{"id":"https://openalex.org/W3128840397","doi":"https://doi.org/10.1109/tsp.2021.3128750","title":"Total Least Squares Phase Retrieval","display_name":"Total Least Squares Phase Retrieval","publication_year":2021,"publication_date":"2021-11-17","ids":{"openalex":"https://openalex.org/W3128840397","doi":"https://doi.org/10.1109/tsp.2021.3128750","mag":"3128840397"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2021.3128750","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3128750","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1109/tsp.2021.3128750","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026441591","display_name":"Sidharth Gupta","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sidharth Gupta","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, 14589 Urbana, Illinois, United States, (e-mail: gupta67@illinois.edu)","***University of Illinois at Urbana-Champaign"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, 14589 Urbana, Illinois, United States, (e-mail: gupta67@illinois.edu)","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"***University of Illinois at Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002015062","display_name":"Ivan Dokmani\u0107","orcid":"https://orcid.org/0000-0001-7132-5214"},"institutions":[{"id":"https://openalex.org/I1850255","display_name":"University of Basel","ror":"https://ror.org/02s6k3f65","country_code":"CH","type":"education","lineage":["https://openalex.org/I1850255"]},{"id":"https://openalex.org/I4210128905","display_name":"Department of Biomedicine Basel","ror":"https://ror.org/03ybx0x41","country_code":"CH","type":"facility","lineage":["https://openalex.org/I4210128905"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Ivan Dokmanic","raw_affiliation_strings":["University of Basel, 27209 Basel, Basel-Stadt, Switzerland, (e-mail: dokmanic@illinois.edu)","University of Basel"],"affiliations":[{"raw_affiliation_string":"University of Basel, 27209 Basel, Basel-Stadt, Switzerland, (e-mail: dokmanic@illinois.edu)","institution_ids":["https://openalex.org/I1850255","https://openalex.org/I4210128905"]},{"raw_affiliation_string":"University of Basel","institution_ids":["https://openalex.org/I1850255"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026441591"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01206065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":null,"first_page":"536","last_page":"549"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9934999942779541,"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/T11484","display_name":"Adaptive optics and wavefront sensing","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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":0.7511732578277588},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.6321885585784912},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6304876208305359},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6042791604995728},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5920695066452026},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.5588833093643188},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5235887765884399},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5231702923774719},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.48684948682785034},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4426463842391968},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32095223665237427},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2943534255027771},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16683071851730347},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12415805459022522},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07845452427864075},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07724446058273315},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.07277074456214905},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06996941566467285},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.06534844636917114}],"concepts":[{"id":"https://openalex.org/C81793267","wikidata":"https://www.wikidata.org/wiki/Q7180962","display_name":"Phase retrieval","level":3,"score":0.7511732578277588},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.6321885585784912},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6304876208305359},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6042791604995728},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5920695066452026},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5588833093643188},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5235887765884399},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5231702923774719},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.48684948682785034},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4426463842391968},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32095223665237427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2943534255027771},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16683071851730347},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12415805459022522},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07845452427864075},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07724446058273315},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.07277074456214905},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