{"id":"https://openalex.org/W2610901965","doi":"https://doi.org/10.1109/tit.2017.2700718","title":"Wavelet Packet Transform for Fractional Brownian Motion: Asymptotic Decorrelation and Selection of Best Bases","display_name":"Wavelet Packet Transform for Fractional Brownian Motion: Asymptotic Decorrelation and Selection of Best Bases","publication_year":2017,"publication_date":"2017-05-03","ids":{"openalex":"https://openalex.org/W2610901965","doi":"https://doi.org/10.1109/tit.2017.2700718","mag":"2610901965"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2700718","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2700718","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/A5044080622","display_name":"Xiaojiang Yu","orcid":"https://orcid.org/0000-0003-3602-1797"},"institutions":[{"id":"https://openalex.org/I198091727","display_name":"Tiangong University","ror":"https://ror.org/00xsr9m91","country_code":"CN","type":"education","lineage":["https://openalex.org/I198091727"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaojiang Yu","raw_affiliation_strings":["Department of Statistics, Tianjin Polytechnic University, Tianjin, China"],"raw_orcid":"https://orcid.org/0000-0003-3602-1797","affiliations":[{"raw_affiliation_string":"Department of Statistics, Tianjin Polytechnic University, Tianjin, China","institution_ids":["https://openalex.org/I198091727"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044080622"],"corresponding_institution_ids":["https://openalex.org/I198091727"],"apc_list":null,"apc_paid":null,"fwci":5.2916,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.9588755,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"63","issue":"7","first_page":"4532","last_page":"4550"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11270","display_name":"Complex Systems and Time Series Analysis","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10282","display_name":"Financial Risk and Volatility Modeling","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9896000027656555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-brownian-motion","display_name":"Fractional Brownian motion","score":0.6965674161911011},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.689592719078064},{"id":"https://openalex.org/keywords/wavelet-packet-decomposition","display_name":"Wavelet packet decomposition","score":0.6839197874069214},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.671454131603241},{"id":"https://openalex.org/keywords/decorrelation","display_name":"Decorrelation","score":0.6549966335296631},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.5042287111282349},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3717961311340332},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34306785464286804},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.3280421793460846},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32683122158050537},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31823620200157166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22796830534934998},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15256842970848083},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11532679200172424}],"concepts":[{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.6965674161911011},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.689592719078064},{"id":"https://openalex.org/C155777637","wikidata":"https://www.wikidata.org/wiki/Q2736187","display_name":"Wavelet packet decomposition","level":4,"score":0.6839197874069214},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.671454131603241},{"id":"https://openalex.org/C177860922","wikidata":"https://www.wikidata.org/wiki/Q788608","display_name":"Decorrelation","level":2,"score":0.6549966335296631},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.5042287111282349},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3717961311340332},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34306785464286804},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.3280421793460846},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32683122158050537},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31823620200157166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22796830534934998},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15256842970848083},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11532679200172424}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2017.2700718","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2700718","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W16095134","https://openalex.org/W228380312","https://openalex.org/W1594563152","https://openalex.org/W1900491136","https://openalex.org/W1967296189","https://openalex.org/W1970669268","https://openalex.org/W1977159695","https://openalex.org/W1988591348","https://openalex.org/W2005568483","https://openalex.org/W2027561985","https://openalex.org/W2031753087","https://openalex.org/W2032268516","https://openalex.org/W2032834517","https://openalex.org/W2040827478","https://openalex.org/W2061893616","https://openalex.org/W2062962812","https://openalex.org/W2072647566","https://openalex.org/W2074153246","https://openalex.org/W2092416301","https://openalex.org/W2096803620","https://openalex.org/W2103613670","https://openalex.org/W2116716902","https://openalex.org/W2129759201","https://openalex.org/W2132132574","https://openalex.org/W2141108224","https://openalex.org/W2147827427","https://openalex.org/W2150090044","https://openalex.org/W2156268185","https://openalex.org/W2156549446","https://openalex.org/W2162189034","https://openalex.org/W2164214015","https://openalex.org/W2169548558","https://openalex.org/W3113221786","https://openalex.org/W4249393990","https://openalex.org/W4255137765","https://openalex.org/W4255272544","https://openalex.org/W4285719527","https://openalex.org/W4292081285","https://openalex.org/W4300293005","https://openalex.org/W6600634069","https://openalex.org/W6674514350"],"related_works":["https://openalex.org/W2110849729","https://openalex.org/W3034439966","https://openalex.org/W2960646972","https://openalex.org/W2054017055","https://openalex.org/W2034318424","https://openalex.org/W2085792030","https://openalex.org/W1588899229","https://openalex.org/W1976022598","https://openalex.org/W4321517526","https://openalex.org/W1918078477"],"abstract_inverted_index":{"Our":[0,73],"first":[1],"goal":[2,75],"in":[3],"this":[4],"paper":[5],"is":[6,76],"to":[7,77],"investigate":[8],"stationarization":[9],"and":[10,33,48,61,65,68,87,91],"asymptotic":[11,80],"decorrelation":[12],"for":[13,104],"fractional":[14],"Brownian":[15],"motion":[16],"(fBm)":[17],"using":[18],"wavelet":[19,23,38,99],"packet":[20,39,100],"transform.":[21],"The":[22],"packets":[24],"are":[25],"generated":[26],"by":[27],"the":[28,37,79,83,95],"Nth-order":[29],"Daubechies":[30],"scaling":[31],"function":[32],"wavelet.":[34],"To":[35],"decorrelate":[36],"coefficients":[40],"asymptotically,":[41],"we":[42],"take":[43],"two":[44],"strategies:":[45],"fix":[46,62],"N":[47,70],"let":[49,69],"absolute":[50,54],"scale":[51,63],"difference":[52,55],"or":[53,107],"between":[56],"time":[57,66],"shifts":[58],"get":[59,71],"large;":[60],"level":[64],"shift":[67],"large.":[72],"second":[74],"present":[78],"properties":[81],"of":[82,97],"entropy-like":[84],"cost":[85,89],"functional":[86,90],"denoising":[88],"their":[92],"impact":[93],"on":[94],"selection":[96],"best":[98],"bases":[101],"when":[102],"used":[103],"fBm":[105],"plus":[106,109],"not":[108],"independent":[110],"Gaussian":[111],"white":[112],"noise.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"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"}
