{"id":"https://openalex.org/W3013665705","doi":"https://doi.org/10.1137/19m1266800","title":"Phase Retrieval with Sparse Phase Constraint","display_name":"Phase Retrieval with Sparse Phase Constraint","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3013665705","doi":"https://doi.org/10.1137/19m1266800","mag":"3013665705"},"language":"en","primary_location":{"id":"doi:10.1137/19m1266800","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1266800","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.1137/19m1266800","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041128611","display_name":"Nguyen Hieu Thao","orcid":"https://orcid.org/0000-0002-1455-9169"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nguyen Hieu Thao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103799880","display_name":"David Luke","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Russell Luke","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043974426","display_name":"Oleg Soloviev","orcid":"https://orcid.org/0000-0003-3761-9192"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Oleg Soloviev","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003504954","display_name":"Michel Verhaegen","orcid":"https://orcid.org/0000-0002-7967-6884"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michel Verhaegen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5041128611"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0611,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.86148795,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"2","issue":"1","first_page":"246","last_page":"263"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9736999869346619,"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":0.963699996471405,"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":0.8795055150985718},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5315929055213928},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.47850361466407776},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47554466128349304},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.45675429701805115},{"id":"https://openalex.org/keywords/ptychography","display_name":"Ptychography","score":0.4394886791706085},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4358898103237152},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.42890509963035583},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38149070739746094},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3607586622238159},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.3127484917640686},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.1640482246875763}],"concepts":[{"id":"https://openalex.org/C81793267","wikidata":"https://www.wikidata.org/wiki/Q7180962","display_name":"Phase retrieval","level":3,"score":0.8795055150985718},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5315929055213928},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.47850361466407776},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47554466128349304},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.45675429701805115},{"id":"https://openalex.org/C78153596","wikidata":"https://www.wikidata.org/wiki/Q7257147","display_name":"Ptychography","level":3,"score":0.4394886791706085},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4358898103237152},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.42890509963035583},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38149070739746094},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3607586622238159},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3127484917640686},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.1640482246875763},{"id":"https://openalex.org/C207114421","wikidata":"https://www.wikidata.org/wiki/Q133900","display_name":"Diffraction","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/19m1266800","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1266800","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},{"id":"pmh:oai:publications.goettingen-research-online.de:2/136143","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/136143","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1137/19m1266800","is_oa":true,"landing_page_url":"https://doi.org/10.1137/19m1266800","pdf_url":null,"source":{"id":"https://openalex.org/S4210229561","display_name":"SIAM Journal on Mathematics of Data Science","issn_l":"2577-0187","issn":["2577-0187"],"is_oa":true,"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 Mathematics of Data Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1624849245","display_name":null,"funder_award_id":"G-1253-304.6","funder_id":"https://openalex.org/F4320320947","funder_display_name":"German-Israeli Foundation for Scientific Research and Development"},{"id":"https://openalex.org/G5131799134","display_name":null,"funder_award_id":"N_ 339681","funder_id":"https://openalex.org/F4320333065","funder_display_name":"Seventh Framework Programme"},{"id":"https://openalex.org/G5418744004","display_name":null,"funder_award_id":"SFB755","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320947","display_name":"German-Israeli Foundation for Scientific Research and Development","ror":"https://ror.org/00tntzp09"},{"id":"https://openalex.org/F4320333065","display_name":"Seventh