{"id":"https://openalex.org/W2938195624","doi":"https://doi.org/10.1109/icassp.2019.8682357","title":"Solving Quadratic Equations via Amplitude-based Nonconvex Optimization","display_name":"Solving Quadratic Equations via Amplitude-based Nonconvex Optimization","publication_year":2019,"publication_date":"2019-04-17","ids":{"openalex":"https://openalex.org/W2938195624","doi":"https://doi.org/10.1109/icassp.2019.8682357","mag":"2938195624"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2019.8682357","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2019.8682357","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-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/A5091017120","display_name":"Vincent Monardo","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vincent Monardo","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003913140","display_name":"Yuanxin Li","orcid":"https://orcid.org/0000-0002-3418-5811"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuanxin Li","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053809095","display_name":"Yuejie Chi","orcid":"https://orcid.org/0000-0002-6766-5459"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuejie Chi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.595,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6831008,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"18","issue":null,"first_page":"5526","last_page":"5530"},"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":0.9976000189781189,"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/T11897","display_name":"Digital Holography and Microscopy","score":0.9894000291824341,"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/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.6646578311920166},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6099278926849365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5534932613372803},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.527588427066803},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5262600183486938},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.503210723400116},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.49826979637145996},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45903539657592773},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4272095561027527},{"id":"https://openalex.org/keywords/phase-retrieval","display_name":"Phase retrieval","score":0.4263143539428711},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.42350366711616516},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4132627844810486},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37497398257255554},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3267049193382263},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.18611007928848267},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.14185813069343567},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.09026730060577393}],"concepts":[{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.6646578311920166},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6099278926849365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5534932613372803},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.527588427066803},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5262600183486938},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.503210723400116},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.49826979637145996},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45903539657592773},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4272095561027527},{"id":"https://openalex.org/C81793267","wikidata":"https://www.wikidata.org/wiki/Q7180962","display_name":"Phase retrieval","level":3,"score":0.4263143539428711},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.42350366711616516},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4132627844810486},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37497398257255554},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3267049193382263},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18611007928848267},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.14185813069343567},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.09026730060577393},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icassp.2019.8682357","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2019.8682357","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1484412996","https://openalex.org/W2007593159","https://openalex.org/W2015911499","https://openalex.org/W2078397124","https://openalex.org/W2091369174","https://openalex.org/W2133105246","https://openalex.org/W2142949395","https://openalex.org/W2145080587","https://openalex.org/W2286769582","https://openalex.org/W2296832563","https://openalex.org/W2511406830","https://openalex.org/W2542482481","https://openalex.org/W2619650408","https://openalex.org/W2768927505","https://openalex.org/W2783859821","https://openalex.org/W2804871173","https://openalex.org/W2806105434","https://openalex.org/W2913806414","https://openalex.org/W2963389324","https://openalex.org/W2963849841","https://openalex.org/W2963865165","https://openalex.org/W2963945345","https://openalex.org/W2964256664","https://openalex.org/W2964262188","https://openalex.org/W2969215180","https://openalex.org/W3017118217","https://openalex.org/W3098494111","https://openalex.org/W3102206315","https://openalex.org/W3123272904","https://openalex.org/W6608805005","https://openalex.org/W6628955290","https://openalex.org/W6697511018","https://openalex.org/W6738499299","https://openalex.org/W6745725969","https://openalex.org/W6747969630","https://openalex.org/W6748269070","https://openalex.org/W6752014180","https://openalex.org/W6752302144","https://openalex.org/W6766302334","https://openalex.org/W6767371102","https://openalex.org/W6789140773"],"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/W2041416246","https://openalex.org/W3020853991","https://openalex.org/W3035836947"],"abstract_inverted_index":{"In":[0],"many":[1],"signal":[2],"processing":[3],"tasks,":[4],"one":[5],"seeks":[6],"to":[7,27,56,62],"recover":[8],"an":[9],"rcolumn":[10],"matrix":[11],"object":[12],"X":[13],"\u03f5":[14],"\u2102":[15],"<sup":[16],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[17],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n\u00d7r</sup>":[18],"from":[19],"a":[20,67],"set":[21],"of":[22,70,101,140],"nonnegative":[23],"quadratic":[24,114],"measurements":[25],"up":[26],"orthonormal":[28],"transforms.":[29],"Example":[30],"applications":[31],"include":[32],"coherence":[33],"retrieval":[34],"in":[35,72,104],"optical":[36],"imaging":[37],"and":[38,60,125,133],"covariance":[39],"sketching":[40],"for":[41,76],"high-dimensional":[42],"streaming":[43],"data.":[44],"To":[45],"this":[46,105],"end,":[47],"efficient":[48],"nonconvex":[49,74],"optimization":[50],"methods":[51,75],"are":[52],"quite":[53],"appealing,":[54],"due":[55],"their":[57,131],"computational":[58,132],"efficiency":[59],"scalability":[61],"large-scale":[63],"problems.":[64],"There":[65],"is":[66],"recent":[68],"surge":[69],"activities":[71],"designing":[73],"the":[77,93,99,113,137],"special":[78],"case":[79],"r":[80],"=":[81],"1,":[82],"known":[83],"as":[84],"phase":[85,102],"retrieval;":[86],"however,":[87],"very":[88],"little":[89],"work":[90],"has":[91],"studied":[92],"general":[94],"rank-r":[95],"setting.":[96],"Motivated":[97],"by":[98],"success":[100],"retrieval,":[103],"paper":[106],"we":[107],"derive":[108],"several":[109],"algorithms":[110],"which":[111],"utilize":[112],"loss":[115],"function":[116],"based":[117],"on":[118],"amplitude":[119],"measurements,":[120],"including":[121],"(stochastic)":[122],"gradient":[123,142],"descent":[124,143],"alternating":[126],"minimization.":[127],"Numerical":[128],"experiments":[129],"demonstrate":[130],"statistical":[134],"performances,":[135],"highlighting":[136],"superior":[138],"performance":[139],"stochastic":[141],"with":[144],"appropriate":[145],"mini-batch":[146],"sizes.":[147]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
