{"id":"https://openalex.org/W2119533424","doi":"https://doi.org/10.1109/tsp.2010.2047330","title":"Frame-Theoretic Analysis of Robust Filter Bank Frames to Quantization and Erasures","display_name":"Frame-Theoretic Analysis of Robust Filter Bank Frames to Quantization and Erasures","publication_year":2010,"publication_date":"2010-04-05","ids":{"openalex":"https://openalex.org/W2119533424","doi":"https://doi.org/10.1109/tsp.2010.2047330","mag":"2119533424"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2010.2047330","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2010.2047330","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/A5100923882","display_name":"Zhiming Xu","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Zhiming Xu","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052617896","display_name":"Anamitra Makur","orcid":"https://orcid.org/0000-0001-6232-923X"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Anamitra Makur","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I172675005"],"apc_list":null,"apc_paid":null,"fwci":2.4489,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.88262268,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"58","issue":"7","first_page":"3531","last_page":"3544"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9987000226974487,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6395197510719299},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5554133057594299},{"id":"https://openalex.org/keywords/subframe","display_name":"Subframe","score":0.5432071089744568},{"id":"https://openalex.org/keywords/filter-bank","display_name":"Filter bank","score":0.5329110622406006},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.5250137448310852},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.460365891456604},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4368015229701996},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3369446396827698},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32763469219207764},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.19429343938827515},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.183883398771286}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6395197510719299},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5554133057594299},{"id":"https://openalex.org/C2776514898","wikidata":"https://www.wikidata.org/wiki/Q7631141","display_name":"Subframe","level":3,"score":0.5432071089744568},{"id":"https://openalex.org/C100515483","wikidata":"https://www.wikidata.org/wiki/Q3268235","display_name":"Filter bank","level":3,"score":0.5329110622406006},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.5250137448310852},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.460365891456604},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4368015229701996},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3369446396827698},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32763469219207764},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.19429343938827515},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.183883398771286},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C138660444","wikidata":"https://www.wikidata.org/wiki/Q5607897","display_name":"Telecommunications link","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2010.2047330","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2010.2047330","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W168917536","https://openalex.org/W391578156","https://openalex.org/W1557036499","https://openalex.org/W1571821595","https://openalex.org/W1966245736","https://openalex.org/W1989995562","https://openalex.org/W1991320383","https://openalex.org/W1994428095","https://openalex.org/W1996415070","https://openalex.org/W2015172824","https://openalex.org/W2072565885","https://openalex.org/W2075433161","https://openalex.org/W2083187425","https://openalex.org/W2094600024","https://openalex.org/W2096971955","https://openalex.org/W2099111195","https://openalex.org/W2104356918","https://openalex.org/W2105037400","https://openalex.org/W2112438131","https://openalex.org/W2113272548","https://openalex.org/W2115683914","https://openalex.org/W2118799423","https://openalex.org/W2124523346","https://openalex.org/W2125308191","https://openalex.org/W2134524318","https://openalex.org/W2136224896","https://openalex.org/W2146483404","https://openalex.org/W2152611675","https://openalex.org/W2172023570","https://openalex.org/W2610857016","https://openalex.org/W4213336330","https://openalex.org/W6675841661"],"related_works":["https://openalex.org/W2392684677","https://openalex.org/W2279289911","https://openalex.org/W2392488746","https://openalex.org/W2006610124","https://openalex.org/W2051375466","https://openalex.org/W2370949617","https://openalex.org/W2468865112","https://openalex.org/W2383838034","https://openalex.org/W2956846030","https://openalex.org/W2125308191"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"the":[3,7,34,41,53,56,60,83,99,103,108,111,119,132,146,165,176,181,189,195,222,245],"theoretic":[4],"analysis":[5,243],"for":[6,55,203],"robustness":[8,71],"of":[9,36,43,52,64,72,107,135,148,178,191,198,213,228,244],"filter":[10],"bank":[11],"(FB)":[12],"frames":[13,67,74,90,138,153,184,202],"in":[14,79,143,155],"infinite":[15],"dimensional":[16],"Hilbert":[17],"space":[18],"<i":[19],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,23],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">l</i>":[21],"<sup":[22],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[24],"(\\BBZ)":[25],"to":[26,75,139,145,235,253],"quantization":[27,140],"and":[28,46,59,85,101,171,216],"erasures":[29,76,179],"as":[30,32,129],"well":[31],"studies":[33],"design":[35,160],"such":[37],"robust":[38,89],"frames,":[39],"from":[40],"perspective":[42],"both":[44],"frame":[45,57,130,209],"FB":[47,66,73,122,137,183,201,208],"theory.":[48],"First,":[49],"a":[50,125],"characterization":[51],"eigenstructure":[54],"operator":[58],"induced":[61],"Gram":[62],"matrix":[63],"general":[65],"is":[68,77,141,169,185,210,233],"presented.":[69],"The":[70,158,206],"investigated":[78],"detail,":[80],"especially":[81],"on":[82,180],"necessary":[84],"sufficient":[86],"condition.":[87],"Maximally":[88],"are":[91,113],"further":[92,236],"analyzed":[93],"by":[94,110,163,187,241],"explicitly":[95],"constructive":[96],"methods.":[97],"Moreover,":[98],"stability":[100],"even":[102],"possible":[104],"FIR":[105],"reconstruction":[106,247],"subframe":[109],"pseudoinverse":[112],"studied":[114,186],"thoroughly.":[115],"Next,":[116],"we":[117],"examine":[118],"optimal":[120,207],"quantized":[121,182],"frames.":[123],"Introducing":[124],"novel":[126],"notion":[127],"named":[128],"energy,":[131],"universal":[133,196],"optimality":[134,147,197],"tight":[136,152,200],"established,":[142],"contrast":[144],"only":[149],"equal":[150,166,214],"norm":[151,167,215,219],"shown":[154,234],"previous":[156],"works.":[157],"added":[159],"freedom":[161],"obtained":[162],"removing":[164],"constraint":[168],"explained":[170],"illustrated":[172],"with":[173],"examples.":[174],"Finally,":[175],"effect":[177],"incorporating":[188],"probability":[190],"erasures,":[192],"which":[193,248],"shows":[194,249],"uniform":[199],"one":[204],"erasure.":[205],"usually":[211],"not":[212],"actually":[217],"its":[218,250],"distribution":[220],"follows":[221],"reverse":[223],"waterfilling":[224],"principle.":[225],"An":[226],"example":[227],"two-state":[229],"erasure":[230],"channel":[231],"model":[232],"explain":[237],"our":[238],"result,":[239],"followed":[240],"an":[242],"successive":[246],"potential":[251],"application":[252],"frame-based":[254],"multiple":[255],"description":[256],"coding.":[257]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}