{"id":"https://openalex.org/W2508384533","doi":"https://doi.org/10.1109/isit.2016.7541384","title":"Phase transition and noise sensitivity of \u2113 <sub>p</sub> -minimization for 0 \u2264 p \u2264 1","display_name":"Phase transition and noise sensitivity of \u2113 <sub>p</sub> -minimization for 0 \u2264 p \u2264 1","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2508384533","doi":"https://doi.org/10.1109/isit.2016.7541384","mag":"2508384533"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2016.7541384","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541384","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5003315201","display_name":"Haolei Weng","orcid":"https://orcid.org/0000-0002-9879-7841"},"institutions":[{"id":"https://openalex.org/I5873027","display_name":"Columbia International University","ror":"https://ror.org/01p2bvc62","country_code":"US","type":"education","lineage":["https://openalex.org/I5873027"]},{"id":"https://openalex.org/I76835614","display_name":"University of Missouri","ror":"https://ror.org/02ymw8z06","country_code":"US","type":"education","lineage":["https://openalex.org/I76835614"]},{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Haolei Weng","raw_affiliation_strings":["Statistics, Columbia University, United States","Statistics Columbia University"],"affiliations":[{"raw_affiliation_string":"Statistics, Columbia University, United States","institution_ids":["https://openalex.org/I78577930","https://openalex.org/I76835614","https://openalex.org/I5873027"]},{"raw_affiliation_string":"Statistics Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100665342","display_name":"Le Zheng","orcid":"https://orcid.org/0000-0002-4972-9199"},"institutions":[{"id":"https://openalex.org/I5873027","display_name":"Columbia International University","ror":"https://ror.org/01p2bvc62","country_code":"US","type":"education","lineage":["https://openalex.org/I5873027"]},{"id":"https://openalex.org/I76835614","display_name":"University of Missouri","ror":"https://ror.org/02ymw8z06","country_code":"US","type":"education","lineage":["https://openalex.org/I76835614"]},{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Le Zheng","raw_affiliation_strings":["Electrical Engineering, Columbia University, United States","Electrical Engineering Columbia University"],"affiliations":[{"raw_affiliation_string":"Electrical Engineering, Columbia University, United States","institution_ids":["https://openalex.org/I78577930","https://openalex.org/I5873027","https://openalex.org/I76835614"]},{"raw_affiliation_string":"Electrical Engineering Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017771205","display_name":"Arian Maleki","orcid":"https://orcid.org/0000-0002-5626-5206"},"institutions":[{"id":"https://openalex.org/I5873027","display_name":"Columbia International University","ror":"https://ror.org/01p2bvc62","country_code":"US","type":"education","lineage":["https://openalex.org/I5873027"]},{"id":"https://openalex.org/I76835614","display_name":"University of Missouri","ror":"https://ror.org/02ymw8z06","country_code":"US","type":"education","lineage":["https://openalex.org/I76835614"]},{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arian Maleki","raw_affiliation_strings":["Statistics, Columbia University, United States","Statistics Columbia University"],"affiliations":[{"raw_affiliation_string":"Statistics, Columbia University, United States","institution_ids":["https://openalex.org/I78577930","https://openalex.org/I76835614","https://openalex.org/I5873027"]},{"raw_affiliation_string":"Statistics Columbia University","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100382658","display_name":"Xiaodong Wang","orcid":"https://orcid.org/0000-0002-2945-9240"},"institutions":[{"id":"https://openalex.org/I5873027","display_name":"Columbia International University","ror":"https://ror.org/01p2bvc62","country_code":"US","type":"education","lineage":["https://openalex.org/I5873027"]},{"id":"https://openalex.org/I76835614","display_name":"University of Missouri","ror":"https://ror.org/02ymw8z06","country_code":"US","type":"education","lineage":["https://openalex.org/I76835614"]},{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaodong Wang","raw_affiliation_strings":["Electrical Engineering, Columbia University, United States","Electrical Engineering Columbia University"],"affiliations":[{"raw_affiliation_string":"Electrical Engineering, Columbia University, United States","institution_ids":["https://openalex.org/I78577930","https://openalex.org/I5873027","https://openalex.org/I76835614"]},{"raw_affiliation_string":"Electrical Engineering Columbia