iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://api.openalex.org/works/doi:10.1109/TIT.2011.2170129
{"id":"https://openalex.org/W3099164072","doi":"https://doi.org/10.1109/tit.2011.2170129","title":"On the Error of Estimating the Sparsest Solution of Underdetermined Linear Systems","display_name":"On the Error of Estimating the Sparsest Solution of Underdetermined Linear Systems","publication_year":2011,"publication_date":"2011-12-01","ids":{"openalex":"https://openalex.org/W3099164072","doi":"https://doi.org/10.1109/tit.2011.2170129","mag":"3099164072"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2170129","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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00649183/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083199991","display_name":"Massoud Babaie\u2010Zadeh","orcid":"https://orcid.org/0000-0001-8864-4756"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Massoud Babaie-Zadeh","raw_affiliation_strings":["Electrical Engineering Department, Sharif University of Technology, Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, Sharif University of Technology, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031796033","display_name":"Christian Jutten","orcid":null},"institutions":[{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]},{"id":"https://openalex.org/I185839726","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266","country_code":"FR","type":"education","lineage":["https://openalex.org/I185839726"]},{"id":"https://openalex.org/I4210124956","display_name":"Grenoble Images Parole Signal Automatique","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christian Jutten","raw_affiliation_strings":["GIPSA-laboratory, University of Grenoble, Saint Martin d'Heres, France","Institut Universitaire de France, Paris, France"],"affiliations":[{"raw_affiliation_string":"GIPSA-laboratory, University of Grenoble, Saint Martin d'Heres, France","institution_ids":["https://openalex.org/I899635006","https://openalex.org/I4210124956"]},{"raw_affiliation_string":"Institut Universitaire de France, Paris, France","institution_ids":["https://openalex.org/I185839726"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033781263","display_name":"Hosein Mohimani","orcid":"https://orcid.org/0000-0003-3980-2505"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hosein Mohimani","raw_affiliation_strings":["Department of Electrical Engineering, University of California, San Diego, La Jolla, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of California, San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]}],"institution_assertions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.627,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":10,"citation_normalized_percentile":{"value":0.708112,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":85,"max":86},"biblio":{"volume":"57","issue":"12","first_page":"7840","last_page":"7855"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Theory and Applications of Compressed Sensing","score":0.9992,"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":"Theory and Applications of Compressed Sensing","score":0.9992,"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/T10792","display_name":"Matrix Algorithms and Iterative Methods","score":0.999,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10963","display_name":"Numerical Optimization Techniques","score":0.9936,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/underdetermined-system","display_name":"Underdetermined system","score":0.62269574},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse Approximation","score":0.619589},{"id":"https://openalex.org/keywords/sparse-linear-systems","display_name":"Sparse Linear Systems","score":0.618961},{"id":"https://openalex.org/keywords/sparse-representations","display_name":"Sparse Representations","score":0.58207},{"id":"https://openalex.org/keywords/sparsity-in-signal-processing","display_name":"Sparsity in Signal Processing","score":0.577125},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed Sensing","score":0.525617}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.62580687},{"id":"https://openalex.org/C179690561","wikidata":"https://www.wikidata.org/wiki/Q4316110","display_name":"Underdetermined system","level":2,"score":0.62269574},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40316957},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36809063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34804678},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3457634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32448956},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12053138}],"mesh":[],"locations_count":7,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2170129","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":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal.science/hal-00649183","pdf_url":"https://hal.science/hal-00649183/document","source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1112.0789","pdf_url":"https://arxiv.org/pdf/1112.0789","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-00649183/document","pdf_url":"https://hal.archives-ouvertes.fr/hal-00649183/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"https://hal.science/hal-00649183/file/Babaieetal-IEEEIT.pdf","pdf_url":"https://hal.science/hal-00649183/file/Babaieetal-IEEEIT.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-00649183/file/Babaieetal-IEEEIT.pdf","pdf_url":"https://hal.archives-ouvertes.fr/hal-00649183/file/Babaieetal-IEEEIT.