{"id":"https://openalex.org/W2109125555","doi":"https://doi.org/10.1109/lsp.2011.2139204","title":"Multidimensional Shrinkage-Thresholding Operator and Group LASSO Penalties","display_name":"Multidimensional Shrinkage-Thresholding Operator and Group LASSO Penalties","publication_year":2011,"publication_date":"2011-04-08","ids":{"openalex":"https://openalex.org/W2109125555","doi":"https://doi.org/10.1109/lsp.2011.2139204","mag":"2109125555"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2011.2139204","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2011.2139204","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","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/A5110014384","display_name":"Arnau Tibau Puig","orcid":null},"institutions":[{"id":"https://openalex.org/I102475099","display_name":"Sup\u00e9lec","ror":"https://ror.org/00n7gwn90","country_code":"FR","type":"education","lineage":["https://openalex.org/I102475099"]},{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Arnau Tibau Puig","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","Signal Processing and Electronic Systems Department, Supelec, E3S-Supelec Systems Sciences, Gif-sur-Yvette, France","Department of Electrical Engineering and Computer Science","Sup\u00e9lec Sciences des Syst\u00e8mes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Signal Processing and Electronic Systems Department, Supelec, E3S-Supelec Systems Sciences, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I102475099"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science","institution_ids":[]},{"raw_affiliation_string":"Sup\u00e9lec Sciences des Syst\u00e8mes","institution_ids":["https://openalex.org/I102475099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091732723","display_name":"Ami Wiesel","orcid":"https://orcid.org/0000-0002-3071-048X"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Ami Wiesel","raw_affiliation_strings":["School of Computer Science and Engineering, Hebrew University of Jerusalem, Jerusalem, Israel","School of Computer Science and Engineering"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Engineering, Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"School of Computer Science and Engineering","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109863250","display_name":"Gilles Fleury","orcid":null},"institutions":[{"id":"https://openalex.org/I102475099","display_name":"Sup\u00e9lec","ror":"https://ror.org/00n7gwn90","country_code":"FR","type":"education","lineage":["https://openalex.org/I102475099"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gilles Fleury","raw_affiliation_strings":["Signal Processing and Electronic Systems Department, Supelec, E3S-Supelec Systems Sciences, Gif-sur-Yvette, France","Sup\u00e9lec Sciences des Syst\u00e8mes"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Signal Processing and Electronic Systems Department, Supelec, E3S-Supelec Systems Sciences, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I102475099"]},{"raw_affiliation_string":"Sup\u00e9lec Sciences des Syst\u00e8mes","institution_ids":["https://openalex.org/I102475099"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077692655","display_name":"Alfred O. Hero","orcid":"https://orcid.org/0000-0002-2531-9670"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alfred O. Hero","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University\uc2a0of\uc2a0Michigan, Ann Arbor, MI, USA","Department of Electrical Engineering and Computer Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University\uc2a0of\uc2a0Michigan, Ann Arbor, MI, USA","institution_ids":[]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.9068,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.97525638,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"18","issue":"6","first_page":"363","last_page":"366"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10534","display_name":"Structural Health Monitoring Techniques","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/thresholding","display_name":"Thresholding","score":0.6315793991088867},{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.5332750082015991},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.468961626291275},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.45939159393310547},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4361559748649597},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40569937229156494},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3909326195716858},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3734055757522583},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37109410762786865},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.08312883973121643},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08275923132896423}],"concepts