{"id":"https://openalex.org/W1983209504","doi":"https://doi.org/10.1137/110833130","title":"$\\ell_1$ Minimization with Noisy Data","display_name":"$\\ell_1$ Minimization with Noisy Data","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1983209504","doi":"https://doi.org/10.1137/110833130","mag":"1983209504"},"language":"en","primary_location":{"id":"doi:10.1137/110833130","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110833130","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5090598096","display_name":"P. Wojtaszczyk","orcid":"https://orcid.org/0000-0001-9100-3693"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"P. Wojtaszczyk","raw_affiliation_strings":["wojtaszczyk@mimuw.edu.pl#TAB#"],"affiliations":[{"raw_affiliation_string":"wojtaszczyk@mimuw.edu.pl#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090598096"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3718,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.79133178,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"50","issue":"2","first_page":"458","last_page":"467"},"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/mathematics","display_name":"Mathematics","score":0.6719101071357727},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6688035726547241},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4369533061981201},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43112945556640625},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.30749550461769104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6719101071357727},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6688035726547241},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4369533061981201},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43112945556640625},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30749550461769104}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110833130","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110833130","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W2015418199","https://openalex.org/W2020390700","https://openalex.org/W2036850226","https://openalex.org/W2098322313","https://openalex.org/W2119667497","https://openalex.org/W2129131372","https://openalex.org/W2164452299","https://openalex.org/W2289917018","https://openalex.org/W2296616510","https://openalex.org/W4250955649"],"related_works":["https://openalex.org/W2351859806","https://openalex.org/W2067743604","https://openalex.org/W2001324813","https://openalex.org/W4239376463","https://openalex.org/W1996810073","https://openalex.org/W2089811522","https://openalex.org/W4253908528","https://openalex.org/W2092244978","https://openalex.org/W1998839353","https://openalex.org/W2613209927"],"abstract_inverted_index":{"Compressed":[0],"sensing":[1],"aims":[2],"at":[3],"recovering":[4],"a":[5,18],"sparse":[6],"signal":[7],"$x\\in":[8],"\\mathbb{R}^N$":[9],"from":[10,63],"few":[11],"nonadaptive,":[12],"linear":[13],"measurements":[14],"$\\Phi(x)$":[15,42],"given":[16],"by":[17,45],"measurement":[19,41],"matrix":[20,53],"$\\Phi$.":[21],"One":[22],"of":[23],"the":[24,37,49,52,56],"fundamental":[25],"recovery":[26],"algorithms":[27],"is":[28,43],"an":[29],"$\\ell_1$":[30],"minimization.":[31],"In":[32],"this":[33],"paper":[34],"we":[35],"investigate":[36],"situation":[38],"when":[39],"our":[40],"contaminated":[44],"arbitrary":[46],"noise":[47],"under":[48],"assumption":[50],"that":[51],"$\\Phi$":[54],"satisfies":[55],"restricted":[57],"isometry":[58],"property.":[59],"This":[60],"complements":[61],"results":[62],"[Cand\u00e8s,":[64],"Romberg,":[65],"and":[66,76,79],"Tao,":[67],"Comm.":[68],"Pure":[69],"Appl.":[70,81],"Math.,":[71],"59":[72],"(2006),":[73],"pp.":[74,87],"1207\u20131223]":[75],"[DeVore,":[77],"Petrova,":[78],"Wojtaszczyk,":[80],"Comput.":[82],"Harmon.":[83],"Anal.,":[84],"27":[85],"(2009),":[86],"275\u2013288].":[88]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}