{"id":"https://openalex.org/W2592585592","doi":"https://doi.org/10.1109/tit.2017.2679053","title":"R-FFAST: A Robust Sub-Linear Time Algorithm for Computing a Sparse DFT","display_name":"R-FFAST: A Robust Sub-Linear Time Algorithm for Computing a Sparse DFT","publication_year":2017,"publication_date":"2017-03-07","ids":{"openalex":"https://openalex.org/W2592585592","doi":"https://doi.org/10.1109/tit.2017.2679053","mag":"2592585592"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2679053","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2679053","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":["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/A5030647153","display_name":"Sameer Pawar","orcid":"https://orcid.org/0000-0001-8954-7747"},"institutions":[{"id":"https://openalex.org/I1343180700","display_name":"Intel (United States)","ror":"https://ror.org/01ek73717","country_code":"US","type":"company","lineage":["https://openalex.org/I1343180700"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sameer Pawar","raw_affiliation_strings":["Intel, Santa Clara, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-8954-7747","affiliations":[{"raw_affiliation_string":"Intel, Santa Clara, CA, USA","institution_ids":["https://openalex.org/I1343180700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030620564","display_name":"Kannan Ramchandran","orcid":"https://orcid.org/0000-0002-4567-328X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kannan Ramchandran","raw_affiliation_strings":["Wireless Foundation, University of California at Berkeley, Berkeley, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wireless Foundation, University of California at Berkeley, Berkeley, CA, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.47,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.8787578,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"64","issue":"1","first_page":"451","last_page":"466"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"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":1.0,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11873","display_name":"PAPR reduction in OFDM","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/alias","display_name":"Alias","score":0.6871875524520874},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6298450827598572},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5602946877479553},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.538784384727478},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4962192177772522},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.4517093598842621},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4515981078147888},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4010908901691437},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37871330976486206},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.36878347396850586},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3415859341621399},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.16062498092651367},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.13739201426506042},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08204904198646545}],"concepts":[{"id":"https://openalex.org/C46681722","wikidata":"https://www.wikidata.org/wiki/Q4725589","display_name":"Alias","level":2,"score":0.6871875524520874},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6298450827598572},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5602946877479553},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.538784384727478},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4962192177772522},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.4517093598842621},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4515981078147888},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4010908901691437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37871330976486206},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.36878347396850586},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3415859341621399},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.16062498092651367},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.13739201426506042},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08204904198646545},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2017.2679053","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2679053","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3074473257","display_name":"EAGER: Ultra-FFAST Alias Codes for Sparse Spectrum Estimation: Next Generation Compressed Sensing","funder_award_id":"1439725","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7554253775","display_name":"CIF:Small:Next-Generation Compressive Phase-Retrieval Using Sparse-Graph Codes: Theory, Design and