{"id":"https://openalex.org/W4292968737","doi":"https://doi.org/10.1109/tsp.2022.3199664","title":"Fast Sampling and Reconstruction for Linear Inverse Problems: From Vectors to Tensors","display_name":"Fast Sampling and Reconstruction for Linear Inverse Problems: From Vectors to Tensors","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4292968737","doi":"https://doi.org/10.1109/tsp.2022.3199664"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2022.3199664","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2022.3199664","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/A5101848669","display_name":"Fen Wang","orcid":"https://orcid.org/0000-0002-9109-4086"},"institutions":[{"id":"https://openalex.org/I4210123185","display_name":"Zhejiang Lab","ror":"https://ror.org/02m2h7991","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210123185"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fen Wang","raw_affiliation_strings":["Zhejiang Lab, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Zhejiang Lab, Hangzhou, China","institution_ids":["https://openalex.org/I4210123185"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038897476","display_name":"Gene Cheung","orcid":"https://orcid.org/0000-0002-5571-4137"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Gene Cheung","raw_affiliation_strings":["Department of EECS, York University, Toronto, ON, Canada","department of EECS, York University, 4700 Keele Street, Toronto, Canada"],"affiliations":[{"raw_affiliation_string":"Department of EECS, York University, Toronto, ON, Canada","institution_ids":["https://openalex.org/I192455969"]},{"raw_affiliation_string":"department of EECS, York University, 4700 Keele Street, Toronto, Canada","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021697903","display_name":"Taihao Li","orcid":"https://orcid.org/0000-0003-3279-7125"},"institutions":[{"id":"https://openalex.org/I4210123185","display_name":"Zhejiang Lab","ror":"https://ror.org/02m2h7991","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210123185"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Taihao Li","raw_affiliation_strings":["Zhejiang Lab, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Zhejiang Lab, Hangzhou, China","institution_ids":["https://openalex.org/I4210123185"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110373346","display_name":"Ying Du","orcid":null},"institutions":[{"id":"https://openalex.org/I4210123185","display_name":"Zhejiang Lab","ror":"https://ror.org/02m2h7991","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210123185"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ying Du","raw_affiliation_strings":["Zhejiang Lab, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Zhejiang Lab, Hangzhou, China","institution_ids":["https://openalex.org/I4210123185"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054105228","display_name":"Yu-Ping Ruan","orcid":"https://orcid.org/0000-0002-9800-3271"},"institutions":[{"id":"https://openalex.org/I4210123185","display_name":"Zhejiang Lab","ror":"https://ror.org/02m2h7991","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210123185"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu-Ping Ruan","raw_affiliation_strings":["Zhejiang Lab, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Zhejiang Lab, Hangzhou, China","institution_ids":["https://openalex.org/I4210123185"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101848669"],"corresponding_institution_ids":["https://openalex.org/I4210123185"],"apc_list":null,"apc_paid":null,"fwci":0.8307,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66085795,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"70","issue":null,"first_page":"6376","last_page":"6391"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mathematics","display_name":"Mathematics","score":0.76507967710495},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5406742691993713},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5184885263442993},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5179118514060974},{"id":"https://openalex.org/keywords/multilinear-algebra","display_name":"Multilinear algebra","score":0.4762420952320099},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.45112624764442444},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.433728963136673},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3663678765296936},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35911107063293457},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34108805656433105},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33376505970954895},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28622186183929443},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16388273239135742},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.13005229830741882}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.76507967710495},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5406742691993713},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5184885263442993},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5179118514060974},{"id":"https://openalex.org/C60321788","wikidata":"https://www.wikidata.org/wiki/Q1197190","display_name":"Multilinear