{"id":"https://openalex.org/W2963103052","doi":"https://doi.org/10.1109/tci.2015.2485078","title":"Iteratively Reweighted <named-content content-type=\"math\" xlink:type=\"simple\"><inline-formula><tex-math notation=\"LaTeX\">$\\ell_1$</tex-math></inline-formula> </named-content> Approaches to Sparse Composite Regularization","display_name":"Iteratively Reweighted <named-content content-type=\"math\" xlink:type=\"simple\"><inline-formula><tex-math notation=\"LaTeX\">$\\ell_1$</tex-math></inline-formula> </named-content> Approaches to Sparse Composite Regularization","publication_year":2015,"publication_date":"2015-10-01","ids":{"openalex":"https://openalex.org/W2963103052","doi":"https://doi.org/10.1109/tci.2015.2485078","mag":"2963103052"},"language":"en","primary_location":{"id":"doi:10.1109/tci.2015.2485078","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tci.2015.2485078","pdf_url":null,"source":{"id":"https://openalex.org/S4210233665","display_name":"IEEE Transactions on Computational Imaging","issn_l":"2333-9403","issn":["2333-9403","2573-0436"],"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 Computational Imaging","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/A5046840331","display_name":"Rizwan Ahmad","orcid":"https://orcid.org/0000-0002-5917-3788"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Rizwan Ahmad","raw_affiliation_strings":["Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, USA","institution_ids":["https://openalex.org/I52357470"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045693581","display_name":"Philip Schniter","orcid":"https://orcid.org/0000-0003-0939-7545"},"institutions":[{"id":"https://openalex.org/I52357470","display_name":"The Ohio State University","ror":"https://ror.org/00rs6vg23","country_code":"US","type":"education","lineage":["https://openalex.org/I52357470"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Philip Schniter","raw_affiliation_strings":["Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH, USA","institution_ids":["https://openalex.org/I52357470"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046840331"],"corresponding_institution_ids":["https://openalex.org/I52357470"],"apc_list":null,"apc_paid":null,"fwci":2.924,"has_fulltext":false,"cited_by_count":73,"citation_normalized_percentile":{"value":0.90403318,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"1","issue":"4","first_page":"220","last_page":"235"},"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":0.9987000226974487,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/type","display_name":"Type (biology)","score":0.5376756191253662},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5213664770126343},{"id":"https://openalex.org/keywords/content","display_name":"Content (measure theory)","score":0.45005109906196594},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4360145628452301},{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.43550971150398254},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42674848437309265},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39770767092704773},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39119017124176025},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37741920351982117},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.14491575956344604},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10075074434280396}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5376756191253662},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5213664770126343},{"id":"https://openalex.org/C2778152352","wikidata":"https://www.wikidata.org/wiki/Q5165061","display_name":"Content (measure theory)","level":2,"score":0.45005109906196594},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4360145628452301},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.43550971150398254},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42674848437309265},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39770767092704773},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39119017124176025},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37741920351982117},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.14491575956344604},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10075074434280396},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tci.2015.2485078","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tci.2015.2485078","pdf_url":null,"source":{"id":"https://openalex.org/S4210233665","display_name":"IEEE Transactions on Computational Imaging","issn_l":"2333-9403","issn":["2333-9403","2573-0436"],"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 Computational Imaging","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.5799999833106995,"display_name":"Quality