{"id":"https://openalex.org/W3129918957","doi":"https://doi.org/10.1587/transfun.2021eap1004","title":"Convex and Differentiable Formulation for Inverse Problems in Hilbert Spaces with Nonlinear Clipping Effects","display_name":"Convex and Differentiable Formulation for Inverse Problems in Hilbert Spaces with Nonlinear Clipping Effects","publication_year":2021,"publication_date":"2021-02-24","ids":{"openalex":"https://openalex.org/W3129918957","doi":"https://doi.org/10.1587/transfun.2021eap1004","mag":"3129918957"},"language":"en","primary_location":{"id":"doi:10.1587/transfun.2021eap1004","is_oa":false,"landing_page_url":"https://doi.org/10.1587/transfun.2021eap1004","pdf_url":null,"source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer 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/A5064535049","display_name":"Natsuki Ueno","orcid":"https://orcid.org/0000-0002-5906-563X"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Natsuki UENO","raw_affiliation_strings":["The University of Tokyo"],"affiliations":[{"raw_affiliation_string":"The University of Tokyo","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026010014","display_name":"Shoichi Koyama","orcid":"https://orcid.org/0000-0003-2283-0884"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Shoichi KOYAMA","raw_affiliation_strings":["The University of Tokyo"],"affiliations":[{"raw_affiliation_string":"The University of Tokyo","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003814223","display_name":"Hiroshi Saruwatari","orcid":"https://orcid.org/0000-0003-0876-5617"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hiroshi SARUWATARI","raw_affiliation_strings":["The University of Tokyo"],"affiliations":[{"raw_affiliation_string":"The University of Tokyo","institution_ids":["https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064535049"],"corresponding_institution_ids":["https://openalex.org/I74801974"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11493823,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"E104.A","issue":"9","first_page":"1293","last_page":"1303"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9991000294685364,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7118219137191772},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5965472459793091},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5648097991943359},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5521633625030518},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5007064342498779},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4710939824581146},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.47029826045036316},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4582918882369995},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.45330485701560974},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4416690170764923},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.43548229336738586},{"id":"https://openalex.org/keywords/clipping","display_name":"Clipping (morphology)","score":0.4283975660800934},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4136619567871094},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32572850584983826},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.22124814987182617}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7118219137191772},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5965472459793091},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5648097991943359},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5521633625030518},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5007064342498779},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4710939824581146},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.47029826045036316},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4582918882369995},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.45330485701560974},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4416690170764923},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.43548229336738586},{"id":"https://openalex.org/C2776848632","wikidata":"https://www.wikidata.org/wiki/Q853463","display_name":"Clipping (morphology)","level":2,"score":0.4283975660800934},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4136619567871094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32572850584983826},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.22124814987182617},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1587/transfun.2021eap1004","is_oa":false,"landing_page_url":"https://doi.org/10.1587/transfun.2021eap1004","pdf_url":null,"source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W89654658","https://openalex.org/W642667799","https://openalex.org/W1540155273","https://openalex.org/W1550164471","https://openalex.org/W1570089119","https://openalex.org/W1969811075","https://openalex.org/W1979384670","https://openalex.org/W1986280275","https://openalex.org/W2029362727","https://openalex.org/W2053159614","https://openalex.org/W2069618050","https://openalex.org/W2100039988","https://openalex.org/W2114424556","https://openalex.org/W2146262488","https://openalex.org/W2160719355","https://openalex.org/W2166500461","https://openalex.org/W2168029744","https://openalex.org/W2169393334","https://openalex.org/W2222562092","https://openalex.org/W2738048051","https://openalex.org/W2768373198","https://openalex.org/W2796079430","https://openalex.org/W2899837588","https://openalex.org/W2902285478","https://openalex.org/W2920551025","https://openalex.org/W2963399478","https://openalex.org/W2972666141","https://openalex.org/W4206097460","https://openalex.org/W4213068077","https://openalex.org/W4298876635"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W4286826125","https://openalex.org/W1633485514","https://openalex.org/W4385382439","https://openalex.org/W2187449906","https://openalex.org/W2962818859"],"abstract_inverted_index":{"We":[0,116],"propose":[1],"a":[2,53,102],"useful":[3],"formulation":[4,55,89],"for":[5],"ill-posed":[6],"inverse":[7,17,123],"problems":[8,18,124],"in":[9,38,56,90],"Hilbert":[10],"spaces":[11],"with":[12,65,78,92,101],"nonlinear":[13,26],"clipping":[14,27,84],"effects.":[15],"Ill-posed":[16],"are":[19],"often":[20],"formulated":[21],"as":[22],"optimization":[23,68,107],"problems,":[24],"and":[25,63,105,135,139],"effects":[28],"may":[29],"cause":[30],"nonconvexity":[31],"or":[32],"nondifferentiability":[33],"of":[34,41,73,82,122,132,143],"the":[35,39,58,71,74,79,83,93,141],"objective":[36,59],"functions":[37],"case":[40],"commonly":[42],"used":[43],"regularized":[44],"least":[45],"squares.":[46],"To":[47],"overcome":[48],"these":[49],"difficulties,":[50],"we":[51,96],"present":[52],"tractable":[54],"which":[57,109],"function":[60,81],"is":[61],"convex":[62],"differentiable":[64,106],"respect":[66],"to":[67,99],"variables,":[69],"on":[70],"basis":[72],"Bregman":[75],"divergence":[76],"associated":[77],"primitive":[80],"function.":[85],"By":[86],"using":[87],"this":[88],"combination":[91],"representer":[94],"theorem,":[95],"need":[97],"only":[98],"deal":[100],"finite-dimensional,":[103],"convex,":[104],"problem,":[108],"can":[110,128],"be":[111,129],"solved":[112],"by":[113,146],"well-established":[114],"algorithms.":[115],"also":[117],"show":[118],"two":[119],"practical":[120],"examples":[121],"where":[125],"our":[126,144],"theory":[127,145],"applied,":[130],"estimation":[131],"band-limited":[133],"signals":[134],"time-harmonic":[136],"acoustic":[137],"fields,":[138],"evaluate":[140],"validity":[142],"numerical":[147],"simulations.":[148]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}