{"id":"https://openalex.org/W4321607984","doi":"https://doi.org/10.1109/tsp.2023.3248493","title":"On the Foundation of Sparsity Constrained Sensing\u2014Part II: Diophantine Sampling With Arbitrary Temporal and Spatial Sparsity","display_name":"On the Foundation of Sparsity Constrained Sensing\u2014Part II: Diophantine Sampling With Arbitrary Temporal and Spatial Sparsity","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4321607984","doi":"https://doi.org/10.1109/tsp.2023.3248493"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2023.3248493","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tsp.2023.3248493","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":["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/A5101702107","display_name":"Hanshen Xiao","orcid":"https://orcid.org/0000-0003-3380-4518"},"institutions":[{"id":"https://openalex.org/I126820664","display_name":"Vassar College","ror":"https://ror.org/022x6qg61","country_code":"US","type":"education","lineage":["https://openalex.org/I126820664"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hanshen Xiao","raw_affiliation_strings":["CSAIL and the EECS Department, MIT, Cambridge, MA, USA"],"raw_orcid":"https://orcid.org/0000-0003-3380-4518","affiliations":[{"raw_affiliation_string":"CSAIL and the EECS Department, MIT, Cambridge, MA, USA","institution_ids":["https://openalex.org/I126820664"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021178964","display_name":"Beining Zhou","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":"Beining Zhou","raw_affiliation_strings":["Department of Computer Science, Stanford University, Stanford, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100677019","display_name":"Yaowen Zhang","orcid":"https://orcid.org/0000-0002-1379-2639"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaowen Zhang","raw_affiliation_strings":["College of Computer and Information Science, Southwest University, Chongqing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer and Information Science, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047341940","display_name":"Guoqiang Xiao","orcid":"https://orcid.org/0000-0003-2165-476X"},"institutions":[{"id":"https://openalex.org/I142108993","display_name":"Southwest University","ror":"https://ror.org/01kj4z117","country_code":"CN","type":"education","lineage":["https://openalex.org/I142108993"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guoqiang Xiao","raw_affiliation_strings":["College of Computer and Information Science, Southwest University, Chongqing, China"],"raw_orcid":"https://orcid.org/0000-0003-2165-476X","affiliations":[{"raw_affiliation_string":"College of Computer and Information Science, Southwest University, Chongqing, China","institution_ids":["https://openalex.org/I142108993"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":0.6539,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.63228753,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"71","issue":null,"first_page":"1277","last_page":"1292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10860","display_name":"Speech and Audio Processing","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10860","display_name":"Speech and Audio Processing","score":0.9997000098228455,"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9995999932289124,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994000196456909,"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/diophantine-equation","display_name":"Diophantine equation","score":0.798125147819519},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.741496205329895},{"id":"https://openalex.org/keywords/coprime-integers","display_name":"Coprime integers","score":0.537750244140625},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5179135203361511},{"id":"https://openalex.org/keywords/nyquist\u2013shannon-sampling-theorem","display_name":"Nyquist\u2013Shannon sampling theorem","score":0.49822521209716797},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4921409487724304},{"id":"https://openalex.org/keywords/underdetermined-system","display_name":"Underdetermined system","score":0.46096181869506836},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4294695556163788},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4222240447998047},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3344349265098572},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2691408395767212},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13211074471473694},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09140932559967041}],"concepts":[{"id":"https://openalex.org/C206530611","wikidata":"https://www.wikidata.org/wiki/Q905896","display_name":"Diophantine equation","level":2,"score":0.798125147819519},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.741496205329895},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.537750244140625},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5179135203361511},{"id":"https://openalex.org/C288623","wikidata":"https://www.wikidata.org/wiki/Q679800","display_name":"Nyquist\u2013Shannon sampling theorem","level":2,"score":0.49822521209716797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4921409487724304},{"id":"https://openalex.org/C179690561","wikidata":"https://www.wikidata.org/wiki/Q4316110","display_name":"Underdetermined