{"id":"https://openalex.org/W3013875899","doi":"https://doi.org/10.1109/tit.2020.2983562","title":"The Estimation Performance of Nonlinear Least Squares for Phase Retrieval","display_name":"The Estimation Performance of Nonlinear Least Squares for Phase Retrieval","publication_year":2020,"publication_date":"2020-03-26","ids":{"openalex":"https://openalex.org/W3013875899","doi":"https://doi.org/10.1109/tit.2020.2983562","mag":"3013875899"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2020.2983562","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2020.2983562","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/A5016124996","display_name":"Meng Huang","orcid":"https://orcid.org/0000-0003-2971-7585"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210145278","display_name":"Institute of Applied Physics and Computational Mathematics","ror":"https://ror.org/03sxpbt26","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210145278"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Meng Huang","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","School of Mathematical Sciences, Institute of Computational Mathematics, University of Chinese Academy of Sciences, Beijing, China","Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China; School of Mathematical Sciences, Institute of Computational Mathematics, University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-2971-7585","affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"School of Mathematical Sciences, Institute of Computational Mathematics, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210145278","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China; School of Mathematical Sciences, Institute of Computational Mathematics, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058662188","display_name":"Zhiqiang Xu","orcid":"https://orcid.org/0000-0002-3995-4448"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210145278","display_name":"Institute of Applied Physics and Computational Mathematics","ror":"https://ror.org/03sxpbt26","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210145278"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhiqiang Xu","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","School of Mathematical Sciences, Institute of Computational Mathematics, University of Chinese Academy of Sciences, Beijing, China","Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China; School of Mathematical Sciences, Institute of Computational Mathematics, University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-3995-4448","affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"School of Mathematical Sciences, Institute of Computational Mathematics, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210145278","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China; School of Mathematical Sciences, Institute of Computational Mathematics, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016124996"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485","https://openalex.org/I4210145278","https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":2.315,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.87772065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"66","issue":"12","first_page":"7967","last_page":"7977"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10638","display_name":"Optical measurement and interference techniques","score":0.9775000214576721,"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"}},{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9771000146865845,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4433038532733917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3834803104400635},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3655172884464264}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4433038532733917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3834803104400635},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3655172884464264}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2020.2983562","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2020.2983562","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/G5853628231","display_name":null,"funder_award_id":"91630203","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6967058303","display_name":null,"funder_award_id":"11688101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7336057937","display_name":null,"funder_award_id":"Z180002","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W7645247","https://openalex.org/W1484412996","https://openalex.org/W1552037902","https://openalex.org/W2007593159","https://openalex.org/W2015911499","https://openalex.org/W2044613770","https://openalex.org/W2077647472","https://openalex.org/W2078397124","https://openalex.org/W2087483236","https://openalex.org/W2097132843","https://openalex.org/W2106453960","https://openalex.org/W2121716262","https://openalex.org/W2142949395","https://openalex.org/W2283023501","https://openalex.org/W2479365550","https://openalex.org/W2542482481","https://openalex.org/W2556597664","https://openalex.org/W2725016515","https://openalex.org/W2783859821","https://openalex.org/W2787248994","https://openalex.org/W2962761770","https://openalex.org/W2962922269","https://openalex.org/W2962941403","https://openalex.org/W2962999772","https://openalex.org/W2963174442","https://openalex.org/W2963443408","https://openalex.org/W2963877580","https://openalex.org/W2964003909","https://openalex.org/W2964130914","https://openalex.org/W2964262188","https://openalex.org/W2966545402","https://openalex.org/W3102206315","https://openalex.org/W3113425034","https://openalex.org/W4250954493","https://openalex.org/W6628955290","https://openalex.org/W6740380664","https://openalex.org/W6747969630"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2317200988","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278"],"abstract_inverted_index":{"Suppose":[0],"that":[1,108],"y":[2],"=":[3],"|Ax":[4],"<sub":[5,13,45,56,67,73,112,118,139,150],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[6,14,19,30,46,57,68,74,113,119,140,151],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</sub>":[7,15,47,58,114,152],"|":[8],"+":[9],"\u03b7":[10,26],"where":[11,148],"x":[12,44,55,111,149],"\u2208":[16,27],"R":[17,28],"<sup":[18,29],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d</sup>":[20],"is":[21,32,41,59,143,153],"the":[22,60,86,90,100,104,123,135,146,157,162,184,188,196,201,207],"target":[23],"signal":[24],"and":[25,168,176,205],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</sup>":[31],"a":[33,128],"noise":[34,185],"vector.":[35],"The":[36],"aim":[37],"of":[38,103,125,160,165,190,210],"phase":[39,166,211],"retrieval":[40,167],"to":[42],"estimate":[43],"from":[48],"y.":[49],"A":[50,126],"popular":[51],"model":[52,105],"for":[53,84,200,206],"estimating":[54],"nonlinear":[61,163,202,208],"least":[62,203],"squares":[63,204],"x\u0302":[64],":=":[65],"argmin":[66],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x</sub>":[69],"|||Ax|":[70],"-":[71,110],"y||":[72],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[75,120,141],".":[76],"One":[77],"has":[78],"already":[79],"developed":[80],"many":[81],"efficient":[82],"algorithms":[83],"solving":[85],"model,":[87],"such":[88],"as":[89],"seminal":[91],"error":[92,137],"reduction":[93],"algorithm.":[94],"In":[95],"this":[96],"paper,":[97],"we":[98,155,177],"present":[99],"estimation":[101,158],"performance":[102,159],"with":[106],"proving":[107],"||x\u0302":[109],"||":[115],"\u2272":[116],"||\u03b7||":[117,138],"/\u221am":[121,142],"under":[122],"assumption":[124],"being":[127],"Gaussian":[129],"random":[130],"matrix.":[131],"We":[132],"also":[133],"prove":[134],"reconstruction":[136],"sharp.":[144],"For":[145],"case":[147],"sparse,":[154],"study":[156],"both":[161],"Lasso":[164,209],"its":[169],"unconstrained":[170],"version.":[171],"Our":[172],"results":[173,194],"are":[174],"non-asymptotic,":[175],"do":[178],"not":[179],"assume":[180],"any":[181],"distribution":[182],"on":[183],"\u03b7.":[186],"To":[187],"best":[189],"our":[191,193],"knowledge,":[192],"represent":[195],"first":[197],"theoretical":[198],"guarantee":[199],"retrieval.":[212]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}