{"id":"https://openalex.org/W2166770524","doi":"https://doi.org/10.1109/tip.2009.2017325","title":"Construction of Arbitrary Dimensional Biorthogonal Multiwavelet Using Lifting Scheme","display_name":"Construction of Arbitrary Dimensional Biorthogonal Multiwavelet Using Lifting Scheme","publication_year":2009,"publication_date":"2009-03-31","ids":{"openalex":"https://openalex.org/W2166770524","doi":"https://doi.org/10.1109/tip.2009.2017325","mag":"2166770524","pmid":"https://pubmed.ncbi.nlm.nih.gov/19342334"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2009.2017325","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2009.2017325","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5010870600","display_name":"Xieping Gao","orcid":"https://orcid.org/0000-0002-7764-3616"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xieping Gao","raw_affiliation_strings":["College of Information Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, China"],"affiliations":[{"raw_affiliation_string":"College of Information Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035423120","display_name":"Fen Xiao","orcid":"https://orcid.org/0000-0001-7511-9418"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fen Xiao","raw_affiliation_strings":["College of Information Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, China"],"affiliations":[{"raw_affiliation_string":"College of Information Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100636618","display_name":"Bodong Li","orcid":"https://orcid.org/0000-0001-7427-9057"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bodong Li","raw_affiliation_strings":["College of Information Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, China"],"affiliations":[{"raw_affiliation_string":"College of Information Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, China","institution_ids":["https://openalex.org/I4610292"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010870600"],"corresponding_institution_ids":["https://openalex.org/I4610292"],"apc_list":null,"apc_paid":null,"fwci":1.2943,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.83745639,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"18","issue":"5","first_page":"942","last_page":"955"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9998000264167786,"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":0.9998000264167786,"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/T10901","display_name":"Advanced Data Compression Techniques","score":0.9923999905586243,"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/biorthogonal-system","display_name":"Biorthogonal system","score":0.9149100184440613},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6730172634124756},{"id":"https://openalex.org/keywords/lifting-scheme","display_name":"Lifting scheme","score":0.598200798034668},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.5964097380638123},{"id":"https://openalex.org/keywords/filter-bank","display_name":"Filter bank","score":0.5111973881721497},{"id":"https://openalex.org/keywords/hermite-interpolation","display_name":"Hermite interpolation","score":0.4848800599575043},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.4780053198337555},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4685588479042053},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4519557058811188},{"id":"https://openalex.org/keywords/multidimensional-systems","display_name":"Multidimensional systems","score":0.45037946105003357},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.44370636343955994},{"id":"https://openalex.org/keywords/biorthogonal-wavelet","display_name":"Biorthogonal wavelet","score":0.42976051568984985},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.42695194482803345},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.410239577293396},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3984631299972534},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3788250684738159},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.36498796939849854},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.29558464884757996},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27269572019577026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24154475331306458},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13791686296463013},{"id":"https://openalex.org/keywords/wavelet-packet-decomposition","display_name":"Wavelet packet decomposition","score":0.13782453536987305}],"concepts":[{"id":"https://openalex.org/C158453530","wikidata":"https://www.wikidata.org/wiki/Q864692","display_name":"Biorthogonal system","level":4,"score":0.9149100184440613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6730172634124756},{"id":"https://openalex.org/C199550912","wikidata":"https://www.wikidata.org/wiki/Q3238415","display_name":"Lifting scheme","level":5,"score":0.598200798034668},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.5964097380638123},{"id":"https://openalex.org/C100515483","wikidata":"https://www.wikidata.org/wiki/Q3268235","display_name":"Filter bank","level":3,"score":0.5111973881721497},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.4848800599575043},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.4780053198337555},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4685588479042053},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4519557058811188},{"id":"https://openalex.org/C158457486","wikidata":"https://www.wikidata.org/wiki/Q17104301","display_name":"Multidimensional systems","level":2,"score":0.45037946105003357},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.44370636343955994},{"id":"https://openalex.org/C2778869661","wikidata":"https://www.wikidata.org/wiki/Q4915256","display_name":"Biorthogonal wavelet","level":5,"score":0.42976051568984985},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.42695194482803345},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.410239577293396},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3984631299972534},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3788250684738159},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.36498796939849854},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29558464884757996},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27269572019577026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24154475331306458},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13791686296463013},{"id":"https://openalex.org/C155777637","wikidata":"https://www.wikidata.org/wiki/Q2736187","display_name":"Wavelet packet decomposition","level":4,"score":0.13782453536987305},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tip.2009.2017325","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2009.2017325","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},{"id":"pmid:19342334","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19342334","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.7599999904632568,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W326883504","https://openalex.org/W1968096799","https://openalex.org/W1991016674","https://openalex.org/W1993673174","https://openalex.org/W1996164095","https://openalex.org/W2004093057","https://openalex.org/W2017416051","https://openalex.org/W2019995276","https://openalex.org/W2031501237","https://openalex.org/W2058195144","https://openalex.org/W2065241096","https://openalex.org/W2075498078","https://openalex.org/W2082247548","https://openalex.org/W2108937556","https://openalex.org/W2117188745","https://openalex.org/W2127547766","https://openalex.org/W2155595938","https://openalex.org/W2167351277","https://openalex.org/W2169997788"],"related_works":["https://openalex.org/W2016058047","https://openalex.org/W1588509767","https://openalex.org/W2966415695","https://openalex.org/W1774449297","https://openalex.org/W2380670016","https://openalex.org/W2389244263","https://openalex.org/W2386462288","https://openalex.org/W1586959851","https://openalex.org/W2143594841","https://openalex.org/W1590155119"],"abstract_inverted_index":{"This":[0],"paper":[1],"focuses":[2],"on":[3,17],"the":[4,11,18,72,80,100],"construction":[5,66],"of":[6,59,71,79,82,99],"multidimensional":[7],"biorthogonal":[8,40],"multiwavelets":[9,41],"and":[10,27,30,42,61,76,91,111],"perfect":[12],"reconstruction":[13],"multifilter":[14],"banks.":[15],"Based":[16],"Hermite-Neville":[19],"filter,":[20],"two":[21],"lifting":[22,74,83],"structures":[23],"have":[24],"been":[25,36],"proposed":[26],"systematically":[28],"investigated,":[29],"a":[31],"general":[32],"design":[33],"framework":[34],"has":[35],"developed":[37],"for":[38,50,103],"building":[39],"Hermite":[43],"interpolation":[44],"filter":[45],"banks":[46],"with":[47,56],"any":[48,51,54,57],"multiplicity":[49],"lattice":[52],"in":[53],"dimension":[55],"number":[58],"primal":[60],"dual":[62],"vanishing":[63,113],"moments.":[64,114],"The":[65],"is":[67],"an":[68],"important":[69],"generalization":[70],"Neville-based":[73],"scheme":[75],"inherits":[77],"all":[78],"advantages":[81],"schemes":[84],"such":[85,105],"as":[86,106],"fast":[87],"transform,":[88],"in-place":[89],"computation":[90],"integer-to-integer":[92],"transforms.":[93],"Our":[94],"multiwavelet":[95],"systems":[96],"preserve":[97],"most":[98],"desirable":[101],"properties":[102],"applications,":[104],"interpolating,":[107],"short":[108],"support,":[109],"symmetry,":[110],"high":[112]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":1}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}
