{"id":"https://openalex.org/W3100672508","doi":"https://doi.org/10.1137/15m1022252","title":"Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise","display_name":"Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W3100672508","doi":"https://doi.org/10.1137/15m1022252","mag":"3100672508"},"language":"en","primary_location":{"id":"doi:10.1137/15m1022252","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1022252","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1506.02126","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Claudia K\u00f6nig","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Claudia K\u00f6nig","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Frank Werner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Frank Werner","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Thorsten Hohage","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thorsten Hohage","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.1095,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.96716807,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"54","issue":"1","first_page":"341","last_page":"360"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.991100013256073,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.991100013256073,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.002199999988079071,"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"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.0008999999845400453,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.7558000087738037},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5509999990463257},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5177000164985657},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.5120999813079834},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5034000277519226},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5026000142097473},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.47780001163482666},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.44350001215934753},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.40549999475479126}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8330000042915344},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.7558000087738037},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5529000163078308},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5509999990463257},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5177000164985657},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.5120999813079834},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5034000277519226},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5026000142097473},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4797999858856201},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.47780001163482666},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.44350001215934753},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.40549999475479126},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.39879998564720154},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3714999854564667},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.34689998626708984},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.3449999988079071},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.33640000224113464},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.32109999656677246},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.31310001015663147},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.29980000853538513},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.29190000891685486},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.28529998660087585},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C27872270","wikidata":"https://www.wikidata.org/wiki/Q4839810","display_name":"Backus\u2013Gilbert method","level":5,"score":0.26809999346733093},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.2542000114917755}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/15m1022252","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1022252","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:arXiv.org:1506.02126","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.02126","pdf_url":"https://arxiv.org/pdf/1506.02126","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1506.02126","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.02126","pdf_url":"https://arxiv.org/pdf/1506.02126","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1913729665","https://openalex.org/W1979072167","https://openalex.org/W1997446124","https://openalex.org/W2002178240","https://openalex.org/W2002384352","https://openalex.org/W2004675040","https://openalex.org/W2009503811","https://openalex.org/W2023206259","https://openalex.org/W2033603511","https://openalex.org/W2053972348","https://openalex.org/W2064556267","https://openalex.org/W2070030655","https://openalex.org/W2072090418","https://openalex.org/W2075120723","https://openalex.org/W2076264645","https://openalex.org/W2110611827","https://openalex.org/W2111841405","https://openalex.org/W2140028288","https://openalex.org/W2155055620","https://openalex.org/W2164893552"],"related_works":[],"abstract_inverted_index":{"This":[0,58],"paper":[1],"is":[2,20,35],"concerned":[3],"with":[4,9,41,50],"exponentially":[5,95,130],"ill-posed":[6,96,131],"operator":[7],"equations":[8],"additive":[10],"impulsive":[11],"noise":[12,19,117],"on":[13,22,91],"the":[14,18,27,67,79,92,110,113,123,155],"right-hand":[15],"side,":[16],"i.e.,":[17,94],"large":[21,116],"a":[23],"small":[24,30],"part":[25],"of":[26,69,81,107,112,115,136,142],"domain":[28],"and":[29,64,145,160],"or":[31],"zero":[32],"outside.":[33],"It":[34,99],"well":[36],"known":[37],"that":[38,102],"Tikhonov":[39,48],"regularization":[40,49],"an":[42,51,161],"$L^1$":[43],"data":[44],"fidelity":[45,53],"term":[46,54],"outperforms":[47],"$L^2$":[52],"in":[55,109,164],"this":[56,76],"case.":[57],"effect":[59],"has":[60],"recently":[61],"been":[62],"explained":[63],"quantified":[65],"for":[66,129,148],"case":[68,80],"finitely":[70],"smoothing":[71,83],"operators.":[72],"Here":[73],"we":[74],"extend":[75],"analysis":[77,138],"to":[78],"infinitely":[82],"forward":[84],"operators":[85],"under":[86],"standard":[87],"Sobolev":[88],"smoothness":[89],"assumptions":[90],"solution,":[93],"inverse":[97,162],"problems.":[98,132],"turns":[100],"out":[101],"high":[103],"order":[104],"polynomial":[105],"rates":[106,127],"convergence":[108,126],"size":[111],"support":[114],"can":[118],"be":[119],"achieved":[120],"rather":[121],"than":[122],"poor":[124],"logarithmic":[125],"typical":[128],"The":[133],"main":[134],"tools":[135],"our":[137],"are":[139],"Banach":[140],"spaces":[141],"analytic":[143],"functions":[144],"interpolation-type":[146],"inequalities":[147],"such":[149],"spaces.":[150],"We":[151],"discuss":[152],"two":[153],"examples,":[154],"(periodic)":[156],"backward":[157],"heat":[158],"equation":[159],"problem":[163],"gradiometry.":[165]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2020-11-23T00:00:00"}
