{"id":"https://openalex.org/W1836917676","doi":"https://doi.org/10.1109/tsp.2015.2481875","title":"Learning Co-Sparse Analysis Operators With Separable Structures","display_name":"Learning Co-Sparse Analysis Operators With Separable Structures","publication_year":2015,"publication_date":"2015-09-24","ids":{"openalex":"https://openalex.org/W1836917676","doi":"https://doi.org/10.1109/tsp.2015.2481875","mag":"1836917676"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2015.2481875","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2481875","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/1503.02398","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065943708","display_name":"Matthias Seibert","orcid":null},"institutions":[{"id":"https://openalex.org/I81321733","display_name":"MTU Aero Engines (Germany)","ror":"https://ror.org/00bxsm637","country_code":"DE","type":"company","lineage":["https://openalex.org/I81321733"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Matthias Seibert","raw_affiliation_strings":["TU M\u00fcnchen, Department of Electrical and Computer Engineering, Munich, Germany","Department of Electrical and Computer Engineering, TU M\u00fcnchen, Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU M\u00fcnchen, Department of Electrical and Computer Engineering, Munich, Germany","institution_ids":["https://openalex.org/I81321733"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, TU M\u00fcnchen, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011285880","display_name":"Julian W\u00f6rmann","orcid":null},"institutions":[{"id":"https://openalex.org/I81321733","display_name":"MTU Aero Engines (Germany)","ror":"https://ror.org/00bxsm637","country_code":"DE","type":"company","lineage":["https://openalex.org/I81321733"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Julian Wormann","raw_affiliation_strings":["TU M\u00fcnchen, Department of Electrical and Computer Engineering, Munich, Germany","Department of Electrical and Computer Engineering, TU M\u00fcnchen, Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU M\u00fcnchen, Department of Electrical and Computer Engineering, Munich, Germany","institution_ids":["https://openalex.org/I81321733"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, TU M\u00fcnchen, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041230403","display_name":"R\u00e9mi Gribonval","orcid":"https://orcid.org/0000-0002-9450-8125"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en informatique et en automatique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Remi Gribonval","raw_affiliation_strings":["Inria & CNRS, PANAMA project-team, Rennes, France","PANAMA project-team, Inria & CNRS, Rennes, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Inria & CNRS, PANAMA project-team, Rennes, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"PANAMA project-team, Inria & CNRS, Rennes, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055847035","display_name":"Martin Kleinsteuber","orcid":"https://orcid.org/0000-0002-4323-9260"},"institutions":[{"id":"https://openalex.org/I81321733","display_name":"MTU Aero Engines (Germany)","ror":"https://ror.org/00bxsm637","country_code":"DE","type":"company","lineage":["https://openalex.org/I81321733"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Kleinsteuber","raw_affiliation_strings":["TU M\u00fcnchen, Department of Electrical and Computer Engineering, Munich, Germany","Department of Electrical and Computer Engineering, TU M\u00fcnchen, Munich, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU M\u00fcnchen, Department of Electrical and Computer Engineering, Munich, Germany","institution_ids":["https://openalex.org/I81321733"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, TU M\u00fcnchen, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5065943708"],"corresponding_institution_ids":["https://openalex.org/I62916508","https://openalex.org/I81321733"],"apc_list":null,"apc_paid":null,"fwci":2.0102,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.84497685,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"64","issue":"1","first_page":"120","last_page":"130"},"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/T10136","display_name":"Statistical Methods and Inference","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.9945999979972839,"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/filter","display_name":"Filter (signal processing)","score":0.5772325992584229},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.55833899974823},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.550028920173645},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5171763300895691},{"id":"https://openalex.org/keywords/sort","display_name":"sort","score":0.490116685628891},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.4469437599182129},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.42459675669670105},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3896687924861908},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37081238627433777},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3648383617401123},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.12384384870529175}],"concepts":[{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.5772325992584229},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.55833899974823},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.550028920173645},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5171763300895691},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.490116685628891},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.4469437599182129},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.42459675669670105},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3896687924861908},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37081238627433777},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3648383617401123},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.12384384870529175},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2015.2481875","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2015.2481875","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:1503.02398","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.02398","pdf_url":"https://arxiv.org/pdf/1503.02398","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":[],"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:HAL:hal-01130411v1","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-01130411","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Signal