{"id":"https://openalex.org/W2104991580","doi":"https://doi.org/10.1109/icassp.2009.4960261","title":"Strong thresholds for &amp;#x2113;&lt;inf&gt;2&lt;/inf&gt;/&amp;#x2113;&lt;inf&gt;1&lt;/inf&gt;-optimization in block-sparse compressed sensing","display_name":"Strong thresholds for &amp;#x2113;&lt;inf&gt;2&lt;/inf&gt;/&amp;#x2113;&lt;inf&gt;1&lt;/inf&gt;-optimization in block-sparse compressed sensing","publication_year":2009,"publication_date":"2009-04-01","ids":{"openalex":"https://openalex.org/W2104991580","doi":"https://doi.org/10.1109/icassp.2009.4960261","mag":"2104991580"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2009.4960261","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2009.4960261","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Conference on Acoustics, Speech and Signal Processing","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/A5065505687","display_name":"Mihailo Stojnic","orcid":null},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mihailo Stojnic","raw_affiliation_strings":["Purdue University, West Lafayette, IN, USA","Purdue University West Lafayette IN USA"],"affiliations":[{"raw_affiliation_string":"Purdue University, West Lafayette, IN, USA","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Purdue University West Lafayette IN USA","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065505687"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":3.502,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.93154565,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"3025","last_page":"3028"},"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/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.9980000257492065,"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"}},{"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/compressed-sensing","display_name":"Compressed sensing","score":0.8024963140487671},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5979905724525452},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5827623605728149},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5740482807159424},{"id":"https://openalex.org/keywords/system-of-linear-equations","display_name":"System of linear equations","score":0.5161186456680298},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48935478925704956},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4664936065673828},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.43828293681144714},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37569642066955566},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3594770133495331},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3272795081138611},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.241603821516037}],"concepts":[{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.8024963140487671},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5979905724525452},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5827623605728149},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5740482807159424},{"id":"https://openalex.org/C94523830","wikidata":"https://www.wikidata.org/wiki/Q11203","display_name":"System of linear equations","level":2,"score":0.5161186456680298},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48935478925704956},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4664936065673828},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43828293681144714},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37569642066955566},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3594770133495331},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3272795081138611},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.241603821516037},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icassp.2009.4960261","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2009.4960261","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE International Conference on Acoustics, Speech and Signal Processing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W4516790","https://openalex.org/W8251247","https://openalex.org/W74946117","https://openalex.org/W123230261","https://openalex.org/W200075024","https://openalex.org/W1579599383","https://openalex.org/W1583589866","https://openalex.org/W1620362451","https://openalex.org/W1835471601","https://openalex.org/W1974774078","https://openalex.org/W2010669260","https://openalex.org/W2020390700","https://openalex.org/W2055064119","https://openalex.org/W2098149254","https://openalex.org/W2098996169","https://openalex.org/W2099641086","https://openalex.org/W2115090644","https://openalex.org/W2120991191","https://openalex.org/W2122548617","https://openalex.org/W2125680629","https://openalex.org/W2129131372","https://openalex.org/W2136235822","https://openalex.org/W2138857456","https://openalex.org/W2149863017","https://openalex.org/W2162409952","https://openalex.org/W2163916252","https://openalex.org/W2164696938","https://openalex.org/W2289917018","https://openalex.org/W2400972628","https://openalex.org/W2541693915","https://openalex.org/W2952164218","https://openalex.org/W3102105495","https://openalex.org/W3125735862","https://openalex.org/W4285719527","https://openalex.org/W6604991282","https://openalex.org/W6664383849"],"related_works":["https://openalex.org/W2158224665","https://openalex.org/W2379589510","https://openalex.org/W2810730439","https://openalex.org/W4300044672","https://openalex.org/W1881631164","https://openalex.org/W2358292267","https://openalex.org/W2378166785","https://openalex.org/W1964277756","https://openalex.org/W2465351041","https://openalex.org/W1976264255"],"abstract_inverted_index":{"It":[0],"has":[1],"been":[2],"known":[3],"for":[4,109,123],"a":[5,30,63],"while":[6],"that":[7,36,83],"l":[8,84],"<sub":[9,85],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[10,86],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[11,87],"-norm":[12,88],"relaxation":[13,89],"can":[14],"in":[15,43,48,91,133],"certain":[16],"cases":[17],"solve":[18],"an":[19],"under-determined":[20],"system":[21,50],"of":[22,40,56,66,69,78,106,117,121,126],"linear":[23],"equations.":[24],"Recently,":[25],"[5,":[26],"10]":[27],"proved":[28],"(in":[29],"large":[31],"dimensional":[32],"and":[33],"statistical":[34],"context)":[35],"if":[37],"the":[38,44,49,54,57,70,76,79,93,104,115,118,124,127],"number":[39,112],"equations":[41,122],"(measurements":[42],"compressed":[45],"sensing":[46],"terminology)":[47],"is":[51,62],"proportional":[52,74],"to":[53,75,114],"length":[55,77,116],"unknown":[58,71,80,119,130],"vector":[59,81],"then":[60],"there":[61],"sparsity":[64,108],"(number":[65],"non-zero":[67],"elements":[68],"vector)":[72,120],"also":[73],"such":[82],"succeeds":[90],"solving":[92],"system.":[94],"In":[95],"this":[96],"paper":[97],"we":[98],"determine":[99],"sharp":[100],"lower":[101],"bounds":[102],"on":[103],"values":[105],"allowable":[107],"any":[110],"given":[111],"(proportional":[113],"case":[125],"so-called":[128],"block-sparse":[129],"vectors":[131],"considered":[132],"[25].":[134]},"counts_by_year":[{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}