{"id":"https://openalex.org/W2952588853","doi":"https://doi.org/10.1137/18m1199149","title":"Sparsity-Inducing Nonconvex Nonseparable Regularization for Convex Image Processing","display_name":"Sparsity-Inducing Nonconvex Nonseparable Regularization for Convex Image Processing","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2952588853","doi":"https://doi.org/10.1137/18m1199149","mag":"2952588853"},"language":"en","primary_location":{"id":"doi:10.1137/18m1199149","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1199149","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11585/717291","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017232084","display_name":"Alessandro Lanza","orcid":"https://orcid.org/0000-0002-4904-0682"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alessandro Lanza","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058921917","display_name":"Serena Morigi","orcid":"https://orcid.org/0000-0001-8334-8798"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Serena Morigi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058321875","display_name":"Ivan Selesnick","orcid":"https://orcid.org/0000-0002-4939-3971"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ivan W. Selesnick","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5081534186","display_name":"Fiorella Sgallari","orcid":"https://orcid.org/0000-0002-9166-8879"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fiorella Sgallari","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5017232084"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.27,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.95436098,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"12","issue":"2","first_page":"1099","last_page":"1134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":1.0,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9962000250816345,"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9957000017166138,"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/deblurring","display_name":"Deblurring","score":0.8081778287887573},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6652398109436035},{"id":"https://openalex.org/keywords/inpainting","display_name":"Inpainting","score":0.62420654296875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6085901856422424},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.554145097732544},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5442405939102173},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5416555404663086},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5099455118179321},{"id":"https://openalex.org/keywords/image-restoration","display_name":"Image restoration","score":0.49589261412620544},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4631910026073456},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.45422083139419556},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.4471184313297272},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.437531977891922},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.42874160408973694},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.38416439294815063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33760225772857666},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23534703254699707}],"concepts":[{"id":"https://openalex.org/C2777693668","wikidata":"https://www.wikidata.org/wiki/Q25053743","display_name":"Deblurring","level":5,"score":0.8081778287887573},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6652398109436035},{"id":"https://openalex.org/C11727466","wikidata":"https://www.wikidata.org/wiki/Q1628157","display_name":"Inpainting","level":3,"score":0.62420654296875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6085901856422424},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.554145097732544},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5442405939102173},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5416555404663086},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5099455118179321},{"id":"https://openalex.org/C106430172","wikidata":"https://www.wikidata.org/wiki/Q6002272","display_name":"Image restoration","level":4,"score":0.49589261412620544},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4631910026073456},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.45422083139419556},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.4471184313297272},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.437531977891922},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.42874160408973694},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.38416439294815063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33760225772857666},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23534703254699707},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1199149","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1199149","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"},{"id":"pmh:oai:cris.unibo.it:11585/717291","is_oa":true,"landing_page_url":"http://hdl.handle.net/11585/717291","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:cris.unibo.it:11585/717291","is_oa":true,"landing_page_url":"http://hdl.handle.net/11585/717291","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5734292937","display_name":null,"funder_award_id":"1525398","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1586417863","https://openalex.org/W1826065584","https://openalex.org/W1976709621","https://openalex.org/W1981487911","https://openalex.org/W1984910122","https://openalex.org/W2007454648","https://openalex.org/W2028781966","https://openalex.org/W2040657720","https://openalex.org/W2087670913","https://openalex.org/W2100556411","https://openalex.org/W2103559027","https://openalex.org/W2103955025","https://openalex.org/W2110505738","https://openalex.org/W2115706991","https://openalex.org/W2118550318","https://openalex.org/W2122950831","https://openalex.org/W2127870457","https://openalex.org/W2145096794","https://openalex.org/W2203973972","https://openalex.org/W2344964557","https://openalex.org/W2405803404","https://openalex.org/W2531491639","https://openalex.org/W2570790349","https://openalex.org/W2588776893","https://openalex.org/W2620850570","https://openalex.org/W2752392650","https://openalex.org/W2781992923","https://openalex.org/W2810325903","https://openalex.org/W2962781485","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W2066613488","https://openalex.org/W2031788393","https://openalex.org/W791927757","https://openalex.org/W2182590612","https://openalex.org/W3153582293","https://openalex.org/W2905397092","https://openalex.org/W2269775642","https://openalex.org/W3080537281","https://openalex.org/W2289746762","https://openalex.org/W2139384960"],"abstract_inverted_index":{"A":[0,150],"popular":[1],"strategy":[2,72],"for":[3,43,157],"determining":[4],"solutions":[5],"to":[6,65,115],"linear":[7],"least-squares":[8],"problems":[9,122],"relies":[10],"on":[11,102],"using":[12],"sparsity-promoting":[13],"regularizers":[14,39,50],"and":[15,29,132,141,145,171],"is":[16,32,99,113,155,168],"widely":[17],"exploited":[18],"in":[19,36],"image":[20,26,120],"processing":[21,121],"applications":[22],"such":[23,51],"as,":[24,52],"e.g.,":[25,53],"denoising,":[27],"deblurring,":[28],"inpainting.":[30],"It":[31],"well":[33],"known":[34],"that,":[35],"general,":[37],"nonconvex":[38,70,81,107],"hold":[40],"the":[41,56,61,68,78,87,129,137,159,166,181,184],"potential":[42],"promoting":[44],"sparsity":[45],"more":[46,104],"effectively":[47],"than":[48,123],"convex":[49,69],"those":[54],"involving":[55],"$\\ell_1$":[57],"norm.":[58],"To":[59],"avoid":[60],"intrinsic":[62],"difficulties":[63],"related":[64,133,160],"non-convex":[66],"optimization,":[67],"(CNC)":[71],"has":[73],"been":[74],"proposed,":[75,100],"which":[76,179],"allows":[77],"use":[79],"of":[80,86,119,136,147,165,183],"regularization":[82],"while":[83],"maintaining":[84],"convexity":[85,130],"total":[88],"objective":[89],"function.":[90],"In":[91],"this":[92],"paper,":[93],"a":[94,103,116],"new":[95],"CNC":[96,125,139],"variational":[97],"model":[98,112],"based":[101],"general":[105],"parametric":[106],"nonseparable":[108],"regularizer.":[109],"The":[110,163],"proposed":[111,156,185],"applicable":[114],"greater":[117],"variety":[118],"prior":[124],"methods.":[126],"We":[127],"derive":[128],"conditions":[131],"theoretical":[134],"properties":[135],"presented":[138,178],"model,":[140],"we":[142],"analyze":[143],"existence":[144],"uniqueness":[146],"its":[148],"solutions.":[149],"primal-dual":[151],"forward-backward":[152],"splitting":[153],"algorithm":[154,167],"solving":[158],"saddle-point":[161],"problem.":[162],"convergence":[164],"demonstrated":[169],"theoretically":[170],"validated":[172],"empirically.":[173],"Several":[174],"numerical":[175],"experiments":[176],"are":[177],"prove":[180],"effectiveness":[182],"approach.":[186]},"counts_by_year":[{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":10},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