Applications","funder_award_id":"1527767","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"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1494749725","https://openalex.org/W1501755821","https://openalex.org/W1983695700","https://openalex.org/W1986545790","https://openalex.org/W2012365979","https://openalex.org/W2019833178","https://openalex.org/W2025934813","https://openalex.org/W2031425559","https://openalex.org/W2103300762","https://openalex.org/W2107625832","https://openalex.org/W2111855076","https://openalex.org/W2113638573","https://openalex.org/W2123629701","https://openalex.org/W2127271355","https://openalex.org/W2128131274","https://openalex.org/W2129131372","https://openalex.org/W2129638195","https://openalex.org/W2141556672","https://openalex.org/W2145096794","https://openalex.org/W2146509513","https://openalex.org/W2149213383","https://openalex.org/W2158537680","https://openalex.org/W2164452299","https://openalex.org/W2296616510","https://openalex.org/W2395231588","https://openalex.org/W2752855532","https://openalex.org/W4242004838","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W2154006536","https://openalex.org/W2348800014","https://openalex.org/W2365391860","https://openalex.org/W1820187807","https://openalex.org/W4362564158","https://openalex.org/W2085939569","https://openalex.org/W4377371889","https://openalex.org/W4389362338","https://openalex.org/W2113623403","https://openalex.org/W2055932080"],"abstract_inverted_index":{"The":[0,85],"fast":[1,60,96],"Fourier":[2,14,61,243,320],"transform":[3,15,64,244],"is":[4,255],"the":[5,12,32,36,74,83,125,133,137,149,194,198,205,236,249,264,287,303,327],"most":[6],"efficiently":[7],"known":[8],"way":[9],"to":[10,93,132],"compute":[11],"discrete":[13],"(DFT)":[16],"of":[17,27,35,106,157,197,212,228,235,239,248,286],"an":[18,107,158,213,224,317],"arbitrary":[19],"n-length":[20,108,159],"signal,":[21],"and":[22,56,97,115,130,182,251,291],"has":[23,39],"a":[24,58,78,95,154,209,282,323],"computational":[25],"complexity":[26],"O(n":[28],"log":[29,117,163,173],"n).":[30],"If":[31],"DFT":[33,75,105,156,211,289,329],"X\u20d7":[34],"signal":[37,109,160,217],"x\u20d7":[38],"only":[40,111,219],"k":[41,45],"non-zero":[42,288],"coefficients":[43,290],"(where":[44],"<;":[46],"n),":[47],"can":[48],"we":[49,123,188,202,296],"do":[50],"better?":[51],"We":[52,146,231],"addressed":[53],"this":[54,121],"question":[55],"presented":[57],"novel":[59],"aliasing-based":[62],"sparse":[63,242,319],"(FFAST)":[65],"algorithm":[66,152,207,305],"that":[67,102,148,204,247,253,302,315],"cleverly":[68],"induces":[69],"sparse-graph":[70,87],"alias":[71,88],"codes":[72,89],"in":[73,82,171],"domain,":[76],"via":[77],"Chinese-remainder-theorem-guided":[79],"sub-sampling":[80],"operation":[81],"time-domain.":[84],"induced":[86],"are":[90,140,278],"then":[91],"exploited":[92],"devise":[94],"iterative":[98],"onion-peeling":[99],"style":[100],"decoder":[101],"computes":[103,153,208],"k-sparse":[104,155],"using":[110,161,218],"O(k)":[112],"time-domain":[113,138,169],"samples":[114,139,170,222],"O(k":[116,162,172],"k)":[118],"computations.":[119],"In":[120,185],"paper,":[122],"generalize":[124],"FFAST":[126],"framework":[127],"by":[128,142],"Pawar":[129],"Ramchandran":[131],"noisy":[134,221],"setting":[135],"where":[136],"corrupted":[141],"white":[143,293],"Gaussian":[144,294],"noise.":[145],"show":[147,203,252],"noiserobust":[150],"R-FFAST":[151,199,206,250,304],"<sup":[164,174],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[165,175],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">3</sup>":[166],"n)":[167,177],"noise-corrupted":[168],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">4</sup>":[176],"complexity,":[178],"i.e.,":[179],"sub-linear":[180],"sample":[181],"time":[183],"complexity.":[184],"Section":[186],"IX,":[187],"provide":[189,233,297],"extensive":[190],"simulation":[191,298],"results":[192,277],"validating":[193],"empirical":[195],"performance":[196,238],"algorithm,":[200,266],"e.g.,":[201],"50-sparse":[210],"\u224810":[214],"million":[215],"length":[216],"4800":[220],"with":[223,246,281,322],"effective":[225],"signal-to-noise":[226],"ratio":[227],"5":[229],"dB.":[230],"also":[232],"comparison":[234],"run-time":[237],"several":[240],"existing":[241],"implementations":[245],"it":[254],"almost":[256],"20":[257],"times":[258],"faster,":[259],"for":[260,279,309,326],"comparable":[261],"settings,":[262],"than":[263],"state-of-the-art":[265],"while":[267],"simultaneously":[268],"providing":[269],"better":[270],"support":[271,285,325],"recovery":[272],"guarantees.":[273],"While":[274],"our":[275],"theoretical":[276],"signals":[280,310],"uniformly":[283],"random":[284],"additive":[292],"noise,":[295],"results,":[299],"which":[300],"demonstrate":[301],"performs":[306],"well":[307],"even":[308],"like":[311],"magnetic":[312],"resonance":[313],"images,":[314],"have":[316],"approximately":[318],"spectrum":[321],"non-uniform":[324],"dominant":[328],"coefficients.":[330]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}
