{"id":"https://openalex.org/W2543875952","doi":"https://doi.org/10.1109/tit.2018.2800768","title":"PhaseMax: Convex Phase Retrieval via Basis Pursuit","display_name":"PhaseMax: Convex Phase Retrieval via Basis Pursuit","publication_year":2018,"publication_date":"2018-02-01","ids":{"openalex":"https://openalex.org/W2543875952","doi":"https://doi.org/10.1109/tit.2018.2800768","mag":"2543875952"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2800768","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2800768","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1610.07531","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060687985","display_name":"Tom Goldstein","orcid":"https://orcid.org/0000-0003-1660-9307"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tom Goldstein","raw_affiliation_strings":["Department of Computer Science, University of Maryland at College Park, College Park, MD, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Maryland at College Park, College Park, MD, USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083617223","display_name":"Christoph Studer","orcid":"https://orcid.org/0000-0001-8950-6267"},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christoph Studer","raw_affiliation_strings":["School of Electrical and Computer Engineering, Cornell University, Ithaca, NY, USA","School of Electrical and Computer Engineering Cornell University Ithaca, NY USA"],"raw_orcid":"https://orcid.org/0000-0001-8950-6267","affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, Cornell University, Ithaca, NY, USA","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"School of Electrical and Computer Engineering Cornell University Ithaca, NY USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.2965,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.94670533,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"64","issue":"4","first_page":"2675","last_page":"2689"},"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":0.9753000140190125,"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/T12549","display_name":"Image and Object Detection Techniques","score":0.9563999772071838,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/phase-retrieval","display_name":"Phase retrieval","score":0.9187492728233337},{"id":"https://openalex.org/keywords/basis-pursuit","display_name":"Basis pursuit","score":0.8110923767089844},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6857945322990417},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.6082250475883484},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5803643465042114},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5741354823112488},{"id":"https://openalex.org/keywords/lift","display_name":"Lift (data mining)","score":0.5463935732841492},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5156237483024597},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5112175941467285},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.499523401260376},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4808867275714874},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.4431689977645874},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4320308566093445},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3852558434009552},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.2534840404987335},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.1581154763698578},{"id":"https://openalex.org/keywords/matching-pursuit","display_name":"Matching pursuit","score":0.09276178479194641},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08801618218421936},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08755171298980713}],"concepts":[{"id":"https://openalex.org/C81793267","wikidata":"https://www.wikidata.org/wiki/Q7180962","display_name":"Phase retrieval","level":3,"score":0.9187492728233337},{"id":"https://openalex.org/C99217422","wikidata":"https://www.wikidata.org/wiki/Q4867576","display_name":"Basis pursuit","level":4,"score":0.8110923767089844},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6857945322990417},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.6082250475883484},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5803643465042114},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5741354823112488},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.5463935732841492},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5156237483024597},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5112175941467285},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.499523401260376},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4808867275714874},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.4431689977645874},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4320308566093445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3852558434009552},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.2534840404987335},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.1581154763698578},{"id":"https://openalex.org/C156872377","wikidata":"https://www.wikidata.org/wiki/Q6786281","display_name":"Matching pursuit","level":3,"score":0.09276178479194641},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08801618218421936},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08755171298980713},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/tit.2018.2800768","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2800768","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"},{"id":"pmh:oai:arXiv.org:1610.07531","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.07531","pdf_url":"https://arxiv.org/pdf/1610.07531","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":"mag:2543875952","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1610.07531.