{"id":"https://openalex.org/W2108982210","doi":"https://doi.org/10.1109/icassp.2006.1660731","title":"Sparse Approximation Via Iterative Thresholding","display_name":"Sparse Approximation Via Iterative Thresholding","publication_year":2006,"publication_date":"2006-08-03","ids":{"openalex":"https://openalex.org/W2108982210","doi":"https://doi.org/10.1109/icassp.2006.1660731","mag":"2108982210"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2006.1660731","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2006.1660731","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings","raw_type":"proceedings-article"},"type":"conference-paper","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/A5055406193","display_name":"Kyle Herrity","orcid":"https://orcid.org/0009-0005-8234-1574"},"institutions":[{"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":["US"],"is_corresponding":false,"raw_author_name":"K.K. Herrity","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, MI, USA","University of Michigan, Department of Mathematics, Ann Arbor, MI 48109"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"University of Michigan, Department of Mathematics, Ann Arbor, MI 48109","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042502878","display_name":"Anna C. Gilbert","orcid":"https://orcid.org/0000-0002-9627-9274"},"institutions":[{"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":["US"],"is_corresponding":false,"raw_author_name":"A.C. Gilbert","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, MI, USA","Dept. of Math., Michigan Univ., Ann Arbor, MI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Dept. of Math., Michigan Univ., Ann Arbor, MI","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000879912","display_name":"Joel A. Tropp","orcid":"https://orcid.org/0000-0003-1024-1791"},"institutions":[{"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":["US"],"is_corresponding":false,"raw_author_name":"J.A. Tropp","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor, MI, USA","Dept. of Math., Michigan Univ., Ann Arbor, MI"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Dept. of Math., Michigan Univ., Ann Arbor, MI","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":140,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"3","issue":null,"first_page":"III","last_page":"624"},"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":1.0,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/matching-pursuit","display_name":"Matching pursuit","score":0.782314658164978},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6204906702041626},{"id":"https://openalex.org/keywords/basis-pursuit","display_name":"Basis pursuit","score":0.6072556376457214},{"id":"https://openalex.org/keywords/shrinkage","display_name":"Shrinkage","score":0.5995412468910217},{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.5931456089019775},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5484730005264282},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5032939314842224},{"id":"https://openalex.org/keywords/coherence","display_name":"Coherence (philosophical gambling strategy)","score":0.5007510185241699},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.48497724533081055},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.45007753372192383},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4459449350833893},{"id":"https://openalex.org/keywords/signal-reconstruction","display_name":"Signal reconstruction","score":0.4199385643005371},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.416089802980423},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4144715666770935},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.3976112902164459},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29256510734558105},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.21927154064178467},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.06813174486160278}],"concepts":[{"id":"https://openalex.org/C156872377","wikidata":"https://www.wikidata.org/wiki/Q6786281","display_name":"Matching pursuit","level":3,"score":0.782314658164978},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6204906702041626},{"id":"https://openalex.org/C99217422","wikidata":"https://www.wikidata.org/wiki/Q4867576","display_name":"Basis pursuit","level":4,"score":0.6072556376457214},{"id":"https://openalex.org/C180145272","wikidata":"https://www.wikidata.org/wiki/Q7504144","display_name":"Shrinkage","level":2,"score":0.5995412468910217},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.5931456089019775},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5484730005264282},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5032939314842224},{"id":"https://openalex.org/C2781181686","wikidata":"https://www.wikidata.org/wiki/Q4226068","display_name":"Coherence (philosophical gambling strategy)","level":2,"score":0.5007510185241699},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.48497724533081055},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.45007753372192383},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4459449350833893},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.4199385643005371},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.416089802980423},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4144715666770935},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.3976112902164459},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29256510734558105},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.21927154064178467},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.06813174486160278},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/icassp.2006.1660731","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2006.1660731","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings","raw_type":"proceedings-article"},{"id":"pmh:oai:authors.library.caltech.edu:9067","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/9067/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Book Section"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.452.1752","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.452.1752","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://authors.library.caltech.edu/9067/1/HERicassp06.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2040073627","https://openalex.org/W2115706991","https://openalex.org/W2116148865","https://openalex.org/W2148556090"],"related_works":["https://openalex.org/W2388133936","https://openalex.org/W2067878805","https://openalex.org/W1992008660","https://openalex.org/W2116148865","https://openalex.org/W1983115982","https://openalex.org/W2086419783","https://openalex.org/W2160547390","https://openalex.org/W59030693","https://openalex.org/W2523302315","https://openalex.org/W1998873033"],"abstract_inverted_index":{"The":[0,31,47],"well-known":[1],"shrinkage":[2,42],"technique":[3],"is":[4,68],"still":[5],"relevant":[6],"for":[7,21,25,59],"contemporary":[8],"signal":[9,67],"processing":[10],"problems":[11],"over":[12],"redundant":[13],"dictionaries.":[14],"We":[15],"present":[16],"theoretical":[17],"and":[18,89],"empirical":[19],"analyses":[20],"two":[22],"iterative":[23],"algorithms":[24,93,96],"sparse":[26,66],"approximation":[27],"that":[28],"use":[29],"shrinkage.":[30],"general":[32,61],"IT":[33,49,62,95],"algorithm":[34,50],"amounts":[35],"to":[36,94],"a":[37,65],"Landweber":[38],"iteration":[39,45],"with":[40],"nonlinear":[41],"at":[43],"each":[44],"step.":[46],"block":[48],"arises":[51],"in":[52,70],"morphological":[53],"components":[54],"analysis.":[55],"A":[56],"sufficient":[57],"condition":[58],"which":[60,71],"exactly":[63],"recovers":[64],"presented,":[69],"the":[72,84],"cumulative":[73],"coherence":[74],"function":[75],"naturally":[76],"arises.":[77],"This":[78],"analysis":[79],"extends":[80],"previous":[81],"results":[82],"concerning":[83],"orthogonal":[85],"matching":[86],"pursuit":[87,91],"(OMP)":[88],"basis":[90],"(BP)":[92]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":18}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
