{"id":"https://openalex.org/W4318962581","doi":"https://doi.org/10.1137/22m147075x","title":"High-Frequency Limit of the Inverse Scattering Problem: Asymptotic Convergence from Inverse Helmholtz to Inverse Liouville","display_name":"High-Frequency Limit of the Inverse Scattering Problem: Asymptotic Convergence from Inverse Helmholtz to Inverse Liouville","publication_year":2023,"publication_date":"2023-01-24","ids":{"openalex":"https://openalex.org/W4318962581","doi":"https://doi.org/10.1137/22m147075x"},"language":"en","primary_location":{"id":"doi:10.1137/22m147075x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m147075x","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/A5033818711","display_name":"Shi Chen","orcid":"https://orcid.org/0000-0003-0556-3542"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shi Chen","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 USA"],"raw_orcid":"https://orcid.org/0000-0003-0556-3542","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026906318","display_name":"Zhiyan Ding","orcid":"https://orcid.org/0000-0001-8863-403X"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhiyan Ding","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 USA. Current address: Department of Mathematics, University of California-Berkeley, Berkeley CA 94720 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 USA. Current address: Department of Mathematics, University of California-Berkeley, Berkeley CA 94720 USA","institution_ids":["https://openalex.org/I135310074","https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100438891","display_name":"Qin Li","orcid":"https://orcid.org/0000-0001-9210-8948"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qin Li","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 USA"],"raw_orcid":"https://orcid.org/0000-0001-9210-8948","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079186251","display_name":"Leonardo Zepeda-N\u00fa\u00f1ez","orcid":"https://orcid.org/0000-0002-7310-6493"},"institutions":[{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]},{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Leonardo Zepeda-N\u00fa\u00f1ez","raw_affiliation_strings":["Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 USA. Current address:: Google Research, Mountain View, CA 94043 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 USA. Current address:: Google Research, Mountain View, CA 94043 USA","institution_ids":["https://openalex.org/I135310074","https://openalex.org/I1291425158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5033818711"],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":0.5481,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.59781476,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"16","issue":"1","first_page":"111","last_page":"143"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9984999895095825,"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":0.9976999759674072,"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/helmholtz-equation","display_name":"Helmholtz equation","score":0.7893152236938477},{"id":"https://openalex.org/keywords/inverse-scattering-transform","display_name":"Inverse scattering transform","score":0.7293373346328735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6960392594337463},{"id":"https://openalex.org/keywords/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.6952263116836548},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6690360903739929},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5601050853729248},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.49796557426452637},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.4859405755996704},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.46561479568481445},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37380683422088623},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.20046594738960266},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14868521690368652},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1445685625076294}],"concepts":[{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.7893152236938477},{"id":"https://openalex.org/C136628613","wikidata":"https://www.wikidata.org/wiki/Q17098188","display_name":"Inverse scattering