{"id":"https://openalex.org/W2625893224","doi":"https://doi.org/10.1109/tsp.2018.2841867","title":"Sparsity Order Estimation From a Single Compressed Observation Vector","display_name":"Sparsity Order Estimation From a Single Compressed Observation Vector","publication_year":2018,"publication_date":"2018-05-30","ids":{"openalex":"https://openalex.org/W2625893224","doi":"https://doi.org/10.1109/tsp.2018.2841867","mag":"2625893224"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2018.2841867","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2018.2841867","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1706.05278","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011824238","display_name":"Sebastian Semper","orcid":"https://orcid.org/0000-0002-2610-7389"},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sebastian Semper","raw_affiliation_strings":["Institute of Mathematics, Technische Universit\u00e4t Ilmenau, Ilmenau, Germany"],"raw_orcid":"https://orcid.org/0000-0002-2610-7389","affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Technische Universit\u00e4t Ilmenau, Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113692116","display_name":"Florian R\u00f6mer","orcid":null},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]},{"id":"https://openalex.org/I202367325","display_name":"Oldenburger Institut f\u00fcr Informatik","ror":"https://ror.org/003sav189","country_code":"DE","type":"facility","lineage":["https://openalex.org/I202367325"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Florian Romer","raw_affiliation_strings":["Institute for Information Technology, Technische Universit\u00e4t Ilmenau, Ilmenau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Information Technology, Technische Universit\u00e4t Ilmenau, Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181","https://openalex.org/I202367325"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006607273","display_name":"Thomas Hotz","orcid":null},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Hotz","raw_affiliation_strings":["Institute of Mathematics, Technische Universit\u00e4t Ilmenau, Ilmenau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Technische Universit\u00e4t Ilmenau, Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112286684","display_name":"Giovanni DelGaldo","orcid":null},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Giovanni DelGaldo","raw_affiliation_strings":["Technische Universit\u00e4t Ilmenau, Ilmenau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Ilmenau, Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4239,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.76375602,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"66","issue":"15","first_page":"3958","last_page":"3971"},"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9986000061035156,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/vandermonde-matrix","display_name":"Vandermonde matrix","score":0.9582556486129761},{"id":"https://openalex.org/keywords/snapshot","display_name":"Snapshot (computer storage)","score":0.801668643951416},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.6720057725906372},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5955134630203247},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.5407190322875977},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5267961621284485},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5068357586860657},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5023093223571777},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44765764474868774},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.4196876883506775},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3359079957008362},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18210598826408386},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08908945322036743}],"concepts":[{"id":"https://openalex.org/C55294529","wikidata":"https://www.wikidata.org/wiki/Q579544","display_name":"Vandermonde matrix","level":3,"score":0.9582556486129761},{"id":"https://openalex.org/C55282118","wikidata":"https://www.wikidata.org/wiki/Q252683","display_name":"Snapshot (computer storage)","level":2,"score":0.801668643951416},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.6720057725906372},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5955134630203247},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.5407190322875977},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5267961621284485},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5068357586860657},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5023093223571777},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44765764474868774},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4196876883506775},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3359079957008362},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18210598826408386},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08908945322036743},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tsp.2018.2841867","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2018.2841867","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1706.05278","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1706.05278","pdf_url":"https://arxiv.org/pdf/1706.05278","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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"},{"id":"pmh:oai:fraunhofer.de:N-534542","is_oa":false,"landing_page_url":"http://publica.fraunhofer.de/documents/N-534542.