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:www.research-collection.ethz.ch:20.500.11850/454766","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11850/454766","pdf_url":null,"source":{"id":"https://openalex.org/S4306402302","display_name":"Repository for Publications and Research Data (ETH Zurich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35440088","host_organization_name":"ETH Zurich","host_organization_lineage":["https://openalex.org/I35440088"],"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":"IEEE Transactions on Information Theory, 64 (4)","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1610.07531","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1610.07531","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"},{"id":"doi:10.3929/ethz-b-000454766","is_oa":true,"landing_page_url":"https://doi.org/10.3929/ethz-b-000454766","pdf_url":null,"source":{"id":"https://openalex.org/S7407051236","display_name":"ETH Z\u00fcrich Research Collection","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"pmh:oai:arXiv.org:1610.07531","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.07531","pdf_url":"https://arxiv.org/pdf/1610.07531","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/G1108935830","display_name":null,"funder_award_id":"CCF-1535897","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1432546747","display_name":null,"funder_award_id":"CNS-1717559","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1722586140","display_name":null,"funder_award_id":"N00014-17-1-2078","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G2069698457","display_name":null,"funder_award_id":"CCF-1535902","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3105170327","display_name":null,"funder_award_id":"CAREER CCF-1652065","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7968611072","display_name":null,"funder_award_id":"ECCS-1408006","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":62,"referenced_works":["https://openalex.org/W1484412996","https://openalex.org/W1503503090","https://openalex.org/W1572529050","https://openalex.org/W1604923712","https://openalex.org/W1871489475","https://openalex.org/W1971664455","https://openalex.org/W1999834501","https://openalex.org/W2001613283","https://openalex.org/W2002182974","https://openalex.org/W2007593159","https://openalex.org/W2016689169","https://openalex.org/W2022072902","https://openalex.org/W2034424857","https://openalex.org/W2040310239","https://openalex.org/W2050565643","https://openalex.org/W2055758906","https://openalex.org/W2070309911","https://openalex.org/W2076261573","https://openalex.org/W2078204800","https://openalex.org/W2078397124","https://openalex.org/W2087483236","https://openalex.org/W2097132843","https://openalex.org/W2102019642","https://openalex.org/W2142949395","https://openalex.org/W2145080587","https://openalex.org/W2146738285","https://openalex.org/W2169501582","https://openalex.org/W2255081686","https://openalex.org/W2294690908","https://openalex.org/W2316383984","https://openalex.org/W2344240472","https://openalex.org/W2542482481","https://openalex.org/W2565094322","https://openalex.org/W2593262341","https://openalex.org/W2593282843","https://openalex.org/W2602335281","https://openalex.org/W2625441823","https://openalex.org/W2698354080","https://openalex.org/W2741276442","https://openalex.org/W2744864415","https://openalex.org/W2747009740","https://openalex.org/W2761315682","https://openalex.org/W2962761770","https://openalex.org/W2962880913","https://openalex.org/W2963095544","https://openalex.org/W2963443408","https://openalex.org/W2963673760","https://openalex.org/W2963841451","https://openalex.org/W2964201439","https://openalex.org/W2964317660","https://openalex.org/W3098696827","https://openalex.org/W3100158133","https://openalex.org/W3113425034","https://openalex.org/W3115592686","https://openalex.org/W4243472923","https://openalex.org/W6608805005","https://openalex.org/W6628955290","https://openalex.org/W6683110664","https://openalex.org/W6697419950","https://openalex.org/W6728487739","https://openalex.org/W6735880944","https://openalex.org/W6741657828"],"related_works":["https://openalex.org/W2007593159","https://openalex.org/W2078397124","https://openalex.org/W1484412996","https://openalex.org/W2533223407","https://openalex.org/W2951840367","https://openalex.org/W2145080587","https://openalex.org/W2963443408","https://openalex.org/W2542482481","https://openalex.org/W2962941403","https://openalex.org/W3113425034","https://openalex.org/W2965497096","https://openalex.org/W2593299318","https://openalex.org/W2962999772","https://openalex.org/W2470746288","https://openalex.org/W2167850383","https://openalex.org/W2963841451","https://openalex.org/W2169501582","https://openalex.org/W2015911499","https://openalex.org/W3102206315","https://openalex.org/W2044613770"],"abstract_inverted_index":{"We":[0,17,60,88,119],"consider":[1],"the":[2,40,56,63,74,94,110,116,125,134],"recovery":[3,129],"of":[4,97,103,112,127,138],"a":[5,22,45,50,100],"(real-":[6],"or":[7],"complex-valued)":[8],"signal":[9,58,86],"from":[10],"magnitude-only":[11],"measurements,":[12],"known":[13],"as":[14,21],"phase":[15,19,41,75],"retrieval.":[16],"formulate":[18],"retrieval":[20,42,76],"convex":[23,32],"optimization":[24],"problem,":[25],"which":[26,71],"we":[27,108,132],"call":[28],"PhaseMax.":[29],"Unlike":[30],"other":[31],"methods":[33],"that":[34,53,62,73],"use":[35,120],"semidefinite":[36],"relaxation":[37,52],"and":[38,107,131,136],"lift":[39],"problem":[43,65],"to":[44,66,123],"higher":[46],"dimension,":[47],"PhaseMax":[48,67,98,139],"is":[49,68],"\u201cnon-lifting\u201d":[51],"operates":[54],"in":[55,140],"original":[57],"dimension.":[59],"show":[61],"dual":[64],"basis":[69],"pursuit,":[70],"implies":[72],"can":[77],"be":[78],"performed":[79],"using":[80],"algorithms":[81],"initially":[82],"designed":[83],"for":[84,99],"sparse":[85],"recovery.":[87],"develop":[89],"sharp":[90],"lower":[91],"bounds":[92],"on":[93,115],"success":[95],"probability":[96],"broad":[101],"range":[102],"random":[104],"measurement":[105,113],"ensembles,":[106],"analyze":[109],"impact":[111],"noise":[114],"solution":[117],"accuracy.":[118],"numerical":[121],"results":[122],"demonstrate":[124],"accuracy":[126],"our":[128],"guarantees,":[130],"showcase":[133],"efficacy":[135],"limits":[137],"practice.":[141]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":5}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}