{"id":"https://openalex.org/W2120685655","doi":"https://doi.org/10.1109/icassp.2009.4960227","title":"On the recovery of nonnegative sparse vectors from sparse measurements inspired by expanders","display_name":"On the recovery of nonnegative sparse vectors from sparse measurements inspired by expanders","publication_year":2009,"publication_date":"2009-04-01","ids":{"openalex":"https://openalex.org/W2120685655","doi":"https://doi.org/10.1109/icassp.2009.4960227","mag":"2120685655"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2009.4960227","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2009.4960227","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Conference on Acoustics, Speech and Signal Processing","raw_type":"proceedings-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/A5069555127","display_name":"Moein Khajehnejad","orcid":"https://orcid.org/0000-0002-2185-4596"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M. Amin Khajehnejad","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","Department of Electrical Engineering, California Institute of Technology, Pasadena 91125, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena 91125, USA#TAB#","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002430773","display_name":"Babak Hassibi","orcid":"https://orcid.org/0000-0002-1375-5838"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Babak Hassibi","raw_affiliation_strings":["Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","Department of Electrical Engineering, California Institute of Technology, Pasadena 91125, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Department of Electrical Engineering, California Institute of Technology, Pasadena 91125, USA#TAB#","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069555127"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17301606,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"2889","last_page":"2892"},"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9994000196456909,"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/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.9984999895095825,"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/adjacency-matrix","display_name":"Adjacency matrix","score":0.7937101125717163},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.7296772003173828},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.586358368396759},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5557345151901245},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5491452813148499},{"id":"https://openalex.org/keywords/expander-graph","display_name":"Expander graph","score":0.5234717130661011},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4977836608886719},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.4950503408908844},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4384545683860779},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42163369059562683},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38727906346321106},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.36642125248908997},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3330006003379822},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09926983714103699}],"concepts":[{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.7937101125717163},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.7296772003173828},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.586358368396759},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5557345151901245},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5491452813148499},{"id":"https://openalex.org/C154547637","wikidata":"https://www.wikidata.org/wiki/Q776602","display_name":"Expander graph","level":3,"score":0.5234717130661011},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4977836608886719},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.4950503408908844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4384545683860779},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42163369059562683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38727906346321106},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.36642125248908997},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3330006003379822},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09926983714103699},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/icassp.2009.4960227","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2009.4960227","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Conference on Acoustics, Speech and Signal Processing","raw_type":"proceedings-article"},{"id":"pmh:oai:authors.library.caltech.edu:18203","is_oa":false,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20100510-094616369","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1620362451","https://openalex.org/W1835471601","https://openalex.org/W1971402995","https://openalex.org/W2010669260","https://openalex.org/W2033375925","https://openalex.org/W2115139597","https://openalex.org/W2141433180","https://openalex.org/W2145096794","https://openalex.org/W2150249649","https://openalex.org/W2163916252","https://openalex.org/W2170929819","https://openalex.org/W7033951358"],"related_works":["https://openalex.org/W4213150077","https://openalex.org/W2369410163","https://openalex.org/W2982430984","https://openalex.org/W2078477160","https://openalex.org/W2059018062","https://openalex.org/W2604585036","https://openalex.org/W1991172810","https://openalex.org/W125803343","https://openalex.org/W1989103179","https://openalex.org/W2117632582"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"compressed":[3],"sensing":[4],"for":[5,60,90,106],"the":[6,19,23,69,77,91,94,122,131,135,142],"recovery":[7],"of":[8,16,22,40,80,99,141,145],"non-negative":[9],"sparse":[10],"vectors":[11],"from":[12],"a":[13,37,54,73,138],"smaller":[14],"number":[15,39,98],"measurements":[17,100],"than":[18],"ambient":[20,95],"dimension":[21,96],"unknown":[24,70],"vector.":[25,71],"We":[26],"focus":[27],"on":[28],"measurement":[29,50],"matrices":[30,51],"that":[31,121,130],"are":[32,125],"sparse,":[33],"i.e.,":[34],"have":[35],"only":[36],"constant":[38],"nonzero":[41],"(and":[42],"non-negative)":[43],"entries":[44],"in":[45],"each":[46],"column.":[47],"For":[48],"such":[49],"we":[52,84],"give":[53],"simple":[55,74,86],"necessary":[56],"and":[57,102,128],"sufficient":[58],"condition":[59],"l":[61,108],"<sub":[62,109],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[63,110],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[64,111],"optimization":[65,112],"to":[66,76],"successfully":[67],"recover":[68],"Using":[72],"ldquoperturbationrdquo":[75],"adjacency":[78,143],"matrix":[79,144],"an":[81,146],"unbalanced":[82],"expander,":[83],"obtain":[85],"closed":[87],"form":[88],"expressions":[89],"threshold":[92],"relating":[93],"n,":[97],"m":[101],"sparsity":[103],"level":[104],"k,":[105],"which":[107],"is":[113],"successful":[114],"with":[115],"overwhelming":[116],"probability.":[117],"Simulation":[118],"results":[119],"suggest":[120],"theoretical":[123],"thresholds":[124],"fairly":[126],"tight":[127],"demonstrate":[129],"ldquoperturbationsrdquo":[132],"significantly":[133],"improve":[134],"performance":[136],"over":[137],"direct":[139],"use":[140],"expander":[147],"graph.":[148]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
