{"id":"https://openalex.org/W4398157302","doi":"https://doi.org/10.48550/arxiv.2405.10754","title":"Stable Phase Retrieval with Mirror Descent","display_name":"Stable Phase Retrieval with Mirror Descent","publication_year":2024,"publication_date":"2024-05-17","ids":{"openalex":"https://openalex.org/W4398157302","doi":"https://doi.org/10.48550/arxiv.2405.10754"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2405.10754","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2405.10754","pdf_url":"https://arxiv.org/pdf/2405.10754","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2405.10754","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025177894","display_name":"Jean-Jacques Godeme","orcid":"https://orcid.org/0009-0005-1040-1005"},"institutions":[{"id":"https://openalex.org/I194210350","display_name":"\u00c9cole Nationale Sup\u00e9rieure d'Ing\u00e9nieurs de Caen","ror":"https://ror.org/01fpqqe90","country_code":"FR","type":"education","lineage":["https://openalex.org/I194210350","https://openalex.org/I4210105918"]},{"id":"https://openalex.org/I4210105918","display_name":"Normandie Universit\u00e9","ror":"https://ror.org/01k40cz91","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918"]},{"id":"https://openalex.org/I4210139483","display_name":"GREYC","ror":"https://ror.org/043749971","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I194210350","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210139483","https://openalex.org/I4210159245","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Godeme, Jean-Jacques","raw_affiliation_strings":["ENSICAEN - \u00c9cole Nationale Sup\u00e9rieure d'Ing\u00e9nieurs de Caen (6, Boulevard du Mar\u00e9chal Juin CS 45053 14050 CAEN cedex 04 - France)","Equipe Image - Laboratoire GREYC - UMR6072 (France)","GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen (Boulevard du Mar\u00e9chal Juin - 14050 CAEN Cedex - France)","NU - Normandie Universit\u00e9 (Esplanade de la Paix - CS 14032 - 14032 Caen Cedex 5 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ENSICAEN - \u00c9cole Nationale Sup\u00e9rieure d'Ing\u00e9nieurs de Caen (6, Boulevard du Mar\u00e9chal Juin CS 45053 14050 CAEN cedex 04 - France)","institution_ids":["https://openalex.org/I194210350"]},{"raw_affiliation_string":"Equipe Image - Laboratoire GREYC - UMR6072 (France)","institution_ids":["https://openalex.org/I4210139483"]},{"raw_affiliation_string":"GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen (Boulevard du Mar\u00e9chal Juin - 14050 CAEN Cedex - France)","institution_ids":["https://openalex.org/I4210139483"]},{"raw_affiliation_string":"NU - Normandie Universit\u00e9 (Esplanade de la Paix - CS 14032 - 14032 Caen Cedex 5 - France)","institution_ids":["https://openalex.org/I4210105918"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008136365","display_name":"Jalal Fadili","orcid":"https://orcid.org/0000-0002-8165-7578"},"institutions":[{"id":"https://openalex.org/I194210350","display_name":"\u00c9cole Nationale Sup\u00e9rieure d'Ing\u00e9nieurs de Caen","ror":"https://ror.org/01fpqqe90","country_code":"FR","type":"education","lineage":["https://openalex.org/I194210350","https://openalex.org/I4210105918"]},{"id":"https://openalex.org/I4210105918","display_name":"Normandie Universit\u00e9","ror":"https://ror.org/01k40cz91","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918"]},{"id":"https://openalex.org/I4210139483","display_name":"GREYC","ror":"https://ror.org/043749971","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I194210350","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210139483","https://openalex.org/I4210159245","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fadili, Jalal","raw_affiliation_strings":["ENSICAEN - \u00c9cole Nationale Sup\u00e9rieure d'Ing\u00e9nieurs de Caen (6, Boulevard du Mar\u00e9chal Juin CS 45053 14050 CAEN cedex 04 - France)","Equipe Image - Laboratoire GREYC - UMR6072 (France)","GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen (Boulevard du Mar\u00e9chal Juin - 14050 CAEN Cedex - France)","NU - Normandie Universit\u00e9 (Esplanade de la Paix - CS 14032 - 14032 Caen Cedex 5 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ENSICAEN - \u00c9cole Nationale Sup\u00e9rieure d'Ing\u00e9nieurs de Caen (6, Boulevard du Mar\u00e9chal Juin CS 45053 14050 CAEN cedex 04 - France)","institution_ids":["https://openalex.org/I194210350"]},{"raw_affiliation_string":"Equipe Image - Laboratoire GREYC - UMR6072 (France)","institution_ids":["https://openalex.org/I4210139483"]},{"raw_affiliation_string":"GREYC - Groupe de Recherche en Informatique, Image et Instrumentation de Caen (Boulevard du Mar\u00e9chal Juin - 14050 CAEN Cedex - France)","institution_ids":["https://openalex.org/I4210139483"]},{"raw_affiliation_string":"NU - Normandie Universit\u00e9 (Esplanade de la Paix - CS 14032 - 14032 Caen Cedex 5 - France)","institution_ids":["https://openalex.org/I4210105918"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014911084","display_name":"Claude Amra","orcid":"https://orcid.org/0000-0002-4618-5931"},"institutions":[{"id":"https://openalex.org/I4210125985","display_name":"Institut Fresnel","ror":"https://ror.org/03br1wy20","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210095849","https://openalex.org/I4210125985","https://openalex.org/I4210142724"]},{"id":"https://openalex.org/I4210159802","display_name":"CSInstruments (France)","ror":"https://ror.org/05gpa6n30","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210159802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Amra, Claude","raw_affiliation_strings":["CONCEPT - CONCEPT (France)","FRESNEL - Institut FRESNEL (Facult\u00e9 des Sciences et Techniques\r\navenue Escadrille Normandie Niemen \r\n13 397 Marseille cedex 20 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CONCEPT - CONCEPT (France)","institution_ids":["https://openalex.org/I4210159802"]},{"raw_affiliation_string":"FRESNEL - Institut FRESNEL (Facult\u00e9 des Sciences et Techniques\r\navenue Escadrille Normandie Niemen \r\n13 397 Marseille cedex 20 - France)","institution_ids":["https://openalex.org/I4210125985"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054580263","display_name":"Myriam Zerrad","orcid":"https://orcid.org/0000-0001-8365-3848"},"institutions":[{"id":"https://openalex.org/I4210125985","display_name":"Institut Fresnel","ror":"https://ror.org/03br1wy20","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210095849","https://openalex.org/I4210125985","https://openalex.org/I4210142724"]},{"id":"https://openalex.org/I4210159802","display_name":"CSInstruments (France)","ror":"https://ror.org/05gpa6n30","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210159802"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Zerrad, Myriam","raw_affiliation_strings":["CONCEPT - CONCEPT (France)","FRESNEL - Institut FRESNEL (Facult\u00e9 des Sciences et Techniques\r\navenue Escadrille Normandie Niemen \r\n13 397 Marseille cedex 20 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CONCEPT - CONCEPT (France)","institution_ids":["https://openalex.org/I4210159802"]},{"raw_affiliation_string":"FRESNEL - Institut FRESNEL (Facult\u00e9 des Sciences et Techniques\r\navenue Escadrille Normandie Niemen \r\n13 397 Marseille cedex 20 - France)","institution_ids":["https://openalex.org/I4210125985"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/phase-retrieval","display_name":"Phase retrieval","score":0.7048913240432739},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6487991213798523},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.6101787686347961},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5825290679931641},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.5388737320899963},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5363242626190186},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5032252669334412},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.482636034488678},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.46320948004722595},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4209180176258087},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.4172404110431671},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.402060329914093},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35755854845046997},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1862649917602539},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13908788561820984},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.12000709772109985},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0967007577419281}],"concepts":[{"id":"https://openalex.org/C81793267","wikidata":"https://www.wikidata.org/wiki/Q7180962","display_name":"Phase