{"id":"https://openalex.org/W4317796996","doi":"https://doi.org/10.1109/lsp.2023.3238878","title":"Improved RIC Bounds in Terms of $\\delta _{\\text{2}s}$ for Hard Thresholding-Based Algorithms","display_name":"Improved RIC Bounds in Terms of $\\delta _{\\text{2}s}$ for Hard Thresholding-Based Algorithms","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4317796996","doi":"https://doi.org/10.1109/lsp.2023.3238878"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2023.3238878","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2023.3238878","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","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/A5039238718","display_name":"Lie-jun Xie","orcid":"https://orcid.org/0000-0003-0482-1650"},"institutions":[{"id":"https://openalex.org/I109935558","display_name":"Ningbo University","ror":"https://ror.org/03et85d35","country_code":"CN","type":"education","lineage":["https://openalex.org/I109935558"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lie-Jun Xie","raw_affiliation_strings":["School of Mathematics and Statistics, Ningbo University, Ningbo, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ningbo University, Ningbo, China","institution_ids":["https://openalex.org/I109935558"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039238718"],"corresponding_institution_ids":["https://openalex.org/I109935558"],"apc_list":null,"apc_paid":null,"fwci":2.8113,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.89983499,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"30","issue":null,"first_page":"21","last_page":"25"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11996","display_name":"Random lasers and scattering media","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/3102","display_name":"Acoustics and Ultrasonics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6116132736206055},{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.5472575426101685},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4878809452056885},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4682309031486511},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4471207857131958},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4226146936416626},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3879631757736206},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36120784282684326},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2973097562789917},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.212650865316391},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.20755913853645325}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6116132736206055},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.5472575426101685},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4878809452056885},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4682309031486511},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4471207857131958},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4226146936416626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3879631757736206},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36120784282684326},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2973097562789917},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.212650865316391},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.20755913853645325},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2023.3238878","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2023.3238878","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G194894491","display_name":null,"funder_award_id":"62071262","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"},{"id":"https://openalex.org/F4320322605","display_name":"Ningbo University","ror":"https://ror.org/03et85d35"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W119997944","https://openalex.org/W143004564","https://openalex.org/W1484715564","https://openalex.org/W1977520307","https://openalex.org/W1980454827","https://openalex.org/W1986931325","https://openalex.org/W2004544971","https://openalex.org/W2005836623","https://openalex.org/W2025079166","https://openalex.org/W2025666718","https://openalex.org/W2078204800","https://openalex.org/W2106967375","https://openalex.org/W2115706991","https://openalex.org/W2123023890","https://openalex.org/W2128659236","https://openalex.org/W2129131372","https://openalex.org/W2146842127","https://openalex.org/W2148556090","https://openalex.org/W2160979406","https://openalex.org/W2168458522","https://openalex.org/W2289917018","https://openalex.org/W2296052754","https://openalex.org/W2963322354","https://openalex.org/W2998383793","https://openalex.org/W3139784355","https://openalex.org/W3161751243","https://openalex.org/W3179233143","https://openalex.org/W4214806317","https://openalex.org/W4309775521"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W2976797620","https://openalex.org/W3016541361","https://openalex.org/W2582835249","https://openalex.org/W1506216622","https://openalex.org/W4367336080","https://openalex.org/W4288772858","https://openalex.org/W2767469168"],"abstract_inverted_index":{"Iterative":[0],"hard":[1,5,14],"thresholding":[2,6],"(IHT)":[3],"and":[4],"pursuit":[7],"(HTP)":[8],"are":[9],"two":[10],"kinds":[11],"of":[12,26,33,47,95,168],"classical":[13],"thresholding-based":[15],"algorithms":[16,35],"widely":[17],"used":[18,63],"in":[19,40,64,93,166],"compressed":[20],"sensing.":[21],"Restricted":[22],"isometry":[23],"constant":[24],"(RIC)":[25],"sensing":[27],"matrix":[28],"which":[29],"ensures":[30],"the":[31,45,54,83,108,124,137,162],"convergence":[32],"iterative":[34],"plays":[36],"a":[37],"key":[38],"role":[39],"guaranteeing":[41],"successful":[42,150],"recovery.":[43],"In":[44,76],"analysis":[46],"sufficient":[48,91,164],"condition":[49,92,139,165],"to":[50,114,123],"ensure":[51],"recovery":[52,151],"performance,":[53],"RIC":[55,109,138],"<inline-formula":[56,68,96,115,127,140,169],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[57,69,97,116,128,141,170],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[58,70,98,117,129,142,171],"notation=\"LaTeX\">$\\delta":[59,71,99,118,130,143,172],"_{\\text{3}s}$</tex-math></inline-formula>":[60],"is":[61,73,87,111,147,161],"generally":[62],"previous":[65],"literature,":[66],"while":[67,89],"_{\\text{2}s}$</tex-math></inline-formula>":[72,100,173],"rarely":[74],"addressed.":[75],"this":[77,105,160],"letter,":[78],"we":[79,158],"first":[80,163],"show":[81],"that":[82],"theoretical":[84],"optimal":[85,106],"step-length":[86],"1":[88],"using":[90],"terms":[94,167],".":[101],"Furthermore,":[102],"based":[103],"on":[104],"step-length,":[107],"bound":[110],"greatly":[112],"improved":[113],"_{\\text{2}s}&lt;":[119,131,144],"(\\sqrt5-1)/(2\\sqrt3)\\approx":[120],"0.3568$</tex-math></inline-formula>":[121],"compared":[122],"existing":[125],"one":[126],"0.25$</tex-math></inline-formula>":[132],"for":[133,149,174],"IHT":[134],"algorithm.":[135,154,176],"Meanwhile,":[136],"\\sqrt7/7\\approx":[145],"0.3780$</tex-math></inline-formula>":[146],"developed":[148],"via":[152],"HTP":[153,175],"As":[155],"far":[156],"as":[157],"know,":[159]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