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400801","display_name":"Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fraunhofer IZFP","raw_type":"article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/256384","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/256384","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"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":"journal article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1706.05278","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1706.05278","pdf_url":"https://arxiv.org/pdf/1706.05278","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"id":"https://metadata.un.org/sdg/16","score":0.7699999809265137,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W143004564","https://openalex.org/W1568017700","https://openalex.org/W1591116419","https://openalex.org/W1643046983","https://openalex.org/W1814500939","https://openalex.org/W1966907097","https://openalex.org/W1972150100","https://openalex.org/W1973503417","https://openalex.org/W1997858671","https://openalex.org/W2006554558","https://openalex.org/W2021932923","https://openalex.org/W2024417168","https://openalex.org/W2032618720","https://openalex.org/W2034248602","https://openalex.org/W2044762091","https://openalex.org/W2089161774","https://openalex.org/W2091256848","https://openalex.org/W2101675075","https://openalex.org/W2101840010","https://openalex.org/W2103519107","https://openalex.org/W2114129195","https://openalex.org/W2122548617","https://openalex.org/W2127271355","https://openalex.org/W2128659236","https://openalex.org/W2129638195","https://openalex.org/W2136274821","https://openalex.org/W2141116650","https://openalex.org/W2145096794","https://openalex.org/W2163742397","https://openalex.org/W2169273233","https://openalex.org/W2200650940","https://openalex.org/W2405858948","https://openalex.org/W2950724699","https://openalex.org/W2963438348","https://openalex.org/W4235713725","https://openalex.org/W6658971160","https://openalex.org/W6675709261","https://openalex.org/W6713435244","https://openalex.org/W6763680886"],"related_works":["https://openalex.org/W2394313973","https://openalex.org/W1258664604","https://openalex.org/W4285223790","https://openalex.org/W2952052090","https://openalex.org/W4293585078","https://openalex.org/W2389636997","https://openalex.org/W2349018871","https://openalex.org/W2135355720","https://openalex.org/W2737338842","https://openalex.org/W3005946484"],"abstract_inverted_index":{"In":[0,88,165],"this":[1,48,155],"paper,":[2],"the":[3,7,16,28,36,40,44,54,71,84,111,125,135,141,151,162],"problem":[4],"of":[5,10,39,98,102,124,137,161,175],"estimating":[6],"unknown":[8],"degree":[9],"sparsity":[11,29,86,112],"from":[12,35],"compressive":[13],"measurements":[14,106],"without":[15],"need":[17],"to":[18,50,69,109,128],"carry":[19],"out":[20],"a":[21,75,99,148,179,187],"sparse":[22],"recovery":[23],"step":[24],"is":[25,61,91,190],"investigated.":[26],"While":[27],"order":[30],"can":[31],"be":[32,51,129],"directly":[33],"inferred":[34],"effective":[37,80,85],"rank":[38,81],"observation":[41],"matrix":[42,76],"in":[43,53,139,147,150,173],"multiple":[45],"snapshot":[46,58],"case,":[47],"appears":[49],"impossible":[52],"more":[55,120],"challenging":[56],"single":[57],"case.":[59],"It":[60],"shown":[62],"that":[63,78,93,95,107,185],"specially":[64],"designed":[65],"measurement":[66,72,142,163],"matrices":[67,94,104,126,170,184],"allow":[68,108],"rearrange":[70],"vector":[73],"into":[74],"such":[77],"its":[79],"coincides":[82],"with":[83],"order.":[87,113],"fact,":[89],"it":[90],"proven":[92],"are":[96,118,171],"composed":[97],"Khatri-Rao":[100,167],"product":[101],"smaller":[103],"generate":[105],"infer":[110],"Moreover,":[114],"if":[115],"some":[116],"samples":[117],"used":[119],"than":[121],"once,":[122],"one":[123],"needs":[127],"Vandermonde.":[130],"These":[131],"structural":[132],"constraints":[133],"reduce":[134],"degrees":[136],"freedom":[138],"choosing":[140],"matrix,":[143],"which":[144],"may":[145],"incur":[146],"degradation":[149],"achievable":[152],"coherence.":[153],"Thus,":[154],"paper":[156],"also":[157],"addresses":[158],"suitable":[159],"choices":[160],"matrices.":[164],"particular,":[166],"and":[168,178],"Vandermonde":[169,183],"analyzed":[172],"terms":[174],"their":[176],"coherence":[177,189],"new":[180],"design":[181],"for":[182],"achieves":[186],"low":[188],"proposed.":[191]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}