transform","level":4,"score":0.7293373346328735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6960392594337463},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.6952263116836548},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6690360903739929},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5601050853729248},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.49796557426452637},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4859405755996704},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.46561479568481445},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37380683422088623},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.20046594738960266},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14868521690368652},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1445685625076294}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m147075x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m147075x","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":[{"score":0.4300000071525574,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G1333341372","display_name":null,"funder_award_id":"DMS-2012292","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3080512194","display_name":null,"funder_award_id":"1740707","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4403718343","display_name":null,"funder_award_id":"DMS-1750488","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7981535081","display_name":null,"funder_award_id":"ONR-N00014-21-1-214","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309434","display_name":"University of Wisconsin-Madison","ror":"https://ror.org/01y2jtd41"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W157344723","https://openalex.org/W831644954","https://openalex.org/W1612263173","https://openalex.org/W1947725959","https://openalex.org/W1969779500","https://openalex.org/W1980688227","https://openalex.org/W1983797262","https://openalex.org/W1989868128","https://openalex.org/W1993876500","https://openalex.org/W1996257290","https://openalex.org/W1998774301","https://openalex.org/W2000359198","https://openalex.org/W2002872997","https://openalex.org/W2005126631","https://openalex.org/W2009552164","https://openalex.org/W2026321310","https://openalex.org/W2030759208","https://openalex.org/W2031521898","https://openalex.org/W2037416698","https://openalex.org/W2041638055","https://openalex.org/W2044489763","https://openalex.org/W2045444089","https://openalex.org/W2045772703","https://openalex.org/W2047706114","https://openalex.org/W2059739202","https://openalex.org/W2067199667","https://openalex.org/W2072953748","https://openalex.org/W2075343570","https://openalex.org/W2077751930","https://openalex.org/W2089798932","https://openalex.org/W2091301787","https://openalex.org/W2100245965","https://openalex.org/W2117870218","https://openalex.org/W2119574014","https://openalex.org/W2120440916","https://openalex.org/W2120704348","https://openalex.org/W2123399460","https://openalex.org/W2169501376","https://openalex.org/W2336632864","https://openalex.org/W2518275436","https://openalex.org/W2614344179","https://openalex.org/W2735627073","https://openalex.org/W2963192679","https://openalex.org/W2963507692","https://openalex.org/W2963643827","https://openalex.org/W2978191791","https://openalex.org/W2993046037","https://openalex.org/W3021013497","https://openalex.org/W3104744297","https://openalex.org/W3105384701","https://openalex.org/W3153899891","https://openalex.org/W3173608018","https://openalex.org/W4207017441","https://openalex.org/W4232720747","https://openalex.org/W4288652121","https://openalex.org/W4293409666","https://openalex.org/W4298264214"],"related_works":["https://openalex.org/W2994306356","https://openalex.org/W2120820547","https://openalex.org/W4388295276","https://openalex.org/W2790147798","https://openalex.org/W4241983757","https://openalex.org/W143225781","https://openalex.org/W3101167575","https://openalex.org/W2520812953","https://openalex.org/W2594185299","https://openalex.org/W1975488373"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,6,11,15,24,31,39,45,49,54,69,74,78,82,86,90,117,121,130,134,140],"asymptotic":[3,32],"relation":[4],"between":[5],"inverse":[7,40,50,64,136],"problems":[8,65],"relying":[9],"on":[10,44,77,85],"Helmholtz":[12,46],"equation":[13,18,56],"and":[14,89,100],"radiative":[16],"transfer":[17],"(RTE)":[19],"as":[20],"physical":[21,79],"models":[22,94],"in":[23,98,120,127],"high-frequency":[25,122],"limit.":[26],"In":[27],"particular,":[28],"we":[29],"evaluate":[30],"convergence":[33],"of":[34,38,53,60,116],"a":[35],"generalized":[36],"version":[37,59],"scattering":[41,51,137],"problem":[42,52,138],"based":[43],"equation,":[47],"to":[48,81],"Liouville":[55],"(a":[57],"simplified":[58],"RTE).":[61],"The":[62,102],"two":[63],"are":[66,143],"connected":[67],"through":[68],"Wigner":[70],"transform":[71,92],"that":[72,93,105],"translates":[73],"wave-type":[75],"description":[76,84],"space":[80],"kinetic-type":[83],"phase":[87],"space,":[88],"Husimi":[91],"data":[95],"localized":[96],"both":[97],"location":[99],"direction.":[101],"finding":[103],"suggests":[104],"impinging":[106],"tightly":[107],"concentrated":[108],"monochromatic":[109],"beams":[110],"can":[111],"indeed":[112],"provide":[113],"stable":[114],"reconstruction":[115,132],"medium,":[118],"asymptotically":[119],"regime.":[123],"This":[124],"fact":[125],"stands":[126],"contrast":[128],"with":[129],"unstable":[131],"for":[133],"classical":[135],"when":[139],"probing":[141],"signals":[142],"plane":[144],"waves.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