retrieval","level":3,"score":0.7048913240432739},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6487991213798523},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.6101787686347961},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5825290679931641},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5388737320899963},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5363242626190186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5032252669334412},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.482636034488678},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.46320948004722595},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4209180176258087},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.4172404110431671},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.402060329914093},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35755854845046997},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1862649917602539},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13908788561820984},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.12000709772109985},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0967007577419281},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2405.10754","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2405.10754","pdf_url":"https://arxiv.org/pdf/2405.10754","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-04579446v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04579446/file/mdbt_stablephaserecovery.pdf","pdf_url":"https://hal.science/hal-04579446/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"https://hal.science/hal-04579446","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-04579446v2","is_oa":true,"landing_page_url":"https://hal.science/hal-04579446","pdf_url":"https://hal.science/hal-04579446v2/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"2024","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2405.10754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2405.10754","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2405.10754","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2405.10754","pdf_url":"https://arxiv.org/pdf/2405.10754","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3010527862","display_name":null,"funder_award_id":"ANR\u201019","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G501721486","display_name":"Far field Intensity for Recovering Surface Topography","funder_award_id":"ANR-19-CE42-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4398157302.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4206903459","https://openalex.org/W2754816816","https://openalex.org/W4366280654","https://openalex.org/W3160167280","https://openalex.org/W4231621013","https://openalex.org/W4362706668","https://openalex.org/W3008318776","https://openalex.org/W3163031201","https://openalex.org/W2041416246","https://openalex.org/W3020853991"],"abstract_inverted_index":{"In":[0,53],"this":[1],"paper,":[2],"we":[3,57,112],"aim":[4],"to":[5,36,48,63,94,126,135,164,191],"reconstruct":[6],"an":[7,17],"n-dimensional":[8],"real":[9],"vector":[10,92,133],"from":[11],"m":[12,147],"phaseless":[13],"measurements":[14,40,101,146],"corrupted":[15],"by":[16],"additive":[18,51],"noise.":[19,52],"We":[20,170],"extend":[21],"the":[22,44,54,68,74,80,85,90,100,106,131,143,193],"noiseless":[23],"framework":[24],"developed":[25],"in":[26],"[15],":[27],"based":[28],"on":[29],"mirror":[30,60,123,181],"descent":[31,61,124,182],"(or":[32],"Bregman":[33],"gradient":[34],"descent),":[35],"deal":[37],"with":[38,120,175],"noisy":[39],"and":[41,72,79,105,187],"prove":[42],"that":[43,59,117,119,180],"procedure":[45],"is":[46,76,82,88,109,148,162,183],"stable":[47],"(small":[49],"enough)":[50],"deterministic":[55],"case,":[56],"show":[58],"converges":[62,125],"a":[64,95,127,136,159,166,185],"critical":[65,86],"point":[66,87],"of":[67,145],"phase":[69,194],"retrieval":[70,195],"problem,":[71],"if":[73,158],"algorithm":[75],"well":[77],"initialized":[78],"noise":[81],"small":[83],"enough,":[84,111],"near":[89,130],"true":[91,132],"up":[93],"global":[96,114,128,137],"sign":[97,138],"change.":[98],"When":[99],"are":[102],"i.i.d":[103],"Gaussian":[104],"signal-to-noise":[107],"ratio":[108],"large":[110,149],"provide":[113,165],"convergence":[115],"guarantees":[116],"ensure":[118],"high":[121],"probability,":[122],"minimizer":[129],"(up":[134],"change),":[139],"as":[140,142],"soon":[141],"number":[144],"enough.":[150],"The":[151],"sample":[152],"complexity":[153],"bound":[154],"can":[155],"be":[156],"improved":[157],"spectral":[160],"method":[161],"used":[163],"good":[167],"initial":[168],"guess.":[169],"complement":[171],"our":[172],"theoretical":[173],"study":[174],"several":[176],"numerical":[177],"results":[178],"showing":[179],"both":[184],"computationally":[186],"statistically":[188],"efficient":[189],"scheme":[190],"solve":[192],"problem.":[196]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