University","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5003315201"],"corresponding_institution_ids":["https://openalex.org/I5873027","https://openalex.org/I76835614","https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.07386235,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"675","last_page":"679"},"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9983000159263611,"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":0.9947999715805054,"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/algorithm","display_name":"Algorithm","score":0.4215453267097473},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3674843907356262},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.36049455404281616}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4215453267097473},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3674843907356262},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36049455404281616}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2016.7541384","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541384","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1786681852","https://openalex.org/W1876208216","https://openalex.org/W1965169081","https://openalex.org/W2004544971","https://openalex.org/W2011236412","https://openalex.org/W2012961725","https://openalex.org/W2019741018","https://openalex.org/W2025666718","https://openalex.org/W2072327470","https://openalex.org/W2093347109","https://openalex.org/W2111067490","https://openalex.org/W2114748345","https://openalex.org/W2120170055","https://openalex.org/W2125768972","https://openalex.org/W2139053635","https://openalex.org/W2160955696","https://openalex.org/W2164595191","https://openalex.org/W2184322798","https://openalex.org/W2310197699","https://openalex.org/W2319338832","https://openalex.org/W2921243010","https://openalex.org/W2963791198","https://openalex.org/W2964026624","https://openalex.org/W3121195152","https://openalex.org/W6639212711","https://openalex.org/W6677895753","https://openalex.org/W6698296029","https://openalex.org/W6759794147"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"Recovering":[0],"a":[1,211],"sparse":[2],"vector":[3],"x":[4,189],"<sub":[5,28,57,73,81,190],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[6,11,22,29,58,74,77,82,85,101,191],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</sub>":[7,30,192],"\u2208":[8,19,89],"\u211d":[9,20],"<sup":[10,21,76,84,100],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</sup>":[12],"from":[13,103],"its":[14],"noisy":[15],"linear":[16],"observations,":[17],"y":[18,25],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[23],"with":[24,181],"=":[26,153],"Ax":[27],"+":[31,79],"w,":[32,217],"has":[33,49],"been":[34],"the":[35,43,53,66,97,108,130,147,174,182,185,196,199],"central":[36],"problem":[37],"of":[38,42,45,55,68,111,120,127,160,165,184,188,198,205,214],"compressed":[39],"sensing.":[40],"One":[41],"classes":[44],"recovery":[46],"algorithms":[47],"that":[48,64],"attracted":[50],"attention":[51],"is":[52,129,218],"class":[54],"\u2113":[56],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</sub>":[59,83],"-regularized":[60],"least":[61],"squares":[62],"(LPLS)":[63],"seeks":[65],"minimum":[67],"1/2":[69],"\u2225y":[70],"-":[71],"Ax\u2225":[72],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sub>":[75],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[78],"\u03bb\u2225x\u2225":[80],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</sup>":[86],"for":[87,132,151,162],"p":[88,136,152,168,206],"[0,":[90],"1].":[91],"In":[92],"this":[93],"paper":[94,114],"we":[95],"employ":[96],"Replica":[98],"method":[99],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sup>":[102],"statistical":[104],"physics":[105],"to":[106],"analyze":[107],"global":[109],"minima":[110],"LPLS.":[112],"Our":[113],"reveals":[115],"several":[116],"surprising":[117],"asymptotic":[118],"properties":[119],"LPLS:":[121],"(i)":[122],"The":[123,156],"phase":[124,140,148,157,200],"transition":[125,141,149,158,201],"curve":[126,150,159],"LPLS":[128,161],"same":[131],"every":[133,163],"0":[134,166],"\u2264":[135,167,169],"<;":[137],"1.":[138,154],"These":[139],"curves":[142],"are":[143],"much":[144],"higher":[145],"than":[146],"(ii)":[155],"value":[164],"1":[170],"depends":[171],"only":[172],"on":[173],"sparsity":[175],"level":[176],"and":[177],"does":[178],"not":[179],"change":[180],"distribution":[183],"non-zero":[186],"coefficients":[187],".":[193],"(iii)":[194],"Despite":[195],"equality":[197],"curves,":[202],"different":[203,208],"values":[204],"show":[207],"performances":[209],"once":[210],"small":[212],"amount":[213],"measurement":[215],"noise,":[216],"added.":[219]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}