https://openalex.org/W2011161612","https://openalex.org/W2014963263","https://openalex.org/W2019739324","https://openalex.org/W2024872356","https://openalex.org/W2032013306","https://openalex.org/W2032433149","https://openalex.org/W2041115669","https://openalex.org/W2049475467","https://openalex.org/W2049633694","https://openalex.org/W2069629287","https://openalex.org/W2093241474","https://openalex.org/W2110264793","https://openalex.org/W2116147316","https://openalex.org/W2139252659","https://openalex.org/W2141390467","https://openalex.org/W2259897490","https://openalex.org/W4230320149","https://openalex.org/W4253554605"],"related_works":["https://openalex.org/W2366023887","https://openalex.org/W2805921369","https://openalex.org/W2118199608","https://openalex.org/W2394283419","https://openalex.org/W2069968238","https://openalex.org/W2807240017","https://openalex.org/W4244092552","https://openalex.org/W2030398504","https://openalex.org/W2355455483","https://openalex.org/W4247967441"],"abstract_inverted_index":{"In":[0,43],"this":[1,176],"paper":[2],"we":[3,101,136,154],"consider":[4],"discrete":[5,151],"inverse":[6,36],"problems":[7],"for":[8,27,108,140,162,231],"which":[9,31],"noise":[10,90,133],"becomes":[11],"negligible":[12],"compared":[13],"to":[14,67,74,143,191],"data":[15,56,164],"with":[16,39,113,209],"increasing":[17,210],"model":[18,71,211],"norm.":[19],"We":[20,92,178],"introduce":[21],"two":[22,98],"novel":[23],"definitions":[24,99],"of":[25,34,88,131,185,197,238],"regularization":[26,129,173,220],"characterizing":[28],"inversion":[29],"methods":[30,142,174,207,233],"provide":[32],"approximations":[33],"ill-conditioned":[35],"operators":[37],"consistent":[38],"such":[40,125,141],"noisy":[41],"data.":[42],"particular,":[44],"these":[45,97],"definitions,":[46],"respectively,":[47],"require":[48],"that":[49,103,124,156],"the":[50,60,70,85,89,94,132,157,166,183,195,200,204,216,226,236],"reconstruction":[51,62],"error":[52,63],"computed":[53],"from":[54],"normalized":[55],"($p$-asymptotic":[57],"regularization)":[58,65],"and":[59,100,146,153,165,188,218,228],"relative":[61],"($p$-relative":[64],"go":[66],"zero":[68],"as":[69,120,213],"norm":[72,212],"tends":[73],"infinity,":[75],"$0":[76],"\\leq":[77],"p":[78],"<":[79],"1$":[80],"being":[81],"a":[82,121,150],"parameter":[83],"controlling":[84],"increase":[86],"rate":[87],"level.":[91],"investigate":[93],"relationship":[95],"between":[96],"prove":[102,155],"they":[104],"are":[105,172],"all":[106],"equivalent":[107],"positively":[109],"homogeneous":[110],"iterative":[111,126],"algorithms":[112,127],"suitable":[114],"stopping":[115],"rules.":[116],"This":[117],"result":[118],"has":[119],"crucial":[122],"consequence":[123],"realize":[128],"independently":[130],"model.":[134],"Then":[135],"give":[137],"sufficient":[138],"conditions":[139],"be":[144,235],"$p$-asymptotic":[145,217,227],"$p$-relative":[147,219,229],"regularizations":[148,230],"in":[149,175,182,194],"setting":[152],"classical":[158],"expectation":[159],"maximization":[160],"algorithm":[161],"Poisson":[163],"Landweber":[167],"algorithm,":[168],"if":[169],"suitably":[170],"stopped,":[171],"sense.":[177],"perform":[179],"numerical":[180],"simulations":[181],"case":[184],"image":[186],"deconvolution":[187],"computerized":[189],"tomography":[190],"show":[192],"that,":[193],"presence":[196],"model-dependent":[198],"noise,":[199],"reconstructions":[201],"provided":[202],"by":[203,215],"above":[205],"mentioned":[206],"improve":[208],"required":[214],"properties.":[221],"More":[222],"extensive":[223],"studies":[224],"on":[225],"Tikhonov-type":[232],"will":[234],"object":[237],"future":[239],"work.":[240]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