Education"}],"awards":[{"id":"https://openalex.org/G324756452","display_name":null,"funder_award_id":"CCF-1218754","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7323262915","display_name":null,"funder_award_id":"CCF-1018368","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":59,"referenced_works":["https://openalex.org/W81972919","https://openalex.org/W169122852","https://openalex.org/W182881619","https://openalex.org/W1590772317","https://openalex.org/W1663973292","https://openalex.org/W1970163214","https://openalex.org/W1975377467","https://openalex.org/W1977777127","https://openalex.org/W1986931325","https://openalex.org/W1988520084","https://openalex.org/W1997301483","https://openalex.org/W2002417691","https://openalex.org/W2008732654","https://openalex.org/W2023722580","https://openalex.org/W2028477434","https://openalex.org/W2049633694","https://openalex.org/W2054110507","https://openalex.org/W2071628472","https://openalex.org/W2092363816","https://openalex.org/W2095106682","https://openalex.org/W2100684614","https://openalex.org/W2100705753","https://openalex.org/W2103559027","https://openalex.org/W2106833843","https://openalex.org/W2107844156","https://openalex.org/W2107861471","https://openalex.org/W2119667497","https://openalex.org/W2119883478","https://openalex.org/W2128744915","https://openalex.org/W2135046866","https://openalex.org/W2142280715","https://openalex.org/W2142374996","https://openalex.org/W2143488385","https://openalex.org/W2144059227","https://openalex.org/W2146571341","https://openalex.org/W2149414429","https://openalex.org/W2154945960","https://openalex.org/W2156706175","https://openalex.org/W2161765392","https://openalex.org/W2164129707","https://openalex.org/W2164278908","https://openalex.org/W2168745297","https://openalex.org/W2518450717","https://openalex.org/W2567948266","https://openalex.org/W2955732252","https://openalex.org/W3105329799","https://openalex.org/W3106348863","https://openalex.org/W3124114587","https://openalex.org/W3133603318","https://openalex.org/W4206310440","https://openalex.org/W4212863985","https://openalex.org/W4247295697","https://openalex.org/W4292363360","https://openalex.org/W6676292492","https://openalex.org/W6681189096","https://openalex.org/W6681410948","https://openalex.org/W6684677280","https://openalex.org/W6726576044","https://openalex.org/W6765435362"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4256576576","https://openalex.org/W3090384609","https://openalex.org/W3194013178","https://openalex.org/W4249086404","https://openalex.org/W2790019364","https://openalex.org/W2486360182","https://openalex.org/W2212119398","https://openalex.org/W4288780803","https://openalex.org/W2187089732"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"the":[2,33,48,53,64,84,93,100],"observation":[3],"that":[4,161],"a":[5,118,138,149],"given":[6],"signal":[7],"x":[8,78],"admits":[9],"sparse":[10,37],"representations":[11],"in":[12],"multiple":[13],"dictionaries":[14],"\u03a8":[15],"d":[18,69,73,77],"but":[19],"with":[20,152],"varying":[21],"levels":[22],"of":[23,35,63,103,110],"sparsity":[24],"across":[25],"dictionaries,":[26],"we":[27],"propose":[28],"two":[29],"new":[30],"algorithms":[31,164],"for":[32],"reconstruction":[34],"(approximately)":[36],"signals":[38],"from":[39,52],"noisy":[40],"linear":[41],"measurements.":[42],"Our":[43,88],"first":[44],"algorithm,":[45,90],"Co-L1,":[46],"extends":[47,92],"well-known":[49,94],"lasso":[50],"algorithm":[51,98],"L1":[54,97,175],"regularizer":[55],"\u2225\u03a8x\u2225":[56],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1":[59,81],"to":[60,99,117,125,133,172],"composite":[61,104],"regularizers":[62],"form":[65],"\u03a3":[66],"\u03bb":[70],"\u2225\u03a8":[74],"while":[82],"self-adjusting":[83],"regularization":[85],"weights":[86],"\u03bbd.":[87],"second":[89],"Co-IRW-L1,":[91],"iteratively":[95],"reweighted":[96],"same":[101],"family":[102],"regularizers.":[105],"We":[106],"provide":[107],"several":[108],"interpretations":[109],"both":[111],"algorithms:":[112],"1)":[113],"majorization-minimization":[114],"(MM)":[115],"applied":[116,124,132],"nonconvex":[119],"log-sum-type":[120],"penalty;":[121,129],"2)":[122],"MM":[123,131],"an":[126],"approximate":[127],"Bo-type":[128],"3)":[130],"Bayesian":[134],"MAP":[135],"inference":[136],"under":[137,148],"particular":[139,150],"hierarchical":[140],"prior;":[141],"and":[142,176],"4)":[143],"variational":[144],"expectation":[145],"maximization":[146],"(VEM)":[147],"prior":[151],"deterministic":[153],"unknown":[154],"parameters.":[155],"A":[156],"detailed":[157],"numerical":[158],"study":[159],"suggests":[160],"our":[162],"proposed":[163],"yield":[165],"significantly":[166],"improved":[167],"recovery":[168],"SNR":[169],"when":[170],"compared":[171],"their":[173],"noncomposite":[174],"IRW-L1":[177],"counterparts.":[178]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":45},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}