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":["Centre National de la Recherche Scientifique"],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":false,"landing_page_url":"https://api.datacite.org/dois/10.48550/arxiv.1112.0789","pdf_url":null,"source":{"id":"https://openalex.org/S4393179698","display_name":"DataCite API","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210145204","host_organization_name":"DataCite","host_organization_lineage":["https://openalex.org/I4210145204"],"host_organization_lineage_names":["DataCite"],"type":"metadata"},"license":null,"license_id":null,"version":null}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://hal.science/hal-00649183","pdf_url":"https://hal.science/hal-00649183/document","source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":["https://openalex.org/W1969486569","https://openalex.org/W3099164072"],"referenced_works_count":53,"referenced_works":["https://openalex.org/W138813470","https://openalex.org/W1492221128","https://openalex.org/W1517634087","https://openalex.org/W1563800729","https://openalex.org/W1577111082","https://openalex.org/W1974755392","https://openalex.org/W1981573335","https://openalex.org/W1986931325","https://openalex.org/W1995636681","https://openalex.org/W1999542175","https://openalex.org/W2012961725","https://openalex.org/W2015418199","https://openalex.org/W2032618720","https://openalex.org/W2038085771","https://openalex.org/W2038237443","https://openalex.org/W2069781242","https://openalex.org/W2072184935","https://openalex.org/W2074054045","https://openalex.org/W2075506710","https://openalex.org/W2076410399","https://openalex.org/W2083042020","https://openalex.org/W2083694956","https://openalex.org/W2084661953","https://openalex.org/W2089794108","https://openalex.org/W2097323375","https://openalex.org/W2100068253","https://openalex.org/W2104266187","https://openalex.org/W2110505738","https://openalex.org/W2111067490","https://openalex.org/W2122315118","https://openalex.org/W2129131372","https://openalex.org/W2129638195","https://openalex.org/W2130514271","https://openalex.org/W2136235822","https://openalex.org/W2137335629","https://openalex.org/W2145096794","https://openalex.org/W2147656689","https://openalex.org/W2148250473","https://openalex.org/W2148556090","https://openalex.org/W2149206122","https://openalex.org/W2151131483","https://openalex.org/W2151693816","https://openalex.org/W2154332973","https://openalex.org/W2154604910","https://openalex.org/W2157434051","https://openalex.org/W2157560371","https://openalex.org/W2164026645","https://openalex.org/W2296616510","https://openalex.org/W2610857016","https://openalex.org/W4229746864","https://openalex.org/W4250955649","https://openalex.org/W4302383908","https://openalex.org/W44377498"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4287906532","https://openalex.org/W3213509687","https://openalex.org/W3011121006","https://openalex.org/W2997320962","https://openalex.org/W2375962929","https://openalex.org/W2084978503","https://openalex.org/W2066796569","https://openalex.org/W2041382836","https://openalex.org/W176802781"],"abstract_inverted_index":{"Let":[0],"${\\bf":[5,37,53,106,179,207,254],"A}$":[6,208],"be":[7,303,311],"an":[8,98,158,314],"Notation=\"TeX\">$n":[13],"\\times":[14],"m$":[15],"matrix":[16],"with":[17,305],"Notation=\"TeX\">$m":[22],">":[23],"n$":[24],",":[25,108],"and":[26,109,131,186,234],"suppose":[27,110],"that":[28,85,111,122,246,267,319],"the":[29,147,162,229,243,282,317,320],"underdetermined":[30],"linear":[31],"system":[32],"A}":[38,258],"{\\bf":[39,42,62,257,259],"s}":[40],"=":[41,256],"x}$":[43],"admits":[44],"a":[45,72,79,89,142,193,214,278,306],"sparse":[46,73,304,324],"solution":[47,74,90,143],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[51,104,252,296],"":[54,107,180],"for":[55],"which":[56,217],"Notation=\"TeX\">$\\Vert":[61,169],"s}_0\\Vert_0":[63],"<":[64],"{1\\over":[65],"2}":[66],"{\\rm":[67],"spark}({\\bf":[68],"A})$":[69],".":[70,209,262],"Such":[71],"is":[75,118,153,184,218,300],"unique":[76],"due":[77],"to":[78,138,146,156,227,276,302,316],"well-known":[80],"uniqueness":[81],"theorem.":[82],"Suppose":[83],"now":[84],"we":[86,190,264],"have":[87],"somehow":[88],"Notation=\"TeX\">$\\mathhat{\\bf":[95,116,298],"s}$":[96,117,299],"as":[97,313],"estimation":[99,163,321],"of":[100,125,200,202,231,284,323],"only":[119],"\u201capproximately":[120],"sparse,\u201d":[121],"is,":[123,247],"many":[124],"its":[126],"components":[127],"are":[128],"very":[129],"small":[130],"nearly":[132],"zero,":[133],"but":[134,221],"not":[135],"mathematically":[136],"equal":[137],"zero.":[139],"Is":[140],"such":[141,192],"necessarily":[144],"close":[145],"true":[148],"sparsest":[149],"solution?":[150],"More":[151],"generally,":[152],"it":[154],"possible":[155],"construct":[157,191],"upper":[159,237],"bound":[160,194],"on":[161,196,281],"error":[164],"\\mathhat{\\bf":[170],"s}-{\\bf":[171,290],"s}_0\\Vert_2$":[172],"without":[173],"knowing":[174],"?":[181],"The":[182],"answer":[183],"positive,":[185],"in":[187],"this":[188],"paper,":[189],"based":[195],"minimal":[197],"singular":[198],"values":[199],"submatrices":[201],"We":[210,239],"will":[211,240,265],"also":[212,241],"state":[213],"tight":[215],"bound,":[216],"more":[219],"complicated,":[220],"besides":[222],"being":[223],"tight,":[224],"enables":[225],"us":[226],"study":[228,242],"case":[230],"random":[232],"dictionaries":[233],"obtain":[235,277],"probabilistic":[236],"bounds.":[238],"noisy":[244],"case,":[245],"where":[248,268,328],"x}":[255],"s}+{\\bf":[260],"n}$":[261],"Moreover,":[263],"see":[266],"Notation=\"TeX\">$\\Vert{{\\bf":[273,333],"s}_0}\\Vert_0$":[274,334],"grows,":[275],"predetermined":[279],"guaranty":[280],"maximum":[283],"Notation=\"TeX\">$\\Vert{\\mathhat{\\bf":[289],"s}_0}\\Vert_2,$":[291],"":[292],"needed":[301],"better":[307],"approximation.":[308],"This":[309],"can":[310],"seen":[312],"explanation":[315],"fact":[318],"quality":[322],"recovery":[325],"algorithms":[326],"degrades":[327],"grows.":[335]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3099164072","counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3}],"updated_date":"2024-11-24T10:53:55.514255","created_date":"2020-11-23"}