{"id":"https://openalex.org/W2902695846","doi":"https://doi.org/10.1007/s10851-019-00911-1","title":"Big in Japan: Regularizing Networks for Solving Inverse Problems","display_name":"Big in Japan: Regularizing Networks for Solving Inverse Problems","publication_year":2019,"publication_date":"2019-10-03","ids":{"openalex":"https://openalex.org/W2902695846","doi":"https://doi.org/10.1007/s10851-019-00911-1","mag":"2902695846","pmid":"https://pubmed.ncbi.nlm.nih.gov/32308256"},"language":"en","primary_location":{"id":"doi:10.1007/s10851-019-00911-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10851-019-00911-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10851-019-00911-1.pdf","source":{"id":"https://openalex.org/S66221708","display_name":"Journal of Mathematical Imaging and Vision","issn_l":"0924-9907","issn":["0924-9907","1573-7683"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Imaging and Vision","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10851-019-00911-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000629409","display_name":"Johannes Schwab","orcid":"https://orcid.org/0000-0002-7144-3031"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Johannes Schwab","raw_affiliation_strings":["Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020 Innsbruck, Austria","Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020, Innsbruck, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020 Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]},{"raw_affiliation_string":"Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014875283","display_name":"Stephan Antholzer","orcid":"https://orcid.org/0000-0002-4923-8146"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Stephan Antholzer","raw_affiliation_strings":["Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020 Innsbruck, Austria","Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020, Innsbruck, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020 Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]},{"raw_affiliation_string":"Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026767648","display_name":"Markus Haltmeier","orcid":"https://orcid.org/0000-0001-5715-0331"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Markus Haltmeier","raw_affiliation_strings":["Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020 Innsbruck, Austria","Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020, Innsbruck, Austria"],"raw_orcid":"https://orcid.org/0000-0001-5715-0331","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020 Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]},{"raw_affiliation_string":"Department of Mathematics, University of Innsbruck, Technikerstrasse 13, 6020, Innsbruck, Austria","institution_ids":["https://openalex.org/I190249584"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026767648"],"corresponding_institution_ids":["https://openalex.org/I190249584"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2780},"fwci":1.8677,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.83760795,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"62","issue":"3","first_page":"445","last_page":"455"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9986000061035156,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9986000061035156,"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":0.9948999881744385,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6550794243812561},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5030996203422546},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42343148589134216},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3577656149864197}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6550794243812561},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5030996203422546},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42343148589134216},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3577656149864197}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10851-019-00911-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10851-019-00911-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10851-019-00911-1.pdf","source":{"id":"https://openalex.org/S66221708","display_name":"Journal of Mathematical Imaging and Vision","issn_l":"0924-9907","issn":["0924-9907","1573-7683"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Imaging and Vision","raw_type":"journal-article"},{"id":"pmid:32308256","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/32308256","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of mathematical imaging and vision","raw_type":null},{"id":"pmh:oai:arXiv.org:1812.00965","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1812.00965","pdf_url":"https://arxiv.org/pdf/1812.00965","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"},{"id":"pmh:oai:pubmedcentral.nih.gov:7144407","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7144407","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"J Math Imaging Vis","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s10851-019-00911-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10851-019-00911-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10851-019-00911-1.pdf","source":{"id":"https://openalex.org/S66221708","display_name":"Journal of Mathematical Imaging and Vision","issn_l":"0924-9907","issn":["0924-9907","1573-7683"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Imaging and Vision","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1600148956","display_name":null,"funder_award_id":"P 30747-N32","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4806285493","display_name":null,"funder_award_id":"P 30747","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7644810043","display_name":null,"funder_award_id":"30747-N32","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2902695846.pdf","grobid_xml":"https://content.openalex.org/works/W2902695846.