{"id":"https://openalex.org/W7155382959","doi":"https://doi.org/10.48550/arxiv.2604.20360","title":"On the convergence of an adaptive denoiser driven iterative regularization with early stopping","display_name":"On the convergence of an adaptive denoiser driven iterative regularization with early stopping","publication_year":2026,"publication_date":"2026-04-22","ids":{"openalex":"https://openalex.org/W7155382959","doi":"https://doi.org/10.48550/arxiv.2604.20360"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.20360","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.20360","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.20360","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020189950","display_name":"Harshit Bajpai","orcid":"https://orcid.org/0000-0002-6811-9361"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bajpai, Harshit","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057291385","display_name":"Ankik Kumar Giri","orcid":"https://orcid.org/0000-0002-6339-4647"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Giri, Ankik Kumar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022550099","display_name":"Tim Jahn","orcid":"https://orcid.org/0000-0002-7633-8265"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jahn, Tim","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134364003","display_name":"Abhinav Jha","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jha, Abhinav","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.43130001425743103,"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":0.43130001425743103,"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/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.22179999947547913,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.06530000269412994,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/deblurring","display_name":"Deblurring","score":0.84579998254776},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.810699999332428},{"id":"https://openalex.org/keywords/early-stopping","display_name":"Early stopping","score":0.6137999892234802},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.611299991607666},{"id":"https://openalex.org/keywords/regularization-perspectives-on-support-vector-machines","display_name":"Regularization perspectives on support vector machines","score":0.45570001006126404},{"id":"https://openalex.org/keywords/backus\u2013gilbert-method","display_name":"Backus\u2013Gilbert method","score":0.4194999933242798},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.3903999924659729},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.37310001254081726}],"concepts":[{"id":"https://openalex.org/C2777693668","wikidata":"https://www.wikidata.org/wiki/Q25053743","display_name":"Deblurring","level":5,"score":0.84579998254776},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.810699999332428},{"id":"https://openalex.org/C5465570","wikidata":"https://www.wikidata.org/wiki/Q5326898","display_name":"Early stopping","level":3,"score":0.6137999892234802},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.611299991607666},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4828000068664551},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4666999876499176},{"id":"https://openalex.org/C141718189","wikidata":"https://www.wikidata.org/wiki/Q7309628","display_name":"Regularization perspectives on support vector machines","level":4,"score":0.45570001006126404},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44830000400543213},{"id":"https://openalex.org/C27872270","wikidata":"https://www.wikidata.org/wiki/Q4839810","display_name":"Backus\u2013Gilbert method","level":5,"score":0.4194999933242798},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4092999994754791},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.3903999924659729},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.3573000133037567},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.35589998960494995},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.35409998893737793},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3125999867916107},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C79248915","wikidata":"https://www.wikidata.org/wiki/Q17086776","display_name":"Proximal gradient methods for learning","level":5,"score":0.2879999876022339},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2865999937057495},{"id":"https://openalex.org/C2983327147","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Image denoising","level":3,"score":0.2847999930381775},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C2983961125","wikidata":"https://www.wikidata.org/wiki/Q1288707","display_name":"Stopping rule","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C2986577269","wikidata":"https://www.wikidata.org/wiki/Q11306265","display_name":"Random noise","level":2,"score":0.2671000063419342}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.20360","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.20360","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.20360","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.20360","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Solving":[0],"inverse":[1],"problems":[2],"requires":[3],"appropriate":[4],"regularization":[5,21,37,60,70,121,145],"techniques":[6],"to":[7,63,91],"ensure":[8,92],"well-posedness":[9],"and":[10,33,98,119,162,174,190],"stability.":[11],"In":[12,42],"recent":[13],"years,":[14],"denoiser-driven":[15,58],"methods":[16],"have":[17],"emerged":[18],"as":[19,64],"effective":[20],"strategies,":[22],"achieving":[23],"state-of-the-art":[24],"performance":[25,151],"in":[26,123,185],"various":[27],"imaging":[28],"applications.":[29],"However,":[30],"their":[31],"stability":[32,93],"convergence":[34],"within":[35,141],"iterative":[36,59],"frameworks":[38],"remain":[39],"largely":[40],"unexplored.":[41],"this":[43,133],"work,":[44],"we":[45,109,148],"extend":[46],"the":[47,112,124,128,135,142,150,153,180,183],"framework":[48,143],"of":[49,130,139,144,152,182,187],"Regularization":[50],"by":[51,54,102],"Denoising":[52],"(RED)":[53],"introducing":[55],"a":[56,68,117],"novel":[57],"scheme,":[61],"referred":[62],"\\texttt{DDIR},":[65],"that":[66,111],"incorporates":[67],"new":[69],"functional":[71],"based":[72],"on":[73,159],"averaged":[74],"denoisers.":[75],"The":[76,177],"proposed":[77,154],"approach":[78],"employs":[79],"an":[80,86],"adaptive":[81],"step-size":[82],"strategy":[83],"together":[84],"with":[85],"\\emph{a":[87],"posteriori}":[88],"stopping":[89],"rule":[90],"while":[94],"alleviating":[95],"oscillatory":[96],"behavior":[97],"semi-convergence":[99],"effects":[100],"induced":[101],"noise.":[103],"As":[104],"our":[105,131],"main":[106],"theoretical":[107],"contribution,":[108],"prove":[110],"resulting":[113],"reconstruction":[114,188],"method":[115,155,184],"constitutes":[116],"stable":[118],"convergent":[120],"scheme":[122],"classical":[125],"sense.":[126],"To":[127],"best":[129],"knowledge,":[132],"provides":[134],"first":[136],"rigorous":[137],"justification":[138],"\\texttt{DDIR}":[140],"theory.":[146],"Finally,":[147],"demonstrate":[149],"through":[156],"numerical":[157],"experiments":[158],"image":[160],"deblurring":[161],"phase":[163],"retrieval":[164],"Computed":[165],"Tomography":[166],"(CT)":[167],"using":[168],"three":[169],"denoisers,":[170],"namely":[171],"median,":[172],"TNRD,":[173],"TV":[175],"proximal.":[176],"results":[178],"highlight":[179],"effectiveness":[181],"terms":[186],"accuracy":[189],"computational":[191],"efficiency.":[192]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-24T00:00:00"}