Processing, 2015, 64 (1), pp.120-130. ⟨10.1109/TSP.2015.2481875⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1503.02398","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.02398","pdf_url":"https://arxiv.org/pdf/1503.02398","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":[],"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":[],"awards":[{"id":"https://openalex.org/G1850372982","display_name":null,"funder_award_id":"KL 2189/8-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5704530987","display_name":null,"funder_award_id":"ERC-StG-2011-277906","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W89497986","https://openalex.org/W114517082","https://openalex.org/W1546851689","https://openalex.org/W1804110266","https://openalex.org/W1933990309","https://openalex.org/W1973839740","https://openalex.org/W1973890885","https://openalex.org/W1980570027","https://openalex.org/W1994281301","https://openalex.org/W1994616650","https://openalex.org/W2009741049","https://openalex.org/W2011464887","https://openalex.org/W2013912476","https://openalex.org/W2023722580","https://openalex.org/W2024254345","https://openalex.org/W2025948329","https://openalex.org/W2049893860","https://openalex.org/W2066771519","https://openalex.org/W2102486516","https://openalex.org/W2103559027","https://openalex.org/W2103888336","https://openalex.org/W2103972570","https://openalex.org/W2112447569","https://openalex.org/W2120047933","https://openalex.org/W2120350480","https://openalex.org/W2135498906","https://openalex.org/W2138674039","https://openalex.org/W2140514146","https://openalex.org/W2150912629","https://openalex.org/W2152171106","https://openalex.org/W2167349346","https://openalex.org/W2171004446","https://openalex.org/W2222512263","https://openalex.org/W2579923771","https://openalex.org/W2963641291","https://openalex.org/W2963811803","https://openalex.org/W2963935689","https://openalex.org/W2989661724","https://openalex.org/W3099751318","https://openalex.org/W3100455090","https://openalex.org/W3102317997","https://openalex.org/W3105628834","https://openalex.org/W3124114587","https://openalex.org/W4205293427","https://openalex.org/W4210556995","https://openalex.org/W6634231340","https://openalex.org/W6675672627","https://openalex.org/W6675683289","https://openalex.org/W6676727762","https://openalex.org/W6712659126","https://openalex.org/W6732517885"],"related_works":["https://openalex.org/W2361805396","https://openalex.org/W2972254340","https://openalex.org/W2009525028","https://openalex.org/W1805912688","https://openalex.org/W4321064619","https://openalex.org/W2373973507","https://openalex.org/W2022231341","https://openalex.org/W4250902763","https://openalex.org/W4255476312","https://openalex.org/W2351154965"],"abstract_inverted_index":{"In":[0,83],"the":[1,16,48,53,58,60,91,122,129,143,165,169,206,210,214],"co-sparse":[2],"analysis":[3,39,185],"model":[4,54],"a":[5,12,31,75,80,97,107,139,175,192],"set":[6],"of":[7,15,19,40,70,114,142,148,168,213],"filters":[8,105],"is":[9,55,64,78,87,151,174],"applied":[10],"to":[11,45,47,57,137,152,182,209],"signal":[13,17,49],"out":[14],"class":[18,77],"interest":[20],"yielding":[21],"sparse":[22],"filter":[23,92,123],"responses.":[24],"As":[25],"such,":[26],"it":[27,63,86],"may":[28],"serve":[29],"as":[30],"prior":[32],"in":[33,96],"inverse":[34],"problems,":[35],"or":[36],"for":[37,65,74,120,156,164],"structural":[38],"signals":[41],"that":[42,90,131,204],"are":[43,94,135,202],"known":[44],"belong":[46],"class.":[50],"The":[51,68,145,172],"more":[52,61],"adapted":[56],"class,":[59],"reliable":[62,140],"these":[66],"purposes.":[67],"task":[69],"learning":[71,170],"such":[72],"operators":[73,113],"given":[76],"therefore":[79],"crucial":[81],"problem.":[82],"many":[84],"applications,":[85],"also":[88,127],"required":[89,136],"responses":[93],"obtained":[95],"timely":[98],"manner,":[99],"which":[100,190],"can":[101,112],"be":[102,117],"achieved":[103],"by":[104,159],"with":[106,187],"separable":[108,188],"structure.":[109],"Not":[110],"only":[111],"this":[115,149,157],"sort":[116],"efficiently":[118],"used":[119],"computing":[121],"responses,":[124],"but":[125],"they":[126],"have":[128],"advantage":[130],"less":[132],"training":[133],"samples":[134],"obtain":[138],"estimate":[141],"operator.":[144],"first":[146],"contribution":[147],"work":[150],"give":[153],"theoretical":[154],"evidence":[155],"claim":[158],"providing":[160],"an":[161,184],"upper":[162],"bound":[163],"sample":[166,207],"complexity":[167,208],"process.":[171],"second":[173],"stochastic":[176],"gradient":[177],"descent":[178],"(SGD)":[179],"method":[180],"designed":[181],"learn":[183],"operator":[186],"structures,":[189],"includes":[191],"novel":[193],"and":[194],"efficient":[195],"step":[196],"size":[197],"selection":[198],"rule.":[199],"Numerical":[200],"experiments":[201],"provided":[203],"link":[205],"convergence":[211],"speed":[212],"SGD":[215],"algorithm.":[216]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}