{"id":"https://openalex.org/W7224098733","doi":"https://doi.org/10.1002/pamm.70251","title":"Gradient Flows on Sparse Representations for PDE\u2010Regularized Inverse Problems","display_name":"Gradient Flows on Sparse Representations for PDE\u2010Regularized Inverse Problems","publication_year":2026,"publication_date":"2026-10-28","ids":{"openalex":"https://openalex.org/W7224098733","doi":"https://doi.org/10.1002/pamm.70251"},"language":"en","primary_location":{"id":"doi:10.1002/pamm.70251","doi":"https://doi.org/10.1002/pamm.70251","is_oa":true,"landing_page_url":"https://doi.org/10.1002/pamm.70251","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/pamm.70251","source":{"id":"https://openalex.org/S4210190971","display_name":"PAMM","issn_l":"1617-7061","issn":["1617-7061"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings in Applied Mathematics and Mechanics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/pamm.70251","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136109621","display_name":"Christian Amend","orcid":"https://orcid.org/0009-0004-3793-5464","observed_orcids":["https://orcid.org/0009-0004-3793-5464"]},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Christian Amend","raw_affiliation_strings":["Department of Applied Mathematics University of Twente Enschede the Netherlands"],"raw_orcid":"https://orcid.org/0009-0004-3793-5464","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics University of Twente Enschede the Netherlands","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086121807","display_name":"Marcello Carioni","orcid":"https://orcid.org/0000-0002-2282-4348","observed_orcids":["https://orcid.org/0000-0002-2282-4348"]},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Marcello Carioni","raw_affiliation_strings":["Department of Applied Mathematics University of Twente Enschede the Netherlands"],"raw_orcid":"https://orcid.org/0000-0002-2282-4348","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics University of Twente Enschede the Netherlands","institution_ids":["https://openalex.org/I94624287"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086121807","https://openalex.org/A5136109621"],"corresponding_institution_ids":["https://openalex.org/I94624287"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.87291078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"4","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":0.7935000061988831,"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":0.7935000061988831,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.0771000012755394,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.07339999824762344,"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/sparse-representation","display_name":"sparse representation","score":0.9670000076293945},{"id":"https://openalex.org/keywords/total-variation-regularization","display_name":"total variation regularization","score":0.9330000281333923},{"id":"https://openalex.org/keywords/laplacian","display_name":"Laplacian","score":0.5960000157356262},{"id":"https://openalex.org/keywords/fundamental-solutions","display_name":"fundamental solutions","score":0.8240000009536743},{"id":"https://openalex.org/keywords/dirac-delta-function","display_name":"Dirac delta function","score":0.7570000290870667},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"convex optimization","score":0.6050000190734863},{"id":"https://openalex.org/keywords/well-posedness","display_name":"well-posedness","score":0.6179999709129333}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7192999720573425},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5857999920845032},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5534999966621399},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5440999865531921},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5310999751091003},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5271999835968018},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5232999920845032},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4973999857902527},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.48989999294281006},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.46860000491142273},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.42579999566078186},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.4074999988079071},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.38019999861717224},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3725000023841858},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.36629998683929443},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3506999909877777},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.3400999903678894},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33410000801086426},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.3140000104904175},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.302700012922287},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.2971000075340271},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.29490000009536743},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2824000120162964},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.2678999900817871},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.25760000944137573},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2538999915122986}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/pamm.70251","doi":"https://doi.org/10.1002/pamm.70251","is_oa":true,"landing_page_url":"https://doi.org/10.1002/pamm.70251","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/pamm.70251","source":{"id":"https://openalex.org/S4210190971","display_name":"PAMM","issn_l":"1617-7061","issn":["1617-7061"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings in Applied Mathematics and Mechanics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1002/pamm.70251","doi":"https://doi.org/10.1002/pamm.70251","is_oa":true,"landing_page_url":"https://doi.org/10.1002/pamm.70251","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/pamm.70251","source":{"id":"https://openalex.org/S4210190971","display_name":"PAMM","issn_l":"1617-7061","issn":["1617-7061"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings in Applied Mathematics and Mechanics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5424482859","display_name":"Curve Ensemble Gradient Descents for Sparse Dynamic Problems","funder_award_id":"OCENW.M.22.302","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224098733.pdf","grobid_xml":"https://content.openalex.org/works/W7224098733.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W109240602","https://openalex.org/W1968647136","https://openalex.org/W2290904946","https://openalex.org/W2890042903","https://openalex.org/W7141451027"],"related_works":["https://openalex.org/W7141451027","https://openalex.org/W2905144957","https://openalex.org/W3156024029","https://openalex.org/W4404604060","https://openalex.org/W4385193363","https://openalex.org/W2908052745","https://openalex.org/W3004898171","https://openalex.org/W2809809415","https://openalex.org/W2462936019","https://openalex.org/W2113740359"],"abstract_inverted_index":{"ABSTRACT":[0],"In":[1],"this":[2,113,152],"short":[3],"paper,":[4],"we":[5,39,73,100,118,148],"summarize":[6],"the":[7,44,51,62,93,97,103,106,121,140,162,179,184],"theory":[8,42],"of":[9,46,54,84,96,105,142,183],"Atomic":[10],"Gradient":[11],"Flows":[12],"(AGF)":[13],"introduced":[14],"in":[15,64,112,151],"(Amend,":[16],"Carioni":[17],"and":[18,132,135,165],"Zemas,":[19],"arxiv:2603.25675,":[20],"2026),":[21],"which":[22],"provides":[23],"a":[24,55,116,137],"framework":[25,109],"to":[26,43,88,139,157,170,174],"construct":[27],"gradient":[28,159],"flows":[29,160],"on":[30,61,145,161],"sparse":[31,76],"representations":[32,77],"for":[33],"convex":[34],"regularized":[35,49,177],"optimization":[36],"problems.":[37],"Then,":[38],"apply":[40],"such":[41],"case":[45],"inverse":[47,175],"problems":[48,176],"with":[50,178],"total":[52,180],"variation":[53,181],"scalar":[56],"partial":[57],"differential":[58],"operator.":[59],"Building":[60],"results":[63],"(Bredies,":[65],"Carioni,":[66],"Calc.":[67],"Var.":[68],"Partial":[69],"Differ.":[70],"Equ.,":[71],"2020),":[72],"show":[74],"that":[75,102,120,150],"can":[78,166],"be":[79,167],"characterized":[80],"as":[81],"linear":[82],"combinations":[83],"fundamental":[85],"solutions":[86,173],"applied":[87],"Dirac":[89],"deltas.":[90],"By":[91],"analyzing":[92],"geometric":[94],"properties":[95,129],"associated":[98],"atoms,":[99],"verify":[101],"assumptions":[104],"general":[107],"AGF":[108],"are":[110,124],"satisfied":[111],"setting.":[114],"As":[115],"consequence,":[117],"prove":[119,149],"corresponding":[122],"AGFs":[123,155],"well\u2010defined,":[125],"enjoy":[126],"key":[127],"structural":[128],"(e.g.,":[130],"uniqueness":[131],"contraction":[133],"estimates)":[134],"admit":[136],"lifting":[138],"space":[141],"probability":[143],"measures":[144],"atoms.":[146],"Finally,":[147],"specific":[153],"case,":[154],"reduce":[156],"Euclidean":[158],"underlying":[163],"domain":[164],"easily":[168],"implemented":[169],"numerically":[171],"compute":[172],"norm":[182],"Laplacian.":[185]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-29T00:00:00"}