{"id":"https://openalex.org/W2077458714","doi":"https://doi.org/10.1109/lsp.2015.2393295","title":"Sparse Signal Recovery from a Mixture of Linear and Magnitude-Only Measurements","display_name":"Sparse Signal Recovery from a Mixture of Linear and Magnitude-Only Measurements","publication_year":2015,"publication_date":"2015-01-15","ids":{"openalex":"https://openalex.org/W2077458714","doi":"https://doi.org/10.1109/lsp.2015.2393295","mag":"2077458714","pmid":"https://pubmed.ncbi.nlm.nih.gov/29187781"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2015.2393295","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2393295","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5703438","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044571053","display_name":"Mehmet Ak\u00e7akaya","orcid":"https://orcid.org/0000-0001-6400-7736"},"institutions":[{"id":"https://openalex.org/I1316535847","display_name":"Beth Israel Deaconess Medical Center","ror":"https://ror.org/04drvxt59","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I1316535847"]},{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mehmet Akcakaya","raw_affiliation_strings":["Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA, 02215","Beth Israel Deaconess Medical Center, Harvard Medical School, Boston,#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA, 02215","institution_ids":["https://openalex.org/I1316535847","https://openalex.org/I136199984"]},{"raw_affiliation_string":"Beth Israel Deaconess Medical Center, Harvard Medical School, Boston,#TAB#","institution_ids":["https://openalex.org/I1316535847"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020766546","display_name":"Vahid Tarokh","orcid":"https://orcid.org/0000-0003-2994-6302"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vahid Tarokh","raw_affiliation_strings":["School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138","[School of Engineering and Applied Sciences, Harvard University, Cambridge]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138","institution_ids":["https://openalex.org/I136199984"]},{"raw_affiliation_string":"[School of Engineering and Applied Sciences, Harvard University, Cambridge]","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2625,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.86611503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","issue":"9","first_page":"1220","last_page":"1223"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/magnitude","display_name":"Magnitude (astronomy)","score":0.8367059230804443},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.6210578083992004},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5038112998008728},{"id":"https://openalex.org/keywords/signal-recovery","display_name":"Signal recovery","score":0.4695606529712677},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.43429094552993774},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42052823305130005},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.3017949163913727},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28365930914878845},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22708278894424438}],"concepts":[{"id":"https://openalex.org/C126691448","wikidata":"https://www.wikidata.org/wiki/Q2028919","display_name":"Magnitude (astronomy)","level":2,"score":0.8367059230804443},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.6210578083992004},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5038112998008728},{"id":"https://openalex.org/C2989281035","wikidata":"https://www.wikidata.org/wiki/Q120811","display_name":"Signal recovery","level":3,"score":0.4695606529712677},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.43429094552993774},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42052823305130005},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.3017949163913727},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28365930914878845},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22708278894424438},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"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":3,"locations":[{"id":"doi:10.1109/lsp.2015.2393295","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2393295","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmid:29187781","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29187781","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE signal processing letters","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:5703438","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5703438","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Signal Process Lett","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:pubmedcentral.nih.gov:5703438","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/5703438","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Signal Process Lett","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3289031096","display_name":null,"funder_award_id":"K99 HL111410","funder_id":"https://openalex.org/F4320337338","funder_display_name":"National Heart, Lung, and Blood Institute"},{"id":"https://openalex.org/G3607392662","display_name":null,"funder_award_id":"K99HL111410-01","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"}],"funders":[{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337338","display_name":"National Heart, Lung, and Blood Institute","ror":"https://ror.org/012pb6c26"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W340244495","https://openalex.org/W1516029860","https://openalex.org/W1530154714","https://openalex.org/W2003959193","https://openalex.org/W2015418199","https://openalex.org/W2031197045","https://openalex.org/W2044613770","https://openalex.org/W2055191162","https://openalex.org/W2078397124","https://openalex.org/W2101675075","https://openalex.org/W2104357403","https://openalex.org/W2105320739","https://openalex.org/W2129569662","https://openalex.org/W2129835277","https://openalex.org/W2140122025","https://openalex.org/W2141116650","https://openalex.org/W2145096794","https://openalex.org/W2145395365","https://openalex.org/W2155309907","https://openalex.org/W2156719288","https://openalex.org/W2164452299","https://openalex.org/W2167850383","https://openalex.org/W2296616510","https://openalex.org/W2499720122","https://openalex.org/W2962914151","https://openalex.org/W2963174442","https://openalex.org/W3100106241","https://openalex.org/W3105972983","https://openalex.org/W4250955649","https://openalex.org/W4293776140","https://openalex.org/W6651127572","https://openalex.org/W6670582991","https://openalex.org/W6683195263"],"related_works":["https://openalex.org/W4310919954","https://openalex.org/W2524358345","https://openalex.org/W2307530626","https://openalex.org/W1500257147","https://openalex.org/W2963863258","https://openalex.org/W2041636092","https://openalex.org/W1593605725","https://openalex.org/W2105702309","https://openalex.org/W2951235295","https://openalex.org/W2049381880"],"abstract_inverted_index":{"We":[0,64],"consider":[1],"the":[2,60,97,100],"problem":[3],"of":[4,12,85,102],"exact":[5],"sparse":[6],"signal":[7,20],"recovery":[8],"from":[9],"a":[10,83],"combination":[11],"linear":[13,103],"and":[14,33,46,57,104],"magnitude-only":[15,105],"(phaseless)":[16],"measurements.":[17,106],"A":[18],"k-sparse":[19,93],"x":[21,94],"\u2208":[22,40,48],"\u2102":[23,41,49],"<sup":[24,42,50],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[25,43,51,70,76],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[26],"is":[27,59],"measured":[28],"as":[29],"r":[30],"=":[31,35],"Bx":[32],"y":[34],"|Cx":[36],"|,":[37],"where":[38],"B":[39],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m1":[44],"\u00d7n</sup>":[45,53],"C":[47],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m2":[52],"are":[54,88],"measurement":[55],"matrices":[56],"|\u00b7|":[58],"element-wise":[61],"absolute":[62],"value.":[63],"show":[65],"that":[66],"if":[67],"max(2m":[68],"<sub":[69,75],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[71],",1)":[72],"+":[73],"m":[74],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[77],"\u2265":[78],"4k":[79],"-":[80],"1,":[81],"then":[82],"set":[84],"generic":[86],"measurements":[87],"sufficient":[89],"to":[90],"recover":[91],"every":[92],"exactly,":[95],"establishing":[96],"trade-off":[98],"between":[99],"number":[101]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}