{"id":"https://openalex.org/W3038054685","doi":"https://doi.org/10.4230/lipics.icalp.2020.58","title":"Sparse Recovery for Orthogonal Polynomial Transforms","display_name":"Sparse Recovery for Orthogonal Polynomial Transforms","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W3038054685","doi":"https://doi.org/10.4230/lipics.icalp.2020.58","mag":"3038054685"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"http://arxiv.org/pdf/1907.08362.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":[],"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/A5042502878","display_name":"Anna C. Gilbert","orcid":"https://orcid.org/0000-0002-9627-9274"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anna C. Gilbert","raw_affiliation_strings":["University of Michigan\u2013Ann Arbor, Ann Arbor, United States"],"affiliations":[{"raw_affiliation_string":"University of Michigan\u2013Ann Arbor, Ann Arbor, United States","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025386668","display_name":"Albert Gu","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Albert Gu","raw_affiliation_strings":["Stanford University, Stanford, United States"],"affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, United States","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103852640","display_name":"Christopher R\u00e9","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher R\u00e9","raw_affiliation_strings":["Stanford University, Stanford, United States"],"affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, United States","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001041485","display_name":"Atri Rudra","orcid":"https://orcid.org/0000-0003-4136-4719"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Atri Rudra","raw_affiliation_strings":["Stanford University, Stanford, United States"],"affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, United States","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022963784","display_name":"Mary Wootters","orcid":"https://orcid.org/0000-0002-2345-2531"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mary Wootters","raw_affiliation_strings":["Stanford University, Stanford, United States"],"affiliations":[{"raw_affiliation_string":"Stanford University, Stanford, United States","institution_ids":["https://openalex.org/I97018004"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":61},"biblio":{"volume":"168","issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.998,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.998,"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/T10924","display_name":"Cardiovascular Health and Disease Prevention","score":0.9926,"subfield":{"id":"https://openalex.org/subfields/2705","display_name":"Cardiology and Cardiovascular Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9919,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.5212729}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6530221},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.6331675},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.55529606},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.5451358},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.5212729},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.5193668},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.4802661},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.45926917},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42748168},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42000058},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38301978},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.38115704},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36153072},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3560355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20392838},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.20165852},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2012634}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"http://arxiv.org/pdf/1907.08362.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W90191732","https://openalex.org/W3179213994","https://openalex.org/W3169127456","https://openalex.org/W3143547601","https://openalex.org/W3126626028","https://openalex.org/W3018936433","https://openalex.org/W3004671407","https://openalex.org/W2888080416","https://openalex.org/W2607865598","https://openalex.org/W2399410829","https://openalex.org/W2182509900","https://openalex.org/W2167854544","https://openalex.org/W2099834462","https://openalex.org/W2096282168","https://openalex.org/W2056559482","https://openalex.org/W2019463665","https://openalex.org/W2010953531","https://openalex.org/W1969941659","https://openalex.org/W1942755802","https://openalex.org/W1621098854"],"abstract_inverted_index":{"In":[0],"this":[1,114,216,253],"paper":[2,115],"we":[3,116,195,208,251],"consider":[4],"the":[5,58,64,96,103,107,125,200,204,231,237],"following":[6],"sparse":[7,78,126,205,233,239],"recovery":[8,127,234,240,255],"problem.":[9],"We":[10],"have":[11,215],"query":[12],"access":[13],"to":[14,39,47,224,236],"a":[15,70,160,226],"vector":[16],"$\\vx":[17],"\\in":[18],"\\R^N$":[19],"such":[20],"that":[21,61,82,133,146,194,210,242],"$\\vhx":[22],"=":[23],"\\vF":[24],"\\vx$":[25],"is":[26,38,63,109,147,193,223],"$k$-sparse":[27,232],"(or":[28,98],"nearly":[29],"$k$-sparse)":[30],"for":[31,91,129,143,244,257],"some":[32],"orthogonal":[33,130,136,149,165,247],"transform":[34,151],"$\\vF$.":[35],"The":[36,156],"goal":[37],"output":[40],"an":[41,44,148,197],"approximation":[42],"(in":[43],"$\\ell_2$":[45],"sense)":[46],"$\\vhx$":[48],"in":[49,57,77,84,120,180],"sublinear":[50],"time.":[51],"This":[52],"problem":[53,128,235,241,256],"has":[54,75],"been":[55],"well-studied":[56],"special":[59,174],"case":[60],"$\\vF$":[62,93,132,145],"Discrete":[65,104],"Fourier":[66,80],"Transform":[67],"(DFT),":[68],"and":[69,170,176,185],"long":[71],"line":[72],"of":[73,163,190,203],"work":[74,192],"resulted":[76],"Fast":[79],"Transforms":[81],"run":[83],"time":[85,121],"$O(k":[86],"\\cdot":[87],"\\mathrm{polylog}":[88],"N)$.":[89],"However,":[90],"transforms":[92,101,131,258],"other":[94],"than":[95],"DFT":[97],"closely":[99],"related":[100],"like":[102,182],"Cosine":[105],"Transform),":[106],"question":[108],"much":[110],"less":[111],"settled.":[112],"\r\nIn":[113],"give":[117,225],"sublinear-time":[118],"algorithms---running":[119],"$\\poly(k":[122],"\\log(N))$---for":[123],"solving":[124],"arise":[134],"from":[135,153,230,260],"polynomials.":[137,155,262],"More":[138],"precisely,":[139],"our":[140,191],"algorithm":[141],"works":[142],"any":[144,245],"polynomial":[150,248],"derived":[152,259],"Jacobi":[154,157,261],"polynomials":[158,166,172],"are":[159],"large":[161],"class":[162],"classical":[164],"(and":[167],"include":[168],"Chebyshev":[169],"Legendre":[171],"as":[173],"cases),":[175],"show":[177],"up":[178],"extensively":[179],"applications":[181],"numerical":[183],"analysis":[184],"signal":[186],"processing.":[187],"One":[188],"caveat":[189],"require":[196],"assumption":[198],"on":[199],"sparsity":[201],"structure":[202],"vector,":[206],"although":[207],"note":[209],"vectors":[211],"with":[212,218],"random":[213],"support":[214],"property":[217],"high":[219],"probability.":[220],"\r\nOur":[221],"approach":[222],"very":[227],"general":[228],"reduction":[229],"$1$-sparse":[238],"holds":[243],"flat":[246],"transform;":[249],"then":[250],"solve":[252],"one-sparse":[254]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3038054685","counts_by_year":[],"updated_date":"2025-01-17T02:51:00.884961","created_date":"2020-07-02"}