Framework Programme","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1484412996","https://openalex.org/W1573659356","https://openalex.org/W1973453651","https://openalex.org/W2001613283","https://openalex.org/W2007593159","https://openalex.org/W2015911499","https://openalex.org/W2038998663","https://openalex.org/W2045286779","https://openalex.org/W2090132301","https://openalex.org/W2092759407","https://openalex.org/W2107479212","https://openalex.org/W2108078415","https://openalex.org/W2132509202","https://openalex.org/W2146166532","https://openalex.org/W2171505904","https://openalex.org/W2279871042","https://openalex.org/W2396782186","https://openalex.org/W2555812794","https://openalex.org/W2593708037","https://openalex.org/W2742629770","https://openalex.org/W2898569439","https://openalex.org/W2964142159","https://openalex.org/W3099645558","https://openalex.org/W3102647677","https://openalex.org/W3102670984","https://openalex.org/W3102690314","https://openalex.org/W3104613222","https://openalex.org/W3143835353"],"related_works":["https://openalex.org/W2255820492","https://openalex.org/W4318484046","https://openalex.org/W4313500194","https://openalex.org/W3205663665","https://openalex.org/W3129005624","https://openalex.org/W2976010825","https://openalex.org/W4311544914","https://openalex.org/W1966115495","https://openalex.org/W2055033105","https://openalex.org/W4321641255"],"abstract_inverted_index":{"In":[0,131,303],"this":[1,132,231,250,342],"paper,":[2,133],"we":[3,134,253,283,355],"propose":[4,135,254],"and":[5,46,119,190,282,379],"investigate":[6],"the":[7,12,17,51,59,70,77,80,83,86,90,93,96,108,143,151,161,166,170,175,184,225,237,260,268,272,290,293,298,306,312,320,327,337,345,352,360,370,382,387],"phase":[8,18,52,173,264],"retrieval":[9],"problem":[10,64,270],"with":[11,297],"a":[13,24,55,102,136,157,199],"priori":[14],"constraint":[15,145,246],"that":[16,183,214,230],"is":[19,65,98,121,154,182,187,207,233,280,289,323],"sparse":[20,71,111],"(SPR),":[21],"which":[22,75,140,221],"encompasses":[23],"number":[25],"of":[26,58,79,85,92,110,146,160,168,204,213,227,292,305,336,351,381],"practical":[27],"applications,":[28],"for":[29,124,129,242,267,315,330,344,359,369,386],"instance,":[30],"in":[31,38,41,47,107,194,271,341],"characterizing":[32],"phase-only":[33],"objects":[34],"such":[35],"as":[36],"microlenses,":[37],"phase-contrast":[39],"microscopy,":[40,45],"optical":[42],"path":[43],"difference":[44],"Fourier":[48],"ptychography,":[49],"where":[50,275],"object":[53],"occupies":[54],"small":[56],"portion":[57],"whole":[60],"field.":[61],"The":[62,148,178,287],"considered":[63],"strictly":[66],"more":[67],"general":[68,195],"than":[69],"signal":[72,81,87,112,164],"recovery":[73,113],"problem,":[74],"assumes":[76],"sparsity":[78,84,91,144,176,261],"because":[82],"trivially":[88],"implies":[89],"phase,":[94],"but":[95],"converse":[97],"not":[99,188,197],"true.":[100],"As":[101],"result,":[103,252],"existing":[104],"solution":[105,127,257,384],"algorithms":[106],"literature":[109],"cannot":[114],"be":[115,326],"applied":[116],"to":[117,155,208,218,224,311,325],"SPR":[118,269,388],"there":[120],"an":[122,210,255,316,331],"appeal":[123],"developing":[125],"new":[126,137,251],"methods":[128],"it.":[130],"regularization":[138,262],"scheme":[139],"efficiently":[141],"captures":[142],"SPR.":[147,228],"idea":[149],"behind":[150],"proposed":[152,383],"approach":[153,385],"perform":[156],"metric":[158],"projection":[159,299,314,329,372],"current":[162],"estimated":[163],"onto":[165,244],"set":[167,186],"all":[169],"signals":[171],"whose":[172],"satisfies":[174],"constraint.":[177],"main":[179],"challenge":[180],"here":[181],"latter":[185],"convex":[189],"its":[191,285],"associated":[192,317,332],"projector":[193,215],"does":[196],"admit":[198],"closed":[200],"form.":[201],"One":[202],"novelty":[203],"our":[205,365],"analysis":[206],"establish":[209],"explicit":[211],"form":[212,241],"when":[216],"restricted":[217],"those":[219],"points":[220],"are":[222],"relevant":[223],"solutions":[226],"Note":[229],"result":[232],"fundamentally":[234],"different":[235],"from":[236],"widely":[238],"known":[239],"calculation":[240],"projections":[243],"intensity":[245],"sets.":[247],"Based":[248],"on":[249,263,364],"efficient":[256],"method,":[258],"named":[259],"(SROP)":[265],"algorithm,":[266],"challenging":[273],"setting":[274],"only":[276],"one":[277,335],"point-spread-function":[278],"image":[279],"given,":[281],"analyze":[284],"convergence.":[286],"algorithm":[288,296,308,322,362],"combination":[291],"Gerchberg--Saxton":[294],"(GS)":[295],"step":[300],"described":[301],"above.":[302],"view":[304],"GS":[307],"being":[309,339],"equivalent":[310],"alternating":[313],"two-set":[318],"feasibility,":[319,334],"SROP":[321,361],"shown":[324],"cyclic":[328,371],"three-set":[333],"sets":[338],"analyzed":[340],"paper":[343],"first":[346],"time.":[347],"Analyzing":[348],"regularity":[349],"properties":[350],"involved":[353],"sets,":[354],"obtain":[356],"convergence":[357,367],"results":[358,375],"based":[363],"recent":[366],"theory":[368],"method.":[373],"Numerical":[374],"show":[376],"clear":[377],"effectiveness":[378],"efficiency":[380],"problem.":[389]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}