{"id":"https://openalex.org/W2291328371","doi":"https://doi.org/10.1109/icsipa.2015.7412246","title":"The optimum running approximation of a matrix filterbank by pseudo inverse matrices","display_name":"The optimum running approximation of a matrix filterbank by pseudo inverse matrices","publication_year":2015,"publication_date":"2015-10-01","ids":{"openalex":"https://openalex.org/W2291328371","doi":"https://doi.org/10.1109/icsipa.2015.7412246","mag":"2291328371"},"language":"en","primary_location":{"id":"doi:10.1109/icsipa.2015.7412246","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icsipa.2015.7412246","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Signal and Image Processing Applications (ICSIPA)","raw_type":"proceedings-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/A5103290287","display_name":"Yuichi Kida","orcid":null},"institutions":[{"id":"https://openalex.org/I30181195","display_name":"Ohu University","ror":"https://ror.org/01fe6f215","country_code":"JP","type":"education","lineage":["https://openalex.org/I30181195"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yuichi Kida","raw_affiliation_strings":["The School of Pharmaceutical Sciences Ohu University, Koriyama-shi, Japan"],"affiliations":[{"raw_affiliation_string":"The School of Pharmaceutical Sciences Ohu University, Koriyama-shi, Japan","institution_ids":["https://openalex.org/I30181195"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111065230","display_name":"Takuro Kida","orcid":null},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Takuro Kida","raw_affiliation_strings":["Emeritus Tokyo Institute of Technology, Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"Emeritus Tokyo Institute of Technology, Tokyo, Japan","institution_ids":["https://openalex.org/I114531698"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103290287"],"corresponding_institution_ids":["https://openalex.org/I30181195"],"apc_list":null,"apc_paid":null,"fwci":0.5743,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.69476998,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"45","issue":null,"first_page":"520","last_page":"525"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9930999875068665,"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"}},"topics":[{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9930999875068665,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9796000123023987,"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9666000008583069,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7080785632133484},{"id":"https://openalex.org/keywords/filter-bank","display_name":"Filter bank","score":0.6188123822212219},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5875449180603027},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5730440616607666},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.4907001256942749},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4875625967979431},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46020716428756714},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.44811588525772095},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.43415719270706177},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34747135639190674},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2976977825164795},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.274239182472229},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17236533761024475},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06542766094207764}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7080785632133484},{"id":"https://openalex.org/C100515483","wikidata":"https://www.wikidata.org/wiki/Q3268235","display_name":"Filter bank","level":3,"score":0.6188123822212219},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5875449180603027},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5730440616607666},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.4907001256942749},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4875625967979431},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46020716428756714},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.44811588525772095},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.43415719270706177},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34747135639190674},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2976977825164795},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.274239182472229},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17236533761024475},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06542766094207764},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icsipa.2015.7412246","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icsipa.2015.7412246","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE International Conference on Signal and Image Processing Applications (ICSIPA)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5299999713897705}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W233593304","https://openalex.org/W1481646516","https://openalex.org/W1535749512","https://openalex.org/W2055576996","https://openalex.org/W2313158455","https://openalex.org/W2756612585","https://openalex.org/W2903136356","https://openalex.org/W3133713399","https://openalex.org/W4252713891","https://openalex.org/W4285719527","https://openalex.org/W6609112683","https://openalex.org/W6628727242","https://openalex.org/W6632381328","https://openalex.org/W6757712248","https://openalex.org/W6801334838"],"related_works":["https://openalex.org/W2021595906","https://openalex.org/W3013085049","https://openalex.org/W1560496689","https://openalex.org/W1992739770","https://openalex.org/W2766087987","https://openalex.org/W4386900933","https://openalex.org/W1606020025","https://openalex.org/W4229058035","https://openalex.org/W3125672081","https://openalex.org/W4299530511"],"abstract_inverted_index":{"Firstly,":[0],"we":[1,72,153,163],"establish":[2],"a":[3,9,52,165,177],"theorem":[4,167],"showing":[5],"that":[6,39,54,155],"approximation":[7,33,84,112],"of":[8,17,20,44,56,76,80,94,101,119,138,147,172],"matrix":[10,103,178],"filterbank,":[11],"which":[12,34,91],"minimizes":[13,40],"the":[14,31,47,57,81,102,108,128,136,145,150],"average":[15],"value":[16],"squared":[18],"norms":[19],"error":[21],"based":[22],"on":[23],"pseudo":[24,88],"inverse":[25,89],"matrices,":[26],"is":[27,35,140],"essentially":[28],"equivalent":[29],"to":[30,144,170],"optimum":[32,82,110],"derived":[36],"by":[37,63,86,113,117],"Kida":[38,114],"various":[41],"worst-case":[42],"measures":[43],"approximation-error":[45],"at":[46],"same":[48],"time.":[49],"Secondly,":[50],"under":[51],"restriction":[53,137],"Fourier-transforms":[55],"input-matrices":[58],"and":[59,98,174],"analysis-matrices":[60,173],"are":[61,92,115,159],"expressed":[62],"Fourier":[64],"series":[65],"with":[66,142,168],"finite":[67],"terms":[68],"having":[69],"bounded":[70],"norms,":[71],"present":[73,164],"concrete":[74],"procedure":[75],"deriving":[77],"synthesis":[78],"matrices":[79,90,97,100],"running":[83,111],"obtained":[85],"taking":[87],"composed":[93],"constant":[95],"coefficient":[96],"sampling":[99],"filterbank.":[104,179],"The":[105],"synthesis-filterbanks":[106,121],"in":[107,123,127,132,176],"past":[109,134],"given":[116],"combinations":[118],"block-wise":[120],"defined":[122],"separate":[124],"small":[125],"domains":[126],"variable":[129],"domain.":[130],"Besides,":[131],"these":[133,156],"contributions,":[135],"continuity":[139],"necessary":[141],"respect":[143,169],"measure":[146],"error.":[148],"Under":[149],"above":[151],"restriction,":[152],"prove":[154],"complex":[157],"restrictions":[158],"not":[160],"necessary.":[161],"Thirdly,":[162],"reciprocal":[166],"exchange":[171],"synthesis-matrices":[175]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}