{"id":"https://openalex.org/W2038441709","doi":"https://doi.org/10.1109/tsp.2012.2226171","title":"New Bounds for Restricted Isometry Constants With Coherent Tight Frames","display_name":"New Bounds for Restricted Isometry Constants With Coherent Tight Frames","publication_year":2012,"publication_date":"2012-10-23","ids":{"openalex":"https://openalex.org/W2038441709","doi":"https://doi.org/10.1109/tsp.2012.2226171","mag":"2038441709"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2012.2226171","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2226171","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","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/A5033892491","display_name":"Junhong Lin","orcid":"https://orcid.org/0000-0002-4507-9424"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junhong Lin","raw_affiliation_strings":["Department of Mathematics, Zhejiang University, Hangzhou, China","Dept. of Math, Zhejiang Univ., Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"Dept. of Math, Zhejiang Univ., Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100448207","display_name":"Song Li","orcid":"https://orcid.org/0000-0002-7307-3935"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Song Li","raw_affiliation_strings":["Department of Mathematics, Zhejiang University, Hangzhou, China","Dept. of Math, Zhejiang Univ., Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"Dept. of Math, Zhejiang Univ., Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089903944","display_name":"Yi Shen","orcid":"https://orcid.org/0000-0002-2554-9812"},"institutions":[{"id":"https://openalex.org/I1328775524","display_name":"Zhejiang Sci-Tech University","ror":"https://ror.org/03893we55","country_code":"CN","type":"education","lineage":["https://openalex.org/I1328775524"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yi Shen","raw_affiliation_strings":["Department of Mathematics and Science, Zhejiang Sci-Tech University, Hangzhou, China","Dept. of Math. & Sci., Zhejiang SciTech Univ., Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Science, Zhejiang Sci-Tech University, Hangzhou, China","institution_ids":["https://openalex.org/I1328775524"]},{"raw_affiliation_string":"Dept. of Math. & Sci., Zhejiang SciTech Univ., Hangzhou, China","institution_ids":["https://openalex.org/I1328775524"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7437,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.92800586,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"61","issue":"3","first_page":"611","last_page":"621"},"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/T12015","display_name":"Photoacoustic and Ultrasonic Imaging","score":0.9990000128746033,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/isometry","display_name":"Isometry (Riemannian geometry)","score":0.49870967864990234},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4382956027984619},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3887472152709961},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32555025815963745},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2938794195652008},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1581205129623413}],"concepts":[{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.49870967864990234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4382956027984619},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3887472152709961},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32555025815963745},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2938794195652008},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1581205129623413}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2012.2226171","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2226171","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","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":45,"referenced_works":["https://openalex.org/W1484715564","https://openalex.org/W1638511702","https://openalex.org/W1966749434","https://openalex.org/W1976709621","https://openalex.org/W1984305442","https://openalex.org/W2012961725","https://openalex.org/W2015418199","https://openalex.org/W2028781966","https://openalex.org/W2030449718","https://openalex.org/W2034260606","https://openalex.org/W2050834445","https://openalex.org/W2051882509","https://openalex.org/W2055064119","https://openalex.org/W2077237786","https://openalex.org/W2078204800","https://openalex.org/W2083587165","https://openalex.org/W2086670019","https://openalex.org/W2097323375","https://openalex.org/W2103955025","https://openalex.org/W2105877514","https://openalex.org/W2107844156","https://openalex.org/W2111067490","https://openalex.org/W2119323121","https://openalex.org/W2128739748","https://openalex.org/W2129131372","https://openalex.org/W2129638195","https://openalex.org/W2137959902","https://openalex.org/W2142058898","https://openalex.org/W2145096794","https://openalex.org/W2151693816","https://openalex.org/W2152171106","https://openalex.org/W2161431029","https://openalex.org/W2164452299","https://openalex.org/W2164717810","https://openalex.org/W2168458522","https://openalex.org/W2289917018","https://openalex.org/W2296616510","https://openalex.org/W2962738640","https://openalex.org/W2963262327","https://openalex.org/W3099751318","https://openalex.org/W3105279496","https://openalex.org/W3105340263","https://openalex.org/W3106234678","https://openalex.org/W4250955649","https://openalex.org/W4290998531"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2800721718","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626"],"abstract_inverted_index":{"This":[0],"paper":[1,99],"discusses":[2],"reconstruction":[3],"of":[4,23,64,72,89,93,97,114,140,177,190,211,222,230],"a":[5,24],"signal":[6,15],"from":[7,77],"undersampled":[8,78],"data":[9,79],"in":[10,21,70,138,173,228,251],"the":[11,14,36,51,94,103,115,151,166,169,178,182,208,212,235,252],"situation":[12],"that":[13,101,164,224],"is":[16],"sparse":[17,20,69,192,227],"or":[18],"approximately":[19,133],"terms":[22,71,139,229],"(possibly)":[25],"highly":[26],"overcomplete":[27],"and":[28,168],"coherent":[29],"tight":[30],"frame":[31],"<i":[32,37,52,73,82,104,111,118,123,134,141,152,196,213,231,236],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[33,38,41,53,74,83,86,105,112,119,124,135,142,153,156,197,200,214,232,237,240],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">D</i>":[34,54,75,106,143,215,233],"via":[35,150,194,234],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">l</i>":[39,84,154,198,238],"<sub":[40,85,155,199,239],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[42,87,157,201,241],"-analysis":[43,158,242],"optimization":[44,159,243],"problem.":[45,160],"Some":[46],"new":[47],"sufficient":[48,179],"conditions":[49,180,247],"on":[50,181],"-restricted":[55,107,216],"isometry":[56,108,185,217],"property":[57,186,218],"are":[58,67,132,144,225],"given":[59],"to":[60,146,207],"guarantee":[61],"stable":[62,188,220],"recovery":[63,189,221],"signals":[65,130,193,223],"which":[66,131],"nearly":[68,191,226],",":[76,128],"with":[80,165],"minimal":[81],"-norm":[88],"transform":[90],"coefficients.":[91],"One":[92],"main":[95],"results":[96],"this":[98,174],"shows":[100],"if":[102],"constant":[109],"\u03b4":[110,122],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">s</i>":[113,125,136],"measurement":[116],"matrix":[117],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">A</i>":[120],"satisfies":[121],"<;":[126],"0.307":[127],"then":[129],"-sparse":[137],"guaranteed":[145],"be":[147,204],"stably":[148],"recovered":[149],"We":[161],"point":[162],"out":[163],"lemmas":[167],"proof":[170],"techniques":[171],"developed":[172],"paper,":[175],"most":[176],"standard":[183,195],"restricted":[184],"for":[187,219],"-minimization,":[202],"can":[203],"similarly":[205],"extended":[206],"general":[209],"case":[210],"problem,":[244],"yielding":[245],"weaker":[246],"than":[248],"previously":[249],"available":[250],"literature.":[253]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
