{"id":"https://openalex.org/W2087984358","doi":"https://doi.org/10.1109/tsp.2012.2218807","title":"A Multilevel Iterated-Shrinkage Approach to $l_{1}$ Penalized Least-Squares Minimization","display_name":"A Multilevel Iterated-Shrinkage Approach to $l_{1}$ Penalized Least-Squares Minimization","publication_year":2012,"publication_date":"2012-09-15","ids":{"openalex":"https://openalex.org/W2087984358","doi":"https://doi.org/10.1109/tsp.2012.2218807","mag":"2087984358"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2012.2218807","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2218807","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/A5042450080","display_name":"Eran Treister","orcid":"https://orcid.org/0000-0002-5351-0966"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"E. Treister","raw_affiliation_strings":["Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel","[Department of Computer Science, Technion, Israel Institute of Technology, Haifa, Israel]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"[Department of Computer Science, Technion, Israel Institute of Technology, Haifa, Israel]","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072314269","display_name":"Irad Yavneh","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"I. Yavneh","raw_affiliation_strings":["Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel","[Department of Computer Science, Technion, Israel Institute of Technology, Haifa, Israel]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"[Department of Computer Science, Technion, Israel Institute of Technology, Haifa, Israel]","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.86746861,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"60","issue":"12","first_page":"6319","last_page":"6329"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9961000084877014,"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/underdetermined-system","display_name":"Underdetermined system","score":0.8809348344802856},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.6104108095169067},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5933642387390137},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5781142115592957},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5282097458839417},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5233518481254578},{"id":"https://openalex.org/keywords/iterative-refinement","display_name":"Iterative refinement","score":0.4580707550048828},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.45125874876976013},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4424362778663635},{"id":"https://openalex.org/keywords/shrinkage","display_name":"Shrinkage","score":0.44138047099113464},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4193534851074219},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4101477265357971},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39602985978126526},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3230966031551361},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.12803462147712708}],"concepts":[{"id":"https://openalex.org/C179690561","wikidata":"https://www.wikidata.org/wiki/Q4316110","display_name":"Underdetermined system","level":2,"score":0.8809348344802856},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.6104108095169067},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5933642387390137},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5781142115592957},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5282097458839417},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5233518481254578},{"id":"https://openalex.org/C2779982483","wikidata":"https://www.wikidata.org/wiki/Q6094420","display_name":"Iterative refinement","level":2,"score":0.4580707550048828},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.45125874876976013},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4424362778663635},{"id":"https://openalex.org/C180145272","wikidata":"https://www.wikidata.org/wiki/Q7504144","display_name":"Shrinkage","level":2,"score":0.44138047099113464},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4193534851074219},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4101477265357971},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39602985978126526},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3230966031551361},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.12803462147712708},{"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2012.2218807","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2218807","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":[],"funders":[{"id":"https://openalex.org/F4320320946","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W1518639170","https://openalex.org/W1540764732","https://openalex.org/W1976709621","https://openalex.org/W1977905043","https://openalex.org/W1980454827","https://openalex.org/W1986931325","https://openalex.org/W1996287810","https://openalex.org/W1997542937","https://openalex.org/W1999174140","https://openalex.org/W2008350622","https://openalex.org/W2009702064","https://openalex.org/W2016278923","https://openalex.org/W2021302824","https://openalex.org/W2021491994","https://openalex.org/W2022611944","https://openalex.org/W2025079166","https://openalex.org/W2028349405","https://openalex.org/W2028452438","https://openalex.org/W2056636001","https://openalex.org/W2079556846","https://openalex.org/W2079756223","https://openalex.org/W2099321050","https://openalex.org/W2100556411","https://openalex.org/W2108982210","https://openalex.org/W2109449402","https://openalex.org/W2110505738","https://openalex.org/W2115706991","https://openalex.org/W2116148865","https://openalex.org/W2116437043","https://openalex.org/W2118297240","https://openalex.org/W2119667497","https://openalex.org/W2119862467","https://openalex.org/W2123023890","https://openalex.org/W2126607811","https://openalex.org/W2127271355","https://openalex.org/W2128659236","https://openalex.org/W2129638195","https://openalex.org/W2140499889","https://openalex.org/W2142940228","https://openalex.org/W2145889472","https://openalex.org/W2147656689","https://openalex.org/W2148556090","https://openalex.org/W2151693816","https://openalex.org/W2157434051","https://openalex.org/W2160547390","https://openalex.org/W2160979406","https://openalex.org/W2163398148","https://openalex.org/W2163985581","https://openalex.org/W2289917018","https://openalex.org/W2293318283","https://openalex.org/W2296616510","https://openalex.org/W2954811775","https://openalex.org/W2963322354","https://openalex.org/W3098745759","https://openalex.org/W4235713725","https://openalex.org/W4250955649","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2084415399","https://openalex.org/W2084978503","https://openalex.org/W2415178532","https://openalex.org/W2136742204","https://openalex.org/W2040458293","https://openalex.org/W2112387511","https://openalex.org/W2065919982","https://openalex.org/W1980944339","https://openalex.org/W2087984358","https://openalex.org/W2075055692"],"abstract_inverted_index":{"The":[0],"area":[1],"of":[2,5,17,21,78,89,94,108,132],"sparse":[3,15,92],"approximation":[4],"signals":[6],"is":[7,142],"drawing":[8],"tremendous":[9],"attention":[10],"in":[11,137],"recent":[12],"years.":[13],"Typically,":[14],"solutions":[16,26],"underdetermined":[18],"linear":[19],"systems":[20],"equations":[22],"are":[23,27,51],"required.":[24],"Such":[25],"often":[28,58],"achieved":[29],"by":[30],"minimizing":[31],"an":[32],"<i":[33],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[34,37],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">l</i>":[35],"<sub":[36],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[38],"penalized":[39],"least":[40],"squares":[41],"functional.":[42],"Various":[43],"iterative-shrinkage":[44],"algorithms":[45,136],"have":[46],"recently":[47],"been":[48],"developed":[49],"and":[50,97,104,119],"quite":[52],"effective":[53],"for":[54,81],"handling":[55],"these":[56,82],"problems,":[57],"surpassing":[59],"traditional":[60],"optimization":[61],"techniques.":[62],"In":[63],"this":[64,124],"paper,":[65],"we":[66],"suggest":[67],"a":[68,106],"new":[69,125],"iterative":[70,134],"multilevel":[71],"approach":[72,126],"that":[73,123],"reduces":[74],"the":[75,90,95,130,140],"computational":[76],"cost":[77],"existing":[79,133],"solvers":[80],"inverse":[83],"problems.":[84],"Our":[85],"method":[86],"takes":[87],"advantage":[88],"typically":[91],"representation":[93],"signal,":[96],"at":[98],"each":[99],"iteration":[100],"it":[101],"adaptively":[102],"creates":[103],"processes":[105],"hierarchy":[107],"lower-dimensional":[109],"problems":[110],"employing":[111],"well-known":[112],"iterated":[113],"shrinkage":[114,135],"methods.":[115],"Analytical":[116],"observations":[117],"suggest,":[118],"numerical":[120],"results":[121],"confirm,":[122],"may":[127],"significantly":[128],"enhance":[129],"performance":[131],"cases":[138],"where":[139],"matrix":[141],"given":[143],"explicitly.":[144]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
