{"id":"https://openalex.org/W4376255255","doi":"https://doi.org/10.1137/22m1506778","title":"A Fast Data-Driven Iteratively Regularized Method with Convex Penalty for Solving Ill-Posed Problems","display_name":"A Fast Data-Driven Iteratively Regularized Method with Convex Penalty for Solving Ill-Posed Problems","publication_year":2023,"publication_date":"2023-05-12","ids":{"openalex":"https://openalex.org/W4376255255","doi":"https://doi.org/10.1137/22m1506778"},"language":"en","primary_location":{"id":"doi:10.1137/22m1506778","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1506778","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078888083","display_name":"Guangyu Gao","orcid":"https://orcid.org/0000-0002-8368-4748"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210161462","display_name":"Heilongjiang Institute of Technology","ror":"https://ror.org/05x0m9n95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210161462"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangyu Gao","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, People\u2019s Republic of China","Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, People's Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-8368-4748","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, People\u2019s Republic of China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, People's Republic of China","institution_ids":["https://openalex.org/I4210161462"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067968002","display_name":"Bo Han","orcid":"https://orcid.org/0000-0003-0968-1474"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210161462","display_name":"Heilongjiang Institute of Technology","ror":"https://ror.org/05x0m9n95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210161462"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Han","raw_affiliation_strings":["Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, People\u2019s Republic of China","Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, People\u2019s Republic of China","institution_ids":["https://openalex.org/I204983213"]},{"raw_affiliation_string":"Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, People's Republic of China","institution_ids":["https://openalex.org/I4210161462"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063661942","display_name":"Zhenwu Fu","orcid":"https://orcid.org/0000-0002-2340-1988"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]},{"id":"https://openalex.org/I4210161462","display_name":"Heilongjiang Institute of Technology","ror":"https://ror.org/05x0m9n95","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210161462"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenwu Fu","raw_affiliation_strings":["Corresponding Author. Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, People\u2019s Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-2340-1988","affiliations":[{"raw_affiliation_string":"Corresponding Author. Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4210161462","https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059817110","display_name":"Shanshan Tong","orcid":"https://orcid.org/0000-0002-4980-6844"},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shanshan Tong","raw_affiliation_strings":["Corresponding Author. School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an, Shaanxi Province, 710119, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Corresponding Author. School of Mathematics and Statistics, Shaanxi Normal University, Xi\u2019an, Shaanxi Province, 710119, People\u2019s Republic of China","institution_ids":["https://openalex.org/I88830068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0721,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.95287052,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"16","issue":"2","first_page":"640","last_page":"670"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"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":0.9998999834060669,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9984999895095825,"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"}},{"id":"https://openalex.org/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9932000041007996,"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/regularization","display_name":"Regularization (linguistics)","score":0.7380045056343079},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5790647864341736},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5623910427093506},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.531100332736969},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5221957564353943},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.49634796380996704},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.45171406865119934},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.41827547550201416},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4125971794128418},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4117972254753113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38967421650886536},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.376990407705307},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11464059352874756},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09978815913200378}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7380045056343079},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5790647864341736},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5623910427093506},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.531100332736969},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5221957564353943},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.49634796380996704},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.45171406865119934},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.41827547550201416},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4125971794128418},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4117972254753113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38967421650886536},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.376990407705307},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11464059352874756},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09978815913200378},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1506778","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1506778","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1429349823","display_name":null,"funder_award_id":"11901373","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3601164423","display_name":null,"funder_award_id":"2022M710969","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G4534103426","display_name":null,"funder_award_id":"12101159","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5138089300","display_name":null,"funder_award_id":"2022M712007","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G8962309242","display_name":null,"funder_award_id":"12271129","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1489458628","https://openalex.org/W1564864701","https://openalex.org/W1570089119","https://openalex.org/W1966214863","https://openalex.org/W1990022370","https://openalex.org/W2002178240","https://openalex.org/W2024569854","https://openalex.org/W2030540937","https://openalex.org/W2034004195","https://openalex.org/W2036254006","https://openalex.org/W2038948856","https://openalex.org/W2058204667","https://openalex.org/W2065324458","https://openalex.org/W2080888649","https://openalex.org/W2103559027","https://openalex.org/W2112796928","https://openalex.org/W2114605231","https://openalex.org/W2125260711","https://openalex.org/W2155346693","https://openalex.org/W2278660525","https://openalex.org/W2673237422","https://openalex.org/W2750954062","https://openalex.org/W2783745237","https://openalex.org/W2915557623","https://openalex.org/W2952020389","https://openalex.org/W2964266347","https://openalex.org/W2965795320","https://openalex.org/W2974546290","https://openalex.org/W2976576775","https://openalex.org/W3013097980","https://openalex.org/W3084093490","https://openalex.org/W3084344204","https://openalex.org/W3102011284","https://openalex.org/W3102252265","https://openalex.org/W3158913794","https://openalex.org/W3197804729","https://openalex.org/W3214405163","https://openalex.org/W4244243830","https://openalex.org/W4285801961"],"related_works":["https://openalex.org/W1965977581","https://openalex.org/W2061980133","https://openalex.org/W1559374272","https://openalex.org/W45494237","https://openalex.org/W1993570333","https://openalex.org/W2387685679","https://openalex.org/W4298004047","https://openalex.org/W2077506191","https://openalex.org/W3134728064","https://openalex.org/W2050855072"],"abstract_inverted_index":{".We":[0],"propose":[1],"a":[2,44,48],"new":[3],"iterative":[4,15,23,94,115],"regularization":[5,24,116],"method":[6,20,89,99,110],"for":[7,114],"solving":[8],"inverse":[9],"problems":[10,55],"in":[11,59],"Hilbert":[12],"spaces.":[13],"The":[14],"process":[16],"of":[17,36,43,69,108,131],"the":[18,34,41,66,80,93,98,109,126],"proposed":[19],"combines":[21],"classical":[22],"format":[25],"and":[26,57,128],"Data-Driven":[27,29],"approach.":[28],"technique":[30],"is":[31,90],"based":[32,85],"on":[33,86],"idea":[35],"deep":[37],"learning":[38],"to":[39,53,64,75,92,124],"estimate":[40],"interior":[42],"black":[45],"box":[46,135],"through":[47],"training":[49],"set,":[50],"so":[51],"as":[52],"solve":[54],"better":[56],"faster":[58],"some":[60],"cases.":[61],"In":[62],"order":[63],"capture":[65],"special":[67],"feature":[68],"solutions,":[70],"convex":[71],"functions":[72],"are":[73,122],"utilized":[74],"be":[76],"penalty":[77],"terms.":[78],"Algorithmically,":[79],"two-point":[81],"gradient":[82],"acceleration":[83,102,129],"strategy":[84],"homotopy":[87],"perturbation":[88],"applied":[91],"scheme,":[95],"which":[96],"makes":[97],"have":[100],"satisfactory":[101],"effect.":[103],"We":[104],"provide":[105],"convergence":[106],"analysis":[107],"under":[111],"standard":[112],"assumptions":[113],"methods.":[117],"Finally,":[118],"several":[119],"numerical":[120],"experiments":[121],"presented":[123],"show":[125],"effectiveness":[127],"effect":[130],"our":[132],"method.Keywordsiterative":[133],"regularizationdata-drivenblack":[134],"strategyconvex":[136],"penaltytwo-point":[137],"gradienthomotopy":[138],"perturbationMSC":[139],"codes65D1565J2065N2165R30":[140]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