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1509296830","https://openalex.org/W1544177383","https://openalex.org/W1570089119","https://openalex.org/W1901129140","https://openalex.org/W2056021135","https://openalex.org/W2062671282","https://openalex.org/W2083642275","https://openalex.org/W2607406448","https://openalex.org/W2621182918","https://openalex.org/W2746434776","https://openalex.org/W2751669091","https://openalex.org/W2765685574","https://openalex.org/W2770205545","https://openalex.org/W2777802649","https://openalex.org/W2789792640","https://openalex.org/W2808122338","https://openalex.org/W2891385369","https://openalex.org/W2901093491","https://openalex.org/W2950936580","https://openalex.org/W2951579423","https://openalex.org/W2962850795","https://openalex.org/W2963392702","https://openalex.org/W2964225427","https://openalex.org/W3002289736","https://openalex.org/W3101765447","https://openalex.org/W3103372211","https://openalex.org/W3105109286","https://openalex.org/W3122499440","https://openalex.org/W4292399988","https://openalex.org/W6600291067","https://openalex.org/W6600364069","https://openalex.org/W6871517530"],"related_works":["https://openalex.org/W2961085424","https://openalex.org/W4306674287","https://openalex.org/W3046775127","https://openalex.org/W3107602296","https://openalex.org/W3170094116","https://openalex.org/W4386462264","https://openalex.org/W4364306694","https://openalex.org/W4312192474","https://openalex.org/W4283697347","https://openalex.org/W4210805261"],"abstract_inverted_index":{"Abstract":[0],"Deep":[1],"learning":[2],"and":[3,14,39,75,148],"(deep)":[4],"neural":[5,29,46],"networks":[6,30,47,113],"are":[7,170],"emerging":[8],"tools":[9],"to":[10,89],"address":[11],"inverse":[12,26,121],"problems":[13,27],"image":[15],"reconstruction":[16],"tasks.":[17],"Despite":[18],"outstanding":[19],"performance,":[20],"the":[21,50,76,91,105,136,159,182,191],"mathematical":[22],"analysis":[23],"for":[24,119,152,172],"solving":[25,120],"by":[28,104],"is":[31,71,87],"mostly":[32],"missing.":[33],"In":[34],"this":[35],"paper,":[36],"we":[37,124],"introduce":[38],"rigorously":[40],"analyze":[41],"families":[42],"of":[43,49,135],"deep":[44],"regularizing":[45,112],"(RegNets)":[48],"form":[51],"$$\\mathbf":[52,66,78],"{B}_\\alpha":[53,60,67,83,98],"+":[54],"\\mathbf":[55,59,82,97],"{N}_{\\theta":[56,79],"(\\alpha":[57,80],")}":[58,81],"$$":[61,68,84,99],"<mml:math":[62,69,85,100],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>\u03b1</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>\u03b8</mml:mi><mml:mo>(</mml:mo><mml:mi>\u03b1</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub><mml:msub><mml:mi>B</mml:mi><mml:mi>\u03b1</mml:mi></mml:msub></mml:mrow></mml:math>":[63],",":[64],"where":[65],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>B</mml:mi><mml:mi>\u03b1</mml:mi></mml:msub></mml:math>":[70],"a":[72,115,132,173],"classical":[73,106,186],"regularization":[74,117,154,187],"network":[77,164],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:msub><mml:mi>N</mml:mi><mml:mrow><mml:mi>\u03b8</mml:mi><mml:mo>(</mml:mo><mml:mi>\u03b1</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub><mml:msub><mml:mi>B</mml:mi><mml:mi>\u03b1</mml:mi></mml:msub></mml:mrow></mml:math>":[86],"trained":[88],"recover":[90,145],"missing":[92],"part":[93],"$${\\text":[94],"{Id}}_X":[95],"-":[96],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:msub><mml:mtext>Id</mml:mtext><mml:mi>X</mml:mi></mml:msub><mml:mo>-</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mi>\u03b1</mml:mi></mml:msub></mml:mrow></mml:math>":[101],"not":[102],"found":[103],"regularization.":[107],"We":[108,140],"show":[109],"that":[110,142,181],"these":[111],"yield":[114],"convergent":[116],"method":[118],"problems.":[122],"Additionally,":[123],"derive":[125],"convergence":[126,147,149],"rates":[127,150],"(quantitative":[128],"error":[129],"estimates)":[130],"assuming":[131],"sufficient":[133],"decay":[134],"associated":[137],"distance":[138],"function.":[139],"demonstrate":[141,180],"our":[143],"results":[144,151,169],"existing":[146],"filter-based":[153],"methods":[155],"as":[156,158,165,188,190],"well":[157,189],"recently":[160],"introduced":[161],"null":[162,192],"space":[163,193],"special":[166],"cases.":[167],"Numerical":[168],"presented":[171],"tomographic":[174],"sparse":[175],"data":[176],"problem,":[177],"which":[178],"clearly":[179],"proposed":[183],"RegNets":[184],"improve":[185],"network.":[194]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}