":[{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.6315793991088867},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.5332750082015991},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.468961626291275},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.45939159393310547},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4361559748649597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40569937229156494},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3909326195716858},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3734055757522583},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37109410762786865},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.08312883973121643},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08275923132896423},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/lsp.2011.2139204","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2011.2139204","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.711.902","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.711.902","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.huji.ac.il/%7Eamiw/tibau_spl2011.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00630478v1","is_oa":false,"landing_page_url":"https://centralesupelec.hal.science/hal-00630478","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 Signal Processing Letters, 2011, 18 (6), pp.363-366. ⟨10.1109/LSP.2011.2139204⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W33214042","https://openalex.org/W1540764732","https://openalex.org/W1953936588","https://openalex.org/W1966626540","https://openalex.org/W1994309289","https://openalex.org/W2006262045","https://openalex.org/W2048679451","https://openalex.org/W2057020849","https://openalex.org/W2057395973","https://openalex.org/W2057950931","https://openalex.org/W2068943497","https://openalex.org/W2100556411","https://openalex.org/W2103519107","https://openalex.org/W2105235982","https://openalex.org/W2115706991","https://openalex.org/W2126607811","https://openalex.org/W2138019504","https://openalex.org/W2146195822","https://openalex.org/W2157879939","https://openalex.org/W2174883827","https://openalex.org/W2296319761","https://openalex.org/W3099503819","https://openalex.org/W6601318844","https://openalex.org/W6681514037"],"related_works":["https://openalex.org/W1542224353","https://openalex.org/W1661087619","https://openalex.org/W2116854923","https://openalex.org/W2750730210","https://openalex.org/W2236974868","https://openalex.org/W4312766348","https://openalex.org/W4233939244","https://openalex.org/W2730764323","https://openalex.org/W3123806511","https://openalex.org/W1976727107"],"abstract_inverted_index":{"The":[0,107,122],"scalar":[1,34,43,69,76,127],"shrinkage-thresholding":[2],"operator":[3,120],"is":[4,36,80,99,114],"a":[5,33,42,63,86,102,148],"key":[6],"ingredient":[7],"in":[8,13,129,186],"variable":[9,35],"selection":[10],"algorithms":[11],"arising":[12],"wavelet":[14],"denoising,":[15],"JPEG2000":[16],"image":[17],"compression":[18],"and":[19,163],"predictive":[20],"analysis":[21],"of":[22,67,85,104,183,189],"gene":[23],"microarray":[24],"data.":[25],"In":[26,48,58,134],"these":[27],"applications,":[28,51],"the":[29,39,68,75,78,83,97,116,126,130,135,140,170,184,187],"decision":[30],"to":[31,41,54,74,109,125,168],"select":[32,55],"given":[37],"as":[38],"solution":[40,108],"sparsity":[44],"penalized":[45,192],"quadratic":[46,88],"optimization.":[47],"some":[49],"other":[50,173],"one":[52],"seeks":[53],"multidimensional":[56,65,117],"variables.":[57],"this":[59,110,160],"work,":[60],"we":[61],"present":[62,179],"natural":[64],"extension":[66],"shrinkage":[70,118,143],"thresholding":[71],"operator.":[72],"Similarly":[73],"case,":[77],"threshold":[79,119],"determined":[81],"by":[82],"minimization":[84],"convex":[87,111,150],"form":[89],"plus":[90],"an":[91,155],"Euclidean":[92],"norm":[93],"penalty,":[94],"however,":[95],"here":[96],"optimization":[98,112,176],"performed":[100],"over":[101],"domain":[103],"dimensionN\u2265":[105],"1.":[106],"problem":[113],"called":[115],"(MSTO).":[121],"MSTO":[123,142,171,185],"reduces":[124],"case":[128,132,137],"special":[131],"ofN=1.":[133],"general":[136],"ofN>;":[138],"1":[139],"optimal":[141],"can":[144],"be":[145],"found":[146],"through":[147],"simple":[149],"line":[151,161],"search.":[152],"We":[153,178],"give":[154],"efficient":[156],"algorithm":[157],"for":[158],"solving":[159],"search":[162],"show":[164],"that":[165],"our":[166],"method":[167],"evaluate":[169],"outperforms":[172],"state-of-the":[174],"art":[175],"approaches.":[177],"several":[180],"illustrative":[181],"applications":[182],"context":[188],"Group":[190],"LASSO":[191],"estimation.":[193]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":5}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}