{"id":"https://openalex.org/W7140773336","doi":"https://doi.org/10.1109/tit.2026.3677729","title":"Gradient Descent Provably Solves Nonlinear Tomographic Reconstruction","display_name":"Gradient Descent Provably Solves Nonlinear Tomographic Reconstruction","publication_year":2026,"publication_date":"2026-03-26","ids":{"openalex":"https://openalex.org/W7140773336","doi":"https://doi.org/10.1109/tit.2026.3677729"},"language":null,"primary_location":{"id":"doi:10.1109/tit.2026.3677729","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2026.3677729","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5049727497","display_name":"Sara Fridovich-Keil","orcid":null},"institutions":[{"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":"Sara Fridovich-Keil","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA"],"raw_orcid":"https://orcid.org/0000-0002-7661-4987","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093116047","display_name":"Fabrizio Valdivia","orcid":null},"institutions":[{"id":"https://openalex.org/I133999245","display_name":"University of Nevada, Las Vegas","ror":"https://ror.org/0406gha72","country_code":"US","type":"education","lineage":["https://openalex.org/I133999245"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fabrizio Valdivia","raw_affiliation_strings":["Department of Computer Science, University of Nevada, Las Vegas, USA"],"raw_orcid":"https://orcid.org/0009-0000-7034-3330","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Nevada, Las Vegas, USA","institution_ids":["https://openalex.org/I133999245"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014044649","display_name":"Gordon Wetzstein","orcid":"https://orcid.org/0000-0002-9243-6885"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gordon Wetzstein","raw_affiliation_strings":["Department of Electrical Engineering, Stanford University, Stanford, USA"],"raw_orcid":"https://orcid.org/0000-0002-9243-6885","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Stanford University, Stanford, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012870568","display_name":"Benjamin Recht","orcid":"https://orcid.org/0000-0002-0293-593X"},"institutions":[{"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":"Benjamin Recht","raw_affiliation_strings":["Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA"],"raw_orcid":"https://orcid.org/0000-0002-0293-593X","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5130709294","display_name":"Mahdi Soltanolkotabi","orcid":null},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mahdi Soltanolkotabi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, USA"],"raw_orcid":"https://orcid.org/0000-0003-2101-6418","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.48531973,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"5","first_page":"3195","last_page":"3211"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.21770000457763672,"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":0.21770000457763672,"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/T10522","display_name":"Medical Imaging Techniques and Applications","score":0.14790000021457672,"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"}},{"id":"https://openalex.org/T12386","display_name":"Advanced X-ray and CT Imaging","score":0.12639999389648438,"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/gradient-descent","display_name":"Gradient descent","score":0.5719000101089478},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49079999327659607},{"id":"https://openalex.org/keywords/iterative-reconstruction","display_name":"Iterative reconstruction","score":0.4659999907016754},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.4052000045776367},{"id":"https://openalex.org/keywords/signal-reconstruction","display_name":"Signal reconstruction","score":0.382099986076355},{"id":"https://openalex.org/keywords/tomographic-reconstruction","display_name":"Tomographic reconstruction","score":0.35199999809265137},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.31049999594688416}],"concepts":[{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5719000101089478},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5231999754905701},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5055999755859375},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49079999327659607},{"id":"https://openalex.org/C141379421","wikidata":"https://www.wikidata.org/wiki/Q6094427","display_name":"Iterative reconstruction","level":2,"score":0.4659999907016754},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42660000920295715},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.4052000045776367},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.382099986076355},{"id":"https://openalex.org/C97742081","wikidata":"https://www.wikidata.org/wiki/Q7820109","display_name":"Tomographic reconstruction","level":3,"score":0.35199999809265137},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.31049999594688416},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.30640000104904175},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3050000071525574},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.29670000076293945},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2865999937057495},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2547000050544739},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2524999976158142},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2026.3677729","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2026.3677729","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1288709608","display_name":"PostDoctoral Research Fellowship","funder_award_id":"2303178","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3677612960","display_name":"CAREER: Guaranteed Nonconvex Optimization for High-Dimensional Learning","funder_award_id":"1846369","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7011083491","display_name":"CIF: Small: Precise Computational and Statistical Tradeoffs for Iterative Signal Estimation and Supervised Learning","funder_award_id":"1813877","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7545230888","display_name":null,"funder_award_id":"DP2LM014564-01","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G8972937638","display_name":"CIF: Small: Machine Learning for Wireless Propagation Channels","funder_award_id":"2008443","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F3586560703","display_name":"Information Innovation Office","ror":null},{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306079","display_name":"David and Lucile Packard Foundation","ror":"https://ror.org/032atxq54"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,75],"computed":[1],"tomography":[2],"(CT),":[3],"the":[4,20,26,52,83,92,109,118,135,139,147,150,161,166,171,216],"forward":[5,94],"model":[6],"consists":[7],"of":[8,22,54,126,141,149,173,218],"a":[9,39,80,113,122],"linear":[10,40,197],"Radon":[11],"transform":[12],"followed":[13],"by":[14,155],"an":[15],"exponential":[16],"nonlinearity":[17,35],"based":[18],"on":[19,165,182],"attenuation":[21],"light":[23],"according":[24],"to":[25,70,108,195,210],"Beer\u2013Lambert":[27],"Law.":[28],"Conventional":[29],"reconstruction":[30,64,177,198],"often":[31],"involves":[32],"inverting":[33],"this":[34,44,76,97],"and":[36,68,184],"then":[37],"solving":[38],"inverse":[41],"problem.":[42],"However,":[43],"nonlinear":[45,93,175],"measurement":[46],"preprocessing":[47,61,206],"is":[48,85,99,143,153,208],"poorly":[49],"conditioned":[50],"in":[51,134,188,215],"vicinity":[53],"high-density":[55,73],"materials,":[56],"such":[57,221],"as":[58,222],"metal.":[59],"This":[60,152],"makes":[62],"CT":[63,176,180],"methods":[65],"numerically":[66],"sensitive":[67],"susceptible":[69],"artifacts":[71,191],"near":[72,123],"regions.":[74],"paper,":[77],"we":[78,101],"study":[79],"technique":[81],"where":[82,138],"signal":[84,120,162],"directly":[86],"reconstructed":[87],"from":[88],"raw":[89],"measurements":[90,142],"through":[91,163],"model.":[95],"Though":[96],"optimization":[98,167],"nonconvex,":[100],"show":[102],"that":[103,204],"gradient":[104],"descent":[105],"provably":[106],"converges":[107],"global":[110],"optimum":[111],"at":[112],"geometric":[114],"rate,":[115],"perfectly":[116],"reconstructing":[117],"underlying":[119],"with":[121,178],"minimal":[124],"number":[125,140],"random":[127],"measurements.":[128],"We":[129,169],"also":[130,202],"prove":[131],"similar":[132],"results":[133],"under-determined":[136],"setting":[137],"significantly":[144],"smaller":[145],"than":[146],"dimension":[148],"signal.":[151],"achieved":[154],"enforcing":[156],"prior":[157],"structural":[158],"information":[159],"about":[160],"constraints":[164],"variables.":[168],"illustrate":[170],"benefits":[172],"direct":[174],"cone-beam":[179],"experiments":[181,201],"synthetic":[183],"real":[185],"3D":[186],"volumes,":[187],"which":[189],"metal":[190,212],"are":[192],"reduced":[193],"compared":[194],"standard":[196],"methods.":[199],"Our":[200],"demonstrate":[203],"logarithmic":[205],"alone":[207],"sufficient":[209],"produce":[211],"artifacts,":[213],"even":[214],"absence":[217],"other":[219],"causes":[220],"beam":[223],"hardening.":[224]},"counts_by_year":[],"updated_date":"2026-04-23T06:14:38.165362","created_date":"2026-03-27T00:00:00"}
