{"id":"https://openalex.org/W2000527318","doi":"https://doi.org/10.1137/130929928","title":"Quasi-linear Compressed Sensing","display_name":"Quasi-linear Compressed Sensing","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2000527318","doi":"https://doi.org/10.1137/130929928","mag":"2000527318"},"language":"en","primary_location":{"id":"doi:10.1137/130929928","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130929928","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1311.1642","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Martin Ehler","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Martin Ehler","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Massimo Fornasier","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Massimo Fornasier","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Juliane Sigl","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Juliane Sigl","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.8277,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.9474988,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"12","issue":"2","first_page":"725","last_page":"754"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.5893999934196472,"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":0.5893999934196472,"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/T10463","display_name":"Pulsars and Gravitational Waves Research","score":0.0706000030040741,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/T11183","display_name":"Advanced X-ray Imaging Techniques","score":0.06319999694824219,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/restricted-isometry-property","display_name":"Restricted isometry property","score":0.8557999730110168},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.7684999704360962},{"id":"https://openalex.org/keywords/identifiability","display_name":"Identifiability","score":0.7016000151634216},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.637499988079071},{"id":"https://openalex.org/keywords/phase-retrieval","display_name":"Phase retrieval","score":0.5475999712944031},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.503000020980835},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.4077000021934509},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4018999934196472}],"concepts":[{"id":"https://openalex.org/C17902559","wikidata":"https://www.wikidata.org/wiki/Q17099734","display_name":"Restricted isometry property","level":3,"score":0.8557999730110168},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.7684999704360962},{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.7016000151634216},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.637499988079071},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5945000052452087},{"id":"https://openalex.org/C81793267","wikidata":"https://www.wikidata.org/wiki/Q7180962","display_name":"Phase retrieval","level":3,"score":0.5475999712944031},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5418000221252441},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.503000020980835},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.4077000021934509},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4018999934196472},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.397599995136261},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3946000039577484},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.39259999990463257},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.3091999888420105},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30149999260902405},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.28940001130104065},{"id":"https://openalex.org/C137270730","wikidata":"https://www.wikidata.org/wiki/Q120811","display_name":"Detection theory","level":3,"score":0.28679999709129333},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.27459999918937683},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130929928","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130929928","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1311.1642","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.1642","pdf_url":"https://arxiv.org/pdf/1311.1642","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1311.1642","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1311.1642","pdf_url":"https://arxiv.org/pdf/1311.1642","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2916271932","display_name":null,"funder_award_id":"VRG12-009","funder_id":"https://openalex.org/F4320321003","funder_display_name":"Vienna Science and Technology Fund"},{"id":"https://openalex.org/G4294472841","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320321004","funder_display_name":"\u00d6sterreichischen Akademie der Wissenschaften"},{"id":"https://openalex.org/G6345853531","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"}],"funders":[{"id":"https://openalex.org/F4320321003","display_name":"Vienna Science and Technology Fund","ror":"https://ror.org/01f9mc681"},{"id":"https://openalex.org/F4320321004","display_name":"\u00d6sterreichischen Akademie der Wissenschaften","ror":"https://ror.org/03anc3s24"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1883653182","https://openalex.org/W2007593159","https://openalex.org/W2023299560","https://openalex.org/W2025655594","https://openalex.org/W2030449718","https://openalex.org/W2030823150","https://openalex.org/W2038517753","https://openalex.org/W2049709948","https://openalex.org/W2058891218","https://openalex.org/W2062052599","https://openalex.org/W2078397124","https://openalex.org/W2083346837","https://openalex.org/W2083503960","https://openalex.org/W2088658556","https://openalex.org/W2105877514","https://openalex.org/W2108078415","https://openalex.org/W2110238624","https://openalex.org/W2115706991","https://openalex.org/W2118550318","https://openalex.org/W2129131372","https://openalex.org/W2129638195","https://openalex.org/W2134474909","https://openalex.org/W2145096794","https://openalex.org/W2150386037","https://openalex.org/W2151693816","https://openalex.org/W2164452299","https://openalex.org/W2289917018","https://openalex.org/W2963302510","https://openalex.org/W2963322354","https://openalex.org/W2963855280","https://openalex.org/W4250955649"],"related_works":[],"abstract_inverted_index":{"Inspired":[0],"by":[1],"significant":[2],"real-life":[3],"applications,":[4,172],"particularly":[5],"sparse":[6,10,52],"phase":[7,82,130],"retrieval":[8,83,131],"and":[9,81,132,161],"pulsation":[11],"frequency":[12],"detection":[13],"in":[14,129],"asteroseismology,":[15],"we":[16,122,147,173],"investigate":[17],"a":[18,98],"general":[19],"framework":[20],"for":[21,69,169,179],"compressed":[22],"sensing,":[23],"where":[24,136],"the":[25,34,57,87,105,137,141,157,170],"measurements":[26,181],"are":[27,153,166,183],"quasi-linear.":[28],"We":[29,66,96],"formulate":[30],"natural":[31,154],"generalizations":[32,155],"of":[33,51,59,77,109,156,186],"well-known":[35,158],"restricted":[36,89],"isometry":[37,90],"property":[38],"(RIP)":[39],"toward":[40],"nonlinear":[41],"measurements,":[42,73],"which":[43,152,182],"allow":[44],"us":[45],"to":[46,62,112],"prove":[47],"both":[48],"unique":[49],"identifiability":[50],"signals":[53],"as":[54,56,121],"well":[55],"convergence":[58],"recovery":[60,177],"algorithms":[61,165],"compute":[63],"them":[64],"efficiently.":[65],"show":[67,123,174],"that":[68,107,124],"certain":[70],"randomized":[71],"quasi-linear":[72,180],"including":[74],"Lipschitz":[75,184],"perturbations":[76,185],"classical":[78],"RIP":[79,187],"matrices":[80],"from":[84],"random":[85],"projections,":[86],"proposed":[88],"properties":[91],"hold":[92],"with":[93],"high":[94],"probability.":[95],"analyze":[97],"generalized":[99],"orthogonal":[100],"least":[101],"squares":[102],"(OLS)":[103],"under":[104],"assumption":[106,139],"magnitudes":[108],"signal":[110,142],"entries":[111],"be":[113],"recovered":[114],"decay":[115,138],"quickly.":[116],"Greed":[117],"is":[118],"good":[119],"again,":[120],"this":[125],"algorithm":[126],"performs":[127],"efficiently":[128],"asteroseismology.":[133],"For":[134],"situations":[135],"on":[140],"does":[143],"not":[144],"necessarily":[145],"hold,":[146],"propose":[148],"two":[149],"alternative":[150],"algorithms,":[151],"iterative":[159],"hard-":[160],"soft-thresholding.":[162],"While":[163],"these":[164],"rarely":[167],"successful":[168],"mentioned":[171],"their":[175],"strong":[176],"guarantees":[178],"matrices.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2016-06-24T00:00:00"}
