{"id":"https://openalex.org/W2516450583","doi":"https://doi.org/10.1137/16m1107747","title":"Phase Retrieval by Linear Algebra","display_name":"Phase Retrieval by Linear Algebra","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2516450583","doi":"https://doi.org/10.1137/16m1107747","mag":"2516450583"},"language":"en","primary_location":{"id":"doi:10.1137/16m1107747","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1107747","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","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/A5066475581","display_name":"Pengwen Chen","orcid":"https://orcid.org/0000-0002-4586-0552"},"institutions":[{"id":"https://openalex.org/I162838928","display_name":"National Chung Hsing University","ror":"https://ror.org/05vn3ca78","country_code":"TW","type":"education","lineage":["https://openalex.org/I162838928"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Pengwen Chen","raw_affiliation_strings":["National Chung-Hsing University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Chung-Hsing University","institution_ids":["https://openalex.org/I162838928"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048863527","display_name":"Albert Fannjiang","orcid":"https://orcid.org/0000-0003-3150-7392"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Albert Fannjiang","raw_affiliation_strings":["University Of California at Davis#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University Of California at Davis#TAB#","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076871780","display_name":"Gi-Ren Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Gi-Ren Liu","raw_affiliation_strings":["Department of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3186,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.77554412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"38","issue":"3","first_page":"854","last_page":"868"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9994000196456909,"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":0.9994000196456909,"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/T12039","display_name":"Electron and X-Ray Spectroscopy Techniques","score":0.975600004196167,"subfield":{"id":"https://openalex.org/subfields/2508","display_name":"Surfaces, Coatings and Films"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11733","display_name":"X-ray Spectroscopy and Fluorescence Analysis","score":0.9710999727249146,"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/mathematics","display_name":"Mathematics","score":0.7715851068496704},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.6702367663383484},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.6133933067321777},{"id":"https://openalex.org/keywords/phase-retrieval","display_name":"Phase retrieval","score":0.43681207299232483},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3040594458580017},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1568424105644226},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10399740934371948},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.09963792562484741}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7715851068496704},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.6702367663383484},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.6133933067321777},{"id":"https://openalex.org/C81793267","wikidata":"https://www.wikidata.org/wiki/Q7180962","display_name":"Phase retrieval","level":3,"score":0.43681207299232483},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3040594458580017},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1568424105644226},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10399740934371948},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.09963792562484741}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/16m1107747","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1107747","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt21s181hr","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/21s181hr","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},{"id":"pmh:qt21s181hr","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/21s181hr","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Chen, P.; Fannjiang, A.; &amp; Liu, G.(2016). Phase Retrieval by Linear Algebra. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/21s181hr","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3965903348","display_name":null,"funder_award_id":"DMS-1413373","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5896609232","display_name":null,"funder_award_id":"U01-HL-114494","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G8585686639","display_name":null,"funder_award_id":"103-2115-M-005-006-MY2","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2007593159","https://openalex.org/W2015911499","https://openalex.org/W2142949395","https://openalex.org/W2151603300","https://openalex.org/W2963443408","https://openalex.org/W3102756287"],"related_works":["https://openalex.org/W4285303061","https://openalex.org/W2525488343","https://openalex.org/W622366405","https://openalex.org/W616292901","https://openalex.org/W2477677129","https://openalex.org/W2378563121","https://openalex.org/W2383666998","https://openalex.org/W2358786979","https://openalex.org/W4285299162","https://openalex.org/W2388645548"],"abstract_inverted_index":{"The":[0],"null":[1,53],"vector":[2,46,54],"method,":[3],"based":[4],"on":[5],"a":[6,34,58],"simple":[7],"linear":[8],"algebraic":[9],"concept,":[10],"is":[11,38],"proposed":[12],"as":[13],"an":[14],"initialization":[15],"method":[16,55],"for":[17,61],"nonconvex":[18],"approaches":[19],"to":[20],"the":[21,26,44,52,62],"phase":[22],"retrieval":[23],"problem.":[24],"For":[25],"stylized":[27],"measurement":[28,64],"with":[29],"random":[30],"complex":[31],"Gaussian":[32],"matrices,":[33],"nonasymptotic":[35],"error":[36],"bound":[37],"derived,":[39],"stronger":[40],"than":[41],"that":[42,51],"of":[43,65],"spectral":[45],"method.":[47],"Numerical":[48],"experiments":[49],"show":[50],"also":[56],"has":[57],"superior":[59],"performance":[60],"realistic":[63],"coded":[66],"diffraction":[67],"patterns":[68],"in":[69],"coherent":[70],"diffractive":[71],"imaging.":[72]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
