{"id":"https://openalex.org/W7161181225","doi":"https://doi.org/10.1109/lsp.2026.3693218","title":"Bound on RIP of Order $s+1$ for HTP Algorithm","display_name":"Bound on RIP of Order $s+1$ for HTP Algorithm","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7161181225","doi":"https://doi.org/10.1109/lsp.2026.3693218"},"language":null,"primary_location":{"id":"doi:10.1109/lsp.2026.3693218","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2026.3693218","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/A5136176864","display_name":"Sk Md Atique Anwar","orcid":"https://orcid.org/0009-0007-7538-2620"},"institutions":[{"id":"https://openalex.org/I84279003","display_name":"Indian Institute of Petroleum","ror":"https://ror.org/04gavx394","country_code":"IN","type":"facility","lineage":["https://openalex.org/I2799351866","https://openalex.org/I4210134808","https://openalex.org/I66760702","https://openalex.org/I84279003"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sk Md Atique Anwar","raw_affiliation_strings":["Department of Humanities and Sciences (Mathematics), Indian Institute of Petroleum &amp; Energy, Visakhapatnam, India"],"raw_orcid":"https://orcid.org/0009-0007-7538-2620","affiliations":[{"raw_affiliation_string":"Department of Humanities and Sciences (Mathematics), Indian Institute of Petroleum &amp; Energy, Visakhapatnam, India","institution_ids":["https://openalex.org/I84279003"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069658303","display_name":"Pradyumna Pradhan","orcid":"https://orcid.org/0009-0008-6807-5195"},"institutions":[{"id":"https://openalex.org/I84279003","display_name":"Indian Institute of Petroleum","ror":"https://ror.org/04gavx394","country_code":"IN","type":"facility","lineage":["https://openalex.org/I2799351866","https://openalex.org/I4210134808","https://openalex.org/I66760702","https://openalex.org/I84279003"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pradyumna Pradhan","raw_affiliation_strings":["Department of Humanities and Sciences (Mathematics), Indian Institute of Petroleum &amp; Energy, Visakhapatnam, India"],"raw_orcid":"https://orcid.org/0009-0008-6807-5195","affiliations":[{"raw_affiliation_string":"Department of Humanities and Sciences (Mathematics), Indian Institute of Petroleum &amp; Energy, Visakhapatnam, India","institution_ids":["https://openalex.org/I84279003"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042992454","display_name":"Pradip Sasmal","orcid":"https://orcid.org/0000-0003-0111-2509"},"institutions":[{"id":"https://openalex.org/I154549908","display_name":"Indian Institute of Technology Jodhpur","ror":"https://ror.org/03yacj906","country_code":"IN","type":"education","lineage":["https://openalex.org/I154549908"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pradip Sasmal","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology, Jodhpur, India"],"raw_orcid":"https://orcid.org/0000-0003-0111-2509","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Jodhpur, India","institution_ids":["https://openalex.org/I154549908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5092865534","display_name":"Ramunaidu Randhi","orcid":"https://orcid.org/0009-0004-4044-9782"},"institutions":[{"id":"https://openalex.org/I84279003","display_name":"Indian Institute of Petroleum","ror":"https://ror.org/04gavx394","country_code":"IN","type":"facility","lineage":["https://openalex.org/I2799351866","https://openalex.org/I4210134808","https://openalex.org/I66760702","https://openalex.org/I84279003"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ramunaidu Randhi","raw_affiliation_strings":["Department of Humanities and Sciences (Mathematics), Indian Institute of Petroleum &amp; Energy, Visakhapatnam, India"],"raw_orcid":"https://orcid.org/0009-0004-4044-9782","affiliations":[{"raw_affiliation_string":"Department of Humanities and Sciences (Mathematics), Indian Institute of Petroleum &amp; Energy, Visakhapatnam, India","institution_ids":["https://openalex.org/I84279003"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.77400582,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":null,"first_page":"2106","last_page":"2110"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.14390000700950623,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.14390000700950623,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.12770000100135803,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.09229999780654907,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.8245000243186951},{"id":"https://openalex.org/keywords/isometry","display_name":"Isometry (Riemannian geometry)","score":0.7354000210762024},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5995000004768372},{"id":"https://openalex.org/keywords/thresholding","display_name":"Thresholding","score":0.5475000143051147},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.42320001125335693},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.3971000015735626},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.375900000333786},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.3725999891757965}],"concepts":[{"id":"https://openalex.org/C17902559","wikidata":"https://www.wikidata.org/wiki/Q17099734","display_name":"Restricted isometry property","level":3,"score":0.8245000243186951},{"id":"https://openalex.org/C82457910","wikidata":"https://www.wikidata.org/wiki/Q740207","display_name":"Isometry (Riemannian geometry)","level":2,"score":0.7354000210762024},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5995000004768372},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5990999937057495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5831999778747559},{"id":"https://openalex.org/C191178318","wikidata":"https://www.wikidata.org/wiki/Q2256906","display_name":"Thresholding","level":3,"score":0.5475000143051147},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.42320001125335693},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3971000015735626},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.3725999891757965},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3628000020980835},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3407999873161316},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.33739998936653137},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.3357999920845032},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3005000054836273},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.29760000109672546},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C13533509","wikidata":"https://www.wikidata.org/wiki/Q1064349","display_name":"Deterministic algorithm","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2648000121116638},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.25290000438690186},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.25189998745918274}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2026.3693218","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2026.3693218","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/G6264657342","display_name":null,"funder_award_id":"SRG/2023/002383","funder_id":"https://openalex.org/F4320334771","funder_display_name":"Science and Engineering Research Board"}],"funders":[{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"Hard":[1],"Thresholding":[2],"Pursuit":[3],"(HTP)":[4],"algorithm":[5],"is":[6],"a":[7,60,67],"widely":[8],"recognized":[9],"method":[10],"for":[11,64,125],"sparse":[12],"signal":[13],"recovery,":[14],"supported":[15],"by":[16,58],"rigorous":[17],"theoretical":[18],"guarantees":[19],"based":[20,107],"on":[21,108],"the":[22,38,96,109,119],"restricted":[23,48,122],"isometry":[24,49,123],"constants":[25],"<inline-formula":[26,32,71,85,100,130],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[27,33,72,86,101,131],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[28,34,73,87,102,132],"notation=\"LaTeX\">$\\delta":[29,35,74,88,103,133],"_{3s}$</tex-math></inline-formula>":[30],"and":[31],"_{2s}$</tex-math></inline-formula>.":[36],"However,":[37],"existing":[39],"analysis":[40],"framework":[41],"has":[42],"not":[43],"been":[44],"extended":[45],"to":[46],"lower-order":[47,121],"conditions.":[50],"In":[51],"this":[52,56,116],"work,":[53],"we":[54,77],"address":[55],"gap":[57],"establishing":[59],"novel":[61],"recovery":[62,83],"guarantee":[63,124],"HTP":[65,80],"under":[66],"relaxed":[68],"condition":[69],"involving":[70],"_{s+1}$</tex-math></inline-formula>.":[75,134],"Specifically,":[76],"show":[78],"that":[79],"achieves":[81],"robust":[82],"whenever":[84],"_{s+1}":[89,104],"&lt;":[90,105],"\\sqrt{1/37}":[91],"\\approx":[92],"0.1644$</tex-math></inline-formula>,":[93],"which":[94],"surpasses":[95],"IHT-based":[97],"bound":[98],"of":[99,129],"0.1545$</tex-math></inline-formula>":[106],"optimal":[110],"step-length":[111],"1.":[112],"To":[113],"our":[114],"knowledge,":[115],"result":[117],"provides":[118],"first":[120],"HTP,":[126],"in":[127],"terms":[128]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-15T00:00:00"}
