{"id":"https://openalex.org/W2962840366","doi":"https://doi.org/10.1109/tit.2016.2573312","title":"Restricted $q$-Isometry Properties Adapted to Frames for Nonconvex $l_q$-Analysis","display_name":"Restricted $q$-Isometry Properties Adapted to Frames for Nonconvex $l_q$-Analysis","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2962840366","doi":"https://doi.org/10.1109/tit.2016.2573312","mag":"2962840366"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2573312","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2573312","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Junhong Lin","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","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":["School of Mathematical Sciences, Zhejiang University, Hangzhou, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2645,"currency":"USD","value_usd":2645},"apc_paid":null,"fwci":2.1549,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.86185787,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"1"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/restricted-isometry-property","display_name":"Restricted isometry property","score":0.8873693346977234},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.7869890928268433},{"id":"https://openalex.org/keywords/isometry","display_name":"Isometry (Riemannian geometry)","score":0.5886173248291016},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5639500021934509},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5047868490219116},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44707056879997253},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42527586221694946},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4055080711841583},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3650144934654236},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20442673563957214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1685115098953247}],"concepts":[{"id":"https://openalex.org/C17902559","wikidata":"https://www.wikidata.org/wiki/Q17099734","display_name":"Restricted isometry property","level":3,"score":0.8873693346977234},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.7869890928268433},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.5886173248291016},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5639500021934509},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5047868490219116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44707056879997253},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42527586221694946},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4055080711841583},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3650144934654236},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20442673563957214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1685115098953247},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2016.2573312","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2573312","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.4300000071525574}],"awards":[{"id":"https://openalex.org/G3432399248","display_name":null,"funder_award_id":"11531013","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G966488364","display_name":"\u6570\u636e\u5904\u7406\u4e2d\u7684\u82e5\u5e72\u6570\u5b66\u903c\u8fd1\u65b9\u6cd5\u95ee\u9898\u7814\u7a76","funder_award_id":"11171299","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W228380312","https://openalex.org/W1481866092","https://openalex.org/W1848983290","https://openalex.org/W1967357291","https://openalex.org/W1973700755","https://openalex.org/W1984305442","https://openalex.org/W1997301483","https://openalex.org/W1999905919","https://openalex.org/W2004544971","https://openalex.org/W2011236412","https://openalex.org/W2012961725","https://openalex.org/W2019741018","https://openalex.org/W2020390700","https://openalex.org/W2021535288","https://openalex.org/W2025666718","https://openalex.org/W2030449718","https://openalex.org/W2047194151","https://openalex.org/W2050834445","https://openalex.org/W2055064119","https://openalex.org/W2069912449","https://openalex.org/W2076198220","https://openalex.org/W2083587165","https://openalex.org/W2083945855","https://openalex.org/W2103955025","https://openalex.org/W2107844156","https://openalex.org/W2110220986","https://openalex.org/W2114748345","https://openalex.org/W2119883478","https://openalex.org/W2129638195","https://openalex.org/W2136235822","https://openalex.org/W2137959902","https://openalex.org/W2142971061","https://openalex.org/W2143168132","https://openalex.org/W2152171106","https://openalex.org/W2159268085","https://openalex.org/W2164452299","https://openalex.org/W2963262327","https://openalex.org/W2963519978","https://openalex.org/W2963851978","https://openalex.org/W3099751318"],"related_works":["https://openalex.org/W1595179898","https://openalex.org/W2949399405","https://openalex.org/W4237430004","https://openalex.org/W4301619540","https://openalex.org/W4297570801","https://openalex.org/W1639246335","https://openalex.org/W116214155","https://openalex.org/W2568623927","https://openalex.org/W2952050240","https://openalex.org/W2025666718"],"abstract_inverted_index":{"This":[0],"paper":[1],"discusses":[2],"the":[3,11,27,44,85,105,118,125,137],"reconstruction":[4,88],"of":[5,22,87,89,107],"signals":[6,14],"from":[7,101,140],"few":[8,102],"measurements":[9,40,59,144],"in":[10,20,75,97],"situation":[12],"that":[13,112,117],"are":[15,41,94],"sparse":[16,19,96],"or":[17],"approximately":[18,135],"terms":[21],"a":[23,114,121],"general":[24],"frame":[25],"via":[26],"lq-analysis":[28],"optimization":[29],"with":[30,48,128,145],"0q-analysis":[31],"optimization.":[32],"We":[33],"then":[34],"determine":[35],"how":[36],"many":[37],"random":[38,142],"Gaussian":[39,143],"needed":[42],"for":[43,60],"condition":[45,54],"to":[46],"hold":[47],"high":[49],"probability.":[50],"The":[51,68],"resulting":[52],"sufficient":[53],"is":[55,72],"met":[56],"by":[57],"fewer":[58,141],"smaller":[61,146],"q":[62,65,131,147,150],"than":[63,148],"when":[64,149],"=":[66,151],"1.":[67,152],"introduced":[69],"generalized":[70,108],"q-RIP":[71],"also":[73],"useful":[74],"compressed":[76,80],"data":[77,81],"separation.":[78],"In":[79],"separation,":[82],"one":[83],"considers":[84],"problem":[86],"signals'":[90],"distinct":[91,138],"subcomponents,":[92],"which":[93],"(approximately)":[95],"morphologically":[98],"different":[99],"dictionaries,":[100],"measurements.":[103],"With":[104],"notion":[106],"q-RIP,":[109],"we":[110],"show":[111],"under":[113],"usual":[115],"assumption":[116],"dictionaries":[119],"satisfy":[120],"mutual":[122],"coherence":[123],"condition,":[124],"lqsplit":[126],"analysis":[127],"0":[129],"<;":[130],"\u2264":[132],"1":[133],"can":[134],"reconstruct":[136],"components":[139]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