06996941566467285},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.06534844636917114},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tsp.2021.3128750","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3128750","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2102.00927","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.00927","pdf_url":"https://arxiv.org/pdf/2102.00927","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"raw_type":"text"},{"id":"mag:3128840397","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2102.00927","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2102.00927","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2102.00927","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article-journal"}],"best_oa_location":{"id":"doi:10.1109/tsp.2021.3128750","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3128750","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8888010212","display_name":null,"funder_award_id":"852821\u2014SWING","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W1484412996","https://openalex.org/W1569123050","https://openalex.org/W1972822190","https://openalex.org/W1984486973","https://openalex.org/W1997267293","https://openalex.org/W2008229822","https://openalex.org/W2015881065","https://openalex.org/W2075788737","https://openalex.org/W2078397124","https://openalex.org/W2090165180","https://openalex.org/W2098166499","https://openalex.org/W2102019642","https://openalex.org/W2103869034","https://openalex.org/W2115727068","https://openalex.org/W2128006912","https://openalex.org/W2142949395","https://openalex.org/W2144299910","https://openalex.org/W2156719288","https://openalex.org/W2158746276","https://openalex.org/W2162876243","https://openalex.org/W2167850383","https://openalex.org/W2268674159","https://openalex.org/W2396681965","https://openalex.org/W2505728881","https://openalex.org/W2542482481","https://openalex.org/W2556597664","https://openalex.org/W2602335281","https://openalex.org/W2617270682","https://openalex.org/W2728611525","https://openalex.org/W2772629285","https://openalex.org/W2795533044","https://openalex.org/W2913047553","https://openalex.org/W2947839108","https://openalex.org/W2962777112","https://openalex.org/W2962941403","https://openalex.org/W2962999772","https://openalex.org/W2963443408","https://openalex.org/W2963841451","https://openalex.org/W2963865165","https://openalex.org/W2964262188","https://openalex.org/W2970745190","https://openalex.org/W3010581177","https://openalex.org/W3044334322","https://openalex.org/W3045689010","https://openalex.org/W3102206315","https://openalex.org/W3129605435","https://openalex.org/W6638203984","https://openalex.org/W6725192724","https://openalex.org/W6735880944","https://openalex.org/W6764604022"],"related_works":["https://openalex.org/W2989714184","https://openalex.org/W2921467946","https://openalex.org/W1515418109","https://openalex.org/W2084510224","https://openalex.org/W3103668644","https://openalex.org/W2554330058","https://openalex.org/W2088743897","https://openalex.org/W2902086637","https://openalex.org/W2160651590","https://openalex.org/W2105464217","https://openalex.org/W2061517489","https://openalex.org/W2038221055","https://openalex.org/W3105974392","https://openalex.org/W3118768524","https://openalex.org/W3159343490","https://openalex.org/W2794361188","https://openalex.org/W2517388912","https://openalex.org/W2183568598","https://openalex.org/W2972089994","https://openalex.org/W3137674426"],"abstract_inverted_index":{"We":[0,34,63,131,145],"address":[1],"the":[2,9,31,42,47,69,73,91,94,102,112,129,148],"phase":[3,18,74,155],"retrieval":[4,19,75,156],"problem":[5,76],"with":[6,60,99],"errors":[7,29,40],"in":[8,30,41,56],"sensing":[10,43,103,166],"vectors.":[11],"A":[12],"number":[13],"of":[14,72,93,150],"recent":[15],"methods":[16],"for":[17],"are":[20],"based":[21],"on":[22,158],"least":[23,49],"squares":[24,50],"(LS)":[25],"formulations":[26],"which":[27,107,124,162],"assume":[28],"quadratic":[32],"measurements.":[33],"extend":[35],"this":[36],"approach":[37,152],"to":[38,80,101,110,134,141],"handle":[39],"vectors":[44,104],"by":[45,153],"adopting":[46],"total":[48],"(TLS)":[51],"framework":[52],"that":[53,136],"is":[54],"used":[55,79],"linear":[57],"inverse":[58],"problems":[59],"operator":[61],"errors.":[62,114,170],"show":[64],"how":[65],"gradient":[66],"descent":[67],"and":[68,84,96,105,168],"specific":[70],"geometry":[71],"can":[77,139],"be":[78],"obtain":[81],"a":[82],"simple":[83],"efficient":[85],"TLS":[86,95],"solution.":[87],"Additionally,":[88],"we":[89,120],"derive":[90],"gradients":[92],"LS":[97],"solutions":[98],"respect":[100],"measurements":[106],"enables":[108],"us":[109],"calculate":[111],"solution":[113],"By":[115],"analyzing":[116],"these":[117],"error":[118],"expressions":[119],"determine":[121],"conditions":[122],"under":[123],"each":[125],"method":[126,138],"should":[127],"outperform":[128],"other.":[130],"run":[132],"simulations":[133],"demonstrate":[135,147],"our":[137,151],"lead":[140],"more":[142],"accurate":[143],"solutions.":[144],"further":[146],"effectiveness":[149],"performing":[154],"experiments":[157],"real":[159],"optical":[160],"hardware":[161],"naturally":[163],"contains":[164],"both":[165],"vector":[167],"measurement":[169]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}