{"id":"https://openalex.org/W2169811219","doi":"https://doi.org/10.1109/allerton.2010.5706975","title":"The Convex algebraic geometry of linear inverse problems","display_name":"The Convex algebraic geometry of linear inverse problems","publication_year":2010,"publication_date":"2010-09-01","ids":{"openalex":"https://openalex.org/W2169811219","doi":"https://doi.org/10.1109/allerton.2010.5706975","mag":"2169811219"},"language":"en","primary_location":{"id":"doi:10.1109/allerton.2010.5706975","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2010.5706975","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/1721.1/72963","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105003932","display_name":"Venkat Chandrasekaran","orcid":null},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Venkat Chandrasekaran","raw_affiliation_strings":["Laboratory of Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Laboratory of Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012870568","display_name":"Benjamin Recht","orcid":"https://orcid.org/0000-0002-0293-593X"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Benjamin Recht","raw_affiliation_strings":["Computer Sciences Department, University of Wisconsin, Madison, WI, USA"],"affiliations":[{"raw_affiliation_string":"Computer Sciences Department, University of Wisconsin, Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031935416","display_name":"Pablo A. Parrilo","orcid":"https://orcid.org/0000-0003-1132-8477"},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pablo A. Parrilo","raw_affiliation_strings":["Laboratory of Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Laboratory of Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107833743","display_name":"Alan S. Willsky","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alan S. Willsky","raw_affiliation_strings":["Laboratory of Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"Laboratory of Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5105003932"],"corresponding_institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":9.9179,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.98729236,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"699","last_page":"703"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10378","display_name":"Advanced MRI Techniques and Applications","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5747789144515991},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5173870325088501},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.47096019983291626},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4682430028915405},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4582705795764923},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.44873932003974915},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4474678337574005},{"id":"https://openalex.org/keywords/convex-geometry","display_name":"Convex geometry","score":0.440066933631897},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4361909031867981},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4347207248210907},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.4276735484600067},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42020758986473083},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4166485369205475},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.41475948691368103},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4098619222640991},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.37191224098205566},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.3553975224494934},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3085854649543762},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20872101187705994},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12210789322853088},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11450675129890442}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5747789144515991},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5173870325088501},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.47096019983291626},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4682430028915405},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4582705795764923},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.44873932003974915},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4474678337574005},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.440066933631897},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4361909031867981},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4347207248210907},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.4276735484600067},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42020758986473083},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4166485369205475},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.41475948691368103},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4098619222640991},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.37191224098205566},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3553975224494934},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3085854649543762},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20872101187705994},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12210789322853088},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11450675129890442},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/allerton.2010.5706975","is_oa":false,"landing_page_url":"https://doi.org/10.1109/allerton.2010.5706975","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)","raw_type":"proceedings-article"},{"id":"pmh:oai:dspace.mit.edu:1721.1/72963","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/72963","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE","raw_type":"http://purl.org/eprint/type/ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/72963","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/72963","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE","raw_type":"http://purl.org/eprint/type/ConferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W74946117","https://openalex.org/W188867022","https://openalex.org/W1539838732","https://openalex.org/W1597196612","https://openalex.org/W1967184028","https://openalex.org/W1986554702","https://openalex.org/W2037928204","https://openalex.org/W2050834445","https://openalex.org/W2092074494","https://openalex.org/W2097476744","https://openalex.org/W2101837693","https://openalex.org/W2118550318","https://openalex.org/W2132267493","https://openalex.org/W2145096794","https://openalex.org/W2296616510","https://openalex.org/W2611328865","https://openalex.org/W2953379763","https://openalex.org/W4206570602","https://openalex.org/W4250955649","https://openalex.org/W4251232133","https://openalex.org/W4299599836","https://openalex.org/W4301425558","https://openalex.org/W6677554766"],"related_works":["https://openalex.org/W36492929","https://openalex.org/W4298361382","https://openalex.org/W2963981982","https://openalex.org/W2508291186","https://openalex.org/W1965005534","https://openalex.org/W54701774","https://openalex.org/W4294007578","https://openalex.org/W2371177213","https://openalex.org/W4367190850","https://openalex.org/W2040676043"],"abstract_inverted_index":{"We":[0,20],"study":[1],"a":[2,30,43,81,109,121],"class":[3],"of":[4,14,33,36,84,115],"ill-posed":[5],"linear":[6,34,85,105,113,126],"inverse":[7],"problems":[8,90],"in":[9,24,50],"which":[10,25,92],"the":[11,22,37],"underlying":[12,38],"model":[13],"interest":[15],"has":[16],"simple":[17],"algebraic":[18],"structure.":[19],"consider":[21],"setting":[23],"we":[26,41],"have":[27],"access":[28],"to":[29,52,91],"limited":[31,104,125],"number":[32,83],"measurements":[35],"model,":[39],"and":[40,69,77,118],"propose":[42],"general":[44],"framework":[45,94],"based":[46,61],"on":[47,62],"convex":[48],"optimization":[49],"order":[51],"recover":[53],"this":[54],"model.":[55],"This":[56],"formulation":[57],"generalizes":[58],"previous":[59],"methods":[60],"\u2113":[63],"<sub":[64],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[65],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[66],"-norm":[67],"minimization":[68,72],"nuclear":[70],"norm":[71],"for":[73],"recovering":[74,99,108,120],"sparse":[75],"vectors":[76],"low-rank":[78,122],"matrices":[79],"from":[80,103,124],"small":[82],"measurements.":[86],"For":[87],"example":[88],"some":[89],"our":[93],"is":[95],"applicable":[96],"include":[97],"(1)":[98],"an":[100],"orthogonal":[101],"matrix":[102],"measurements,":[106],"(2)":[107],"measure":[110],"given":[111],"random":[112],"combinations":[114],"its":[116],"moments,":[117],"(3)":[119],"tensor":[123],"observations.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":16}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