algebra","level":5,"score":0.4762420952320099},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.45112624764442444},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.433728963136673},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3663678765296936},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35911107063293457},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34108805656433105},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33376505970954895},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28622186183929443},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16388273239135742},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.13005229830741882},{"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/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"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/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2022.3199664","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2022.3199664","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":[],"awards":[{"id":"https://openalex.org/G2254045896","display_name":null,"funder_award_id":"2021TQ0309","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G4251215508","display_name":null,"funder_award_id":"RGPAS-2019-00110","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G968945561","display_name":null,"funder_award_id":"RGPIN-2019-06271","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W391578156","https://openalex.org/W1557991152","https://openalex.org/W1576820654","https://openalex.org/W1665592999","https://openalex.org/W1687080872","https://openalex.org/W1964077898","https://openalex.org/W1971835972","https://openalex.org/W1972959470","https://openalex.org/W1987484735","https://openalex.org/W2064314582","https://openalex.org/W2066792693","https://openalex.org/W2119237435","https://openalex.org/W2119412403","https://openalex.org/W2139182243","https://openalex.org/W2169207653","https://openalex.org/W2469230926","https://openalex.org/W2606654184","https://openalex.org/W2611875623","https://openalex.org/W2686306198","https://openalex.org/W2747803690","https://openalex.org/W2782517596","https://openalex.org/W2796431263","https://openalex.org/W2810526380","https://openalex.org/W2918728295","https://openalex.org/W2963341069","https://openalex.org/W2972918686","https://openalex.org/W2983221284","https://openalex.org/W2989504803","https://openalex.org/W3011038560","https://openalex.org/W3018660603","https://openalex.org/W3035497236","https://openalex.org/W3095079835","https://openalex.org/W3134389820","https://openalex.org/W4234163981","https://openalex.org/W4240790602","https://openalex.org/W4241632258","https://openalex.org/W4249713861","https://openalex.org/W4254714429","https://openalex.org/W4300031234","https://openalex.org/W6744287318"],"related_works":["https://openalex.org/W1610250788","https://openalex.org/W4289304899","https://openalex.org/W4387947274","https://openalex.org/W3081577676","https://openalex.org/W2593392256","https://openalex.org/W2034350517","https://openalex.org/W2088837947","https://openalex.org/W2756431649","https://openalex.org/W2592897906","https://openalex.org/W567465994"],"abstract_inverted_index":{"Signals":[0],"typical":[1],"in":[2,27],"the":[3,28,156,161,189,228,265,286,300],"real":[4],"world":[5],"have":[6],"different":[7],"modes,":[8],"expressed":[9],"as":[10,118],"vectors,":[11],"matrices,":[12],"or":[13],"higher-order":[14,76,246],"tensors.":[15],"In":[16,85],"practice,":[17],"a":[18,45,90,109,134,181,196,199,223,237],"target":[19],"signal":[20,111],"is":[21,53,116,131,219],"commonly":[22],"assumed":[23],"to":[24,54,79,102,195,226,253,284,297,308],"be":[25,38,149],"linear":[26,46,132],"residing":[29],"factor":[30,123],"mode(s)":[31],"with":[32,105,112,198],"low-dimensional":[33],"parameters,":[34],"and":[35,82,98,170,185,192,241,292,302],"thus":[36,263],"can":[37,148],"recovered":[39],"from":[40,151,295],"partial":[41,152],"samples":[42,154,169],"by":[43,256],"solving":[44],"inverse":[47],"problem":[48,184,197,230],"(LIP).":[49],"Sampling":[50],"for":[51,58,67,75,94],"LIPs":[52],"partially":[55],"query":[56],"signals":[57,96,294],"better":[59],"recovery.":[60],"There":[61],"exist":[62],"many":[63],"fast":[64,91,224],"sampling":[65,92,229,251,276],"methods":[66],"vector":[68,95,211],"signals,":[69,212],"but":[70],"they":[71],"are":[72],"not":[73],"applicable":[74],"tensors":[77,104,298],"due":[78],"high":[80],"computation":[81],"storage":[83],"costs.":[84],"this":[86],"paper,":[87],"we":[88,179,221,248,278],"propose":[89,222,279],"algorithm":[93,225,252],"first":[97],"then":[99],"extend":[100,249],"it":[101,147,187],"sample":[103],"low":[106],"complexity.":[107],"Specifically,":[108],"tensor":[110],"<inline-formula><tex-math":[113,121,125,136,143,172,203,214,259,269],"notation=\"LaTeX\">$R$</tex-math></inline-formula>":[114,122],"modes":[115],"modelled":[117],"multilinear":[119],"on":[120,133,167,236,290],"matrices":[124,258],"notation=\"LaTeX\">${\\mathbf":[126],"\\{U_{i}\\}}^{R}_{i=1}$</tex-math></inline-formula>,":[127],"whose":[128],"vectorized":[129],"version":[130],"matrix":[135,171,238],"notation=\"LaTeX\">$\\pmb":[137,173,204,215,270],"{\\Phi":[138,174,205,207,216,271],"}$</tex-math></inline-formula>&#x2014;the":[139],"Kronecker":[140],"product":[141],"of":[142,177,202,267,304],"notation=\"LaTeX\">$\\mathbf":[144,260],"{U}_{i}$</tex-math></inline-formula>&#x0027;s.":[145],"Thus,":[146],"estimated":[150],"noisy":[153],"via":[155,231],"least-squares":[157],"(LS)":[158],"method,":[159],"where":[160,213],"mean":[162],"square":[163],"error":[164],"(MSE)":[165],"depends":[166],"chosen":[168],"}$</tex-math></inline-formula>.":[175],"Instead":[176],"MSE,":[178],"minimize":[180],"modified":[182],"MSE":[183],"prove":[186],"has":[188],"same":[190],"optimal":[191],"greedy":[193,242],"solutions":[194],"sample-dependent":[200],"sub-matrix":[201],"}\\pmb":[206],"}^\\top$</tex-math></inline-formula>.":[208],"For":[209,245],"one-order":[210],"}=\\mathbf":[217],"{U}_{1}$</tex-math></inline-formula>":[218],"given,":[220],"solve":[227],"simple":[232],"vector-vector":[233],"multiplications":[234],"based":[235],"inversion":[239],"formula":[240],"solution":[243],"reuse.":[244],"tensors,":[247],"our":[250,275,305],"select":[254],"entries":[255],"addressing":[257],"{U}_{i}$</tex-math></inline-formula>&#x0027;s":[261],"directly,":[262],"removing":[264],"burden":[266],"obtaining":[268],"}$</tex-math></inline-formula>":[272],"explicitly.":[273],"Accompanying":[274],"strategy,":[277],"an":[280],"iterative":[281],"reconstruction":[282],"scheme":[283],"estimate":[285],"LS":[287],"solution.":[288],"Experiments":[289],"synthetic":[291],"real-world":[293],"vectors":[296],"validated":[299],"performance":[301],"efficacy":[303],"strategy":[306],"compared":[307],"previous":[309],"methods.":[310]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}