system","level":2,"score":0.46096181869506836},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4294695556163788},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4222240447998047},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3344349265098572},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2691408395767212},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13211074471473694},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09140932559967041},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2023.3248493","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/tsp.2023.3248493","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"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7599999904632568,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W975662943","https://openalex.org/W1483611562","https://openalex.org/W1556226109","https://openalex.org/W1964521756","https://openalex.org/W1987415890","https://openalex.org/W2003157621","https://openalex.org/W2006324729","https://openalex.org/W2012227645","https://openalex.org/W2021794072","https://openalex.org/W2026783525","https://openalex.org/W2030693357","https://openalex.org/W2076597612","https://openalex.org/W2098174516","https://openalex.org/W2104313426","https://openalex.org/W2121157816","https://openalex.org/W2126700042","https://openalex.org/W2148372454","https://openalex.org/W2149551443","https://openalex.org/W2164390589","https://openalex.org/W2168873548","https://openalex.org/W2172082699","https://openalex.org/W2267105192","https://openalex.org/W2324447404","https://openalex.org/W2342925881","https://openalex.org/W2343667351","https://openalex.org/W2346607232","https://openalex.org/W2357400875","https://openalex.org/W2497079801","https://openalex.org/W2530510227","https://openalex.org/W2538651761","https://openalex.org/W2549794316","https://openalex.org/W2586607074","https://openalex.org/W2616555170","https://openalex.org/W2742609933","https://openalex.org/W2794140489","https://openalex.org/W2807984534","https://openalex.org/W2888009369","https://openalex.org/W2888363820","https://openalex.org/W2908607157","https://openalex.org/W2914570530","https://openalex.org/W2914623695","https://openalex.org/W2942508766","https://openalex.org/W2943802243","https://openalex.org/W2963668942","https://openalex.org/W2968170916","https://openalex.org/W2989768113","https://openalex.org/W3088022619","https://openalex.org/W4321484021","https://openalex.org/W6625621987","https://openalex.org/W6658224768"],"related_works":["https://openalex.org/W1268734874","https://openalex.org/W2963315227","https://openalex.org/W2795270377","https://openalex.org/W2896356600","https://openalex.org/W4384405297","https://openalex.org/W1552705069","https://openalex.org/W2949121685","https://openalex.org/W2094929658","https://openalex.org/W4293509788","https://openalex.org/W1546581161"],"abstract_inverted_index":{"In":[0,228],"the":[1,5,13,39,43,49,62,96,106,113,131,156,165,170,198,230,235],"second":[2],"part":[3],"of":[4,16,45,64,98,125,158,167,173],"series":[6],"papers,":[7],"we":[8,23,143,189],"set":[9],"out":[10],"to":[11,95,119,128,164],"study":[12],"algorithmic":[14],"efficiency":[15],"sparsity-constrained":[17],"sensing.":[18],"Stemmed":[19],"from":[20],"co-prime":[21,58,89],"sampling/array,":[22],"propose":[24,190],"a":[25,65,123,181,208],"generalized":[26],"framework,":[27],"termed":[28],"Diophantine":[29,133],"sensing,":[30],"which":[31,179,211],"utilizes":[32],"genericDiophantine":[33],"equationtheory":[34],"and":[35,48,169],"higher-ordersparse":[36],"rulerto":[37],"strengthen":[38],"sampling":[40,50,90,92,153,183],"time":[41,93],"(delay),":[42],"degree":[44],"freedom":[46],"(DoF),":[47],"sparsity,":[51],"simultaneously.":[52],"It":[53],"is":[54,161],"well":[55],"known":[56,237],"that":[57,145,196,213],"sensing":[59],"can":[60,203],"reconstruct":[61],"autocorrelation":[63],"sequence":[66],"with":[67],"significantly":[68],"more":[69],"lags":[70],"based":[71],"on":[72,140,186],"B\u00e9zout":[73,76],"theorem.":[74],"However,":[75],"theorem":[77],"also":[78],"puts":[79],"two":[80,136,191],"practical":[81],"constraints":[82],"in":[83],"this":[84],"framework.":[85],"For":[86],"frequency":[87,141],"estimation,":[88,105,188],"needs":[91,118],"proportional":[94,163],"product":[97],"down-sampling":[99,149],"rates;":[100],"As":[101],"for":[102,176],"Direction-of-arrival":[103],"(DoA)":[104],"array":[107,193,217,232],"cannot":[108],"be":[109,120,204],"arbitrarily":[110,147,215,219],"sparse,":[111],"where":[112,155],"least":[114,171],"sensor":[115],"inter":[116],"spacing":[117,200],"less":[121],"than":[122],"half":[124],"wavelength.":[126],"Resorting":[127],"higher-moment":[129],"statistics,":[130],"proposed":[132,231],"framework":[134],"presents":[135],"fundamental":[137],"improvements.":[138],"First,":[139],"estimation":[142],"prove":[144],"given":[146,224],"large":[148,206],"rates,":[150],"there":[151],"exist":[152],"schemes":[154],"number":[157,172],"samples":[159],"needed":[160],"only":[162],"sum":[166],"DoF":[168,239],"snapshots":[174],"required":[175],"each":[177],"lag,":[178],"implies":[180],"linear":[182],"time.":[184],"Second,":[185],"DoA":[187],"generic":[192],"constructions":[194],"such":[195],"given$N$sensors,":[197],"minimal":[199],"among":[201],"sensors":[202],"as":[205,207],"polynomial":[209],"of$N$,":[210],"indicates":[212],"an":[214],"sparse":[216],"(with":[218],"small":[220],"mutual":[221],"coupling)":[222],"exists":[223],"sufficiently":[225],"many":[226],"sensors.":[227],"addition,":[229],"configurations":[233],"produce":[234],"best":[236],"asymptotic":[238],"bound.":[240]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
