{"id":"https://openalex.org/W1979905766","doi":"https://doi.org/10.1155/2012/130939","title":"Constructions of Vector\u2010Valued Filters and Vector\u2010Valued Wavelets","display_name":"Constructions of Vector\u2010Valued Filters and Vector\u2010Valued Wavelets","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1979905766","doi":"https://doi.org/10.1155/2012/130939","mag":"1979905766"},"language":"en","primary_location":{"id":"doi:10.1155/2012/130939","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/130939","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/130939.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/130939.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002448174","display_name":"Jianxun He","orcid":"https://orcid.org/0000-0002-7141-8987"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianxun He","raw_affiliation_strings":["Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China","School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China","Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006","School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006","institution_ids":["https://openalex.org/I37987034"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103030441","display_name":"Shouyou Huang","orcid":"https://orcid.org/0000-0003-2705-5370"},"institutions":[{"id":"https://openalex.org/I37987034","display_name":"Guangzhou University","ror":"https://ror.org/05ar8rn06","country_code":"CN","type":"education","lineage":["https://openalex.org/I37987034"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shouyou Huang","raw_affiliation_strings":["Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China","School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China","Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006","School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006","institution_ids":["https://openalex.org/I37987034"]},{"raw_affiliation_string":"School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006","institution_ids":["https://openalex.org/I37987034"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002448174"],"corresponding_institution_ids":["https://openalex.org/I37987034"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08464244,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2012","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9976000189781189,"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":0.9944000244140625,"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/algorithm","display_name":"Algorithm","score":0.5983573198318481},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39193448424339294},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3627813756465912}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5983573198318481},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39193448424339294},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3627813756465912}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/130939","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/130939","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/130939.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1355495197","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1355495197","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:130939","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/130939.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:79a7637eb38b470c87be249df266a0a1","is_oa":true,"landing_page_url":"https://doaj.org/article/79a7637eb38b470c87be249df266a0a1","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/130939","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/130939","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/130939.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3755039695","display_name":null,"funder_award_id":"200810780002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7905778336","display_name":null,"funder_award_id":"10971039","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1979905766.pdf","grobid_xml":"https://content.openalex.org/works/W1979905766.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1489213177","https://openalex.org/W1968710617","https://openalex.org/W1980149518","https://openalex.org/W1998630480","https://openalex.org/W2048705932","https://openalex.org/W2062308863","https://openalex.org/W2081550440","https://openalex.org/W2096684483","https://openalex.org/W2126777570","https://openalex.org/W2339602636","https://openalex.org/W2798707604","https://openalex.org/W2907408682","https://openalex.org/W4236500581","https://openalex.org/W4238865235","https://openalex.org/W4250577669","https://openalex.org/W4255272544","https://openalex.org/W4255333822","https://openalex.org/W6704301488"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"Let":[0],"a":[1,4,7,11],"=":[2],"(":[3],"1":[5],",":[6,9],"2":[8],"\u2026,":[10],"m":[12,15,18,28,30],")\u2208":[13],"\u2102":[14],"be":[16,24],"an":[17,27],"\u2010dimensional":[19],"vector.":[20],"Then,":[21],"it":[22],"can":[23],"identified":[25],"with":[26,75],"\u00d7":[29],"circulant":[31],"matrix.":[32],"By":[33],"using":[34],"the":[35,47,76],"theory":[36],"of":[37,57,60,78],"matrix\u2010valued":[38,82],"wavelet":[39,68],"analysis":[40],"(Walden":[41],"and":[42,67],"Serroukh,":[43],"2002),":[44],"we":[45,52,73],"discuss":[46],"vector\u2010valued":[48,61],"multiresolution":[49],"analysis.":[50],"Also,":[51],"derive":[53],"several":[54],"different":[55],"designs":[56],"finite":[58],"length":[59],"filters.":[62],"The":[63],"corresponding":[64],"scaling":[65],"functions":[66,69,83],"are":[70],"given.":[71],"Specially,":[72],"deal":[74],"construction":[77],"filters":[79],"on":[80],"symmetric":[81],"space.